Theoretical chess rating question...
Cyber Linguist
last night, and came up with the following questions:
What would be the estimated ELO ratings of:
* "Ghod Almighty" -- knows all the possible combinations,
-- Wins if possible as quickly as possible,
-- Draws if a win isn't possible,
-- Loses in as many moves as possible if inevitable
* "Random" -- Makes a list of the N legal moves each turn, chooses 1.
* "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
Assume each of these players were to be entered in standard competition.
It's easy to see the first would be champion quickly, ELO > 2800, but what
exactly? 3500? Would it keep rising without bound?
Would the third achieve ELO 0, or even lower?
It would be interesting to see what the second one's ("Random") rating would
be -- would be a sort of benchmark for those just learning the game...
If someone wants to try this as an experiment, probably someone with some
sort of rating and way too much free time 8-), I'd be willing to play the
part of "Random" in an email chess game.
"Ghod" knows I'm neither the first nor (thankfully) the third! 8-)
ObDisclaimer:
-------------
This is not a religious post/flame. I'm posting to chess newsgroups with
a theoretical question. The "Ghod" in question may or may not exist. We
may or may not know of his/her/its/their existance. Your actual ELO mileage
may vary. Then again, it may not. 8-) Me? I'm a devout agnostic.
--
Eric Carr <ca...@cs.odu.edu> | http://www.cs.odu.edu/~carr
----------------------------------------------------------------------------
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tv-- b++++ D--- B---- e>++ O++ PS+ PE- Y+ PGP X- DI++ h+ r-- n---- !y>+
Paul Rubin
Cyber Linguist <ca...@tigerlily.cs.odu.edu> wrote:
>Was thinking about ELO ratings after having had way too much caffeine
>last night, and came up with the following questions:
>
>What would be the estimated ELO ratings of:
>
>* "Ghod Almighty" -- knows all the possible combinations,
> -- Wins if possible as quickly as possible,
> -- Draws if a win isn't possible,
> -- Loses in as many moves as possible if inevitable
>
>* "Random" -- Makes a list of the N legal moves each turn, chooses 1.
>
>* "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
>
>
>Assume each of these players were to be entered in standard competition.
>It's easy to see the first would be champion quickly, ELO > 2800, but what
>exactly? 3500? Would it keep rising without bound?
>Would the third achieve ELO 0, or even lower?
>It would be interesting to see what the second one's ("Random") rating would
>be -- would be a sort of benchmark for those just learning the game...
Hard questions. "Random" has been tried, I don't remember the results
but maybe 500 or something. There are actual players with lower ratings.
"Ghod AllAwful": you have to change the rules a little, i.e. disallow
resignation, make captures mandatory or something.
"Ghod Almighty": incomplete specification. What happens when the
position is objectively drawn, but sharp? The strategy is to keep
the position as sharp as possible while remaining in the drawn part
of the tree, hoping the opponent will make a mistake. But it might
be easier to trap a human opponent by going temporarily into the LOST
part of the tree. At that point, "loses as slowly as possible" is
no longer really a Ghodlike strategy. It might be better to steer
towards positions the human is likely to screw up.
Famous (Saavedra) endgame study:
-- ** -- ** -- ** -- **
** -- ** -- ** -- ** --
-- WK WP ** -- ** -- **
** -- ** BR ** -- ** --
-- ** -- ** -- ** -- **
** -- ** -- ** -- ** --
-- ** -- ** -- ** -- **
BK -- ** -- ** -- ** --
Human plays white, to move and win. Ghod Almighty plays black.
With the "longest loss" rule, white wins rather straightforwardly.
But with a trick defense, it is easy for white to overlook the win.
Try to figure it out yourself before reading further!
The "longest loss" involves letting the pawn promote and defending
a lost Q vs R ending. Black can hold out for quite a few moves that way
but White doesn't have any real problems in the end.
The famous "solution" to the study is nothing short of amazing though.
1. c7 Rd6+ 2. Kb5! (2. Kb7 Rd7 followed by Rxc7 Kxc7 draws) ... Rd5+,
3. Kb4! (3. Kb6 Rd6+ repeats position, 3. Kc6 Rd1 4. c8=Q Rc1+ draws, etc.),
3. ... Rd4+ 4. Kd3 Rd3+ (more of the same, but now): 5. Kc2 Rc4!!
and now White has to spot 6. c8=R!!! in order to win. If 6. c8=Q,
then 6. ... Rc4+ Qcx4 stalemate!!!! Try figuring THAT out over the board!
Chris Whittington
>
> Was thinking about ELO ratings after having had way too much caffeine
> last night, and came up with the following questions:
>
> What would be the estimated ELO ratings of:
>
> * "Ghod Almighty" -- knows all the possible combinations,
> -- Wins if possible as quickly as possible,
> -- Draws if a win isn't possible,
> -- Loses in as many moves as possible if inevitable
>
> * "Random" -- Makes a list of the N legal moves each turn, chooses 1.
>
> * "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
>
>
Statistical mathematics and the way of working out the ELO says this:
Ghod almighty: 400 ELO greater than the World Champion (eg 3200 or so)
Random: 1400
Wants to lose - tricky, not the same as lose by default because can't
move a piece, because doesn't know the rules - this would be 1000 ELO
What happens when wants to lose plays random ?
Wants to lose won't ever win a game (by definition).
Might draw some via 'not enough material' or something
Will lose occasionally when random hits the right move.
So >1000 but <1400. Maybe 1200 or so ?
Chris Whittington (yes I like useless acedemic exercises too)
Chris Whittington
> >Was thinking about ELO ratings after having had way too much caffeine
> >last night, and came up with the following questions:
> >
> >What would be the estimated ELO ratings of:
> >
> >* "Ghod Almighty" -- knows all the possible combinations,
> > -- Wins if possible as quickly as possible,
> > -- Draws if a win isn't possible,
> > -- Loses in as many moves as possible if inevitable
> >
> >* "Random" -- Makes a list of the N legal moves each turn, chooses 1.
> >
> >* "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
> >
> >
> >It's easy to see the first would be champion quickly, ELO > 2800, but what
> >exactly? 3500? Would it keep rising without bound?
> >Would the third achieve ELO 0, or even lower?
> >It would be interesting to see what the second one's ("Random") rating would
> >be -- would be a sort of benchmark for those just learning the game...
>
> Hard questions. "Random" has been tried, I don't remember the results
> but maybe 500 or something. There are actual players with lower ratings.
>
How this ? 1000 Elo is the base. How to be worse then the worst ?
Chris Whittington
Kenneth Sloan
Chris Whittington <chr...@cpsoft.demon.co.uk> wrote:
>
>How this ? 1000 Elo is the base. How to be worse then the worst ?
>
Please cite a source for this claim.
--
Kenneth Sloan sl...@cis.uab.edu
Computer and Information Sciences (205) 934-2213
University of Alabama at Birmingham FAX (205) 934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/info/faculty/sloan/
Ed Seedhouse
>How this ? 1000 Elo is the base. How to be worse then the worst ?
1000 is *not* the base. There is no base, actually, and it is
perfectly possible for a player to have a rating of less than zero in
the unmodified Elo system. In the USA I believe they have
"legislated" a base of 0 or 1. There are hosts of scholastic players
with ratings less than 1000, and quite a few with ratings under 100.
Ed Seedhouse
President, Victoria Chess Club.
CFC Rating: 2058
Paul Rubin
Chris Whittington <chr...@cpsoft.demon.co.uk> wrote:
>ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
>>
>> Was thinking about ELO ratings after having had way too much caffeine
>> last night, and came up with the following questions:
>>
>> What would be the estimated ELO ratings of:
>>
>> * "Ghod Almighty" -- knows all the possible combinations,
>> -- Wins if possible as quickly as possible,
>> -- Draws if a win isn't possible,
>> -- Loses in as many moves as possible if inevitable
>>
>> * "Random" -- Makes a list of the N legal moves each turn, chooses 1.
>>
>> * "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
>>
>>
>
>
>Ghod almighty: 400 ELO greater than the World Champion (eg 3200 or so)
>
>Random: 1400
>
>Wants to lose - tricky, not the same as lose by default because can't
>move a piece, because doesn't know the rules - this would be 1000 ELO
> What happens when wants to lose plays random ?
>Wants to lose won't ever win a game (by definition).
>Might draw some via 'not enough material' or something
>Will lose occasionally when random hits the right move.
>So >1000 but <1400. Maybe 1200 or so ?
How do you get these numbers? If Kasparov played a 100 game
match against Ghod Almighty, are you saying the score would
be 100-0? This seems like a deep question about how well
people play chess these days. I could believe Kasparov might
get some draws with the white pieces.
Enrico SMARGIASSI
: ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
: > [snip]
: > * "Random" -- Makes a list of the N legal moves each turn, chooses 1.
: >
: > * "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
: Statistical mathematics and the way of working out the ELO says this:
: Ghod almighty: 400 ELO greater than the World Champion (eg 3200 or so)
: Random: 1400
On which scale are you working? On the scales I have experience of
(UK, Italian, French), 1400 for a random player looks awfully
overestimated. If your estimates were correct, any program capable to
make legal moves would be 1400 (just replace the analysis and eval
functions with a call to rand()). But I distinctly recall playing
programs, around the year 1980, which were able to make legal moves
but were nowhere close to 1400 (I could beat them!).
: Wants to lose - tricky, not the same as lose by default because can't
: move a piece, because doesn't know the rules - this would be 1000 ELO
Ghosh. On the UK list I saw several people rated lower than 1000. How
could they do worse than make the worst possible move every time?
(Sort of super-masochist players :-) ?)
---------------------------------------------------------------
Enrico Smargiassi
Centre Europeen de Calcul Atomique et Moleculaire (CECAM)
Ecole Normale Superieure de Lyon
46, Allee d'Italie - Aile LR5
69364 Lyon CEDEX 07, France
phone: +33 72 72 86 32
fax : +33 72 72 86 36
URL : http://www.cecam.fr/~esmargia
Karl Juhnke
: Was thinking about ELO ratings after having had way too much caffeine
: last night, and came up with the following questions:
: What would be the estimated ELO ratings of:
: * "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
I think distinctions would be tricky on the lower end. Anyone trying
to lose should be able to succeed 100% of the time against even a beginner
trying to win. And two players trying to lose to each other will draw
every time. So how can any sensible rating be assigned?
Maybe the only way someone trying to lose could even be connected to the
normal rating scale is if their opponent was too clueless to avoid
stalemate. Throw in some draws against a 400-rated, and then you've got a
legitimate rating!
Peace,
Fritz
Cyber Linguist
>> >ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
>
>> >>
>> >>
>> >> * "Random"
>> >>
>> >> * "Ghod AllAwful"
>> >>
>> >
[snip]
>
>I dunno about Kasparov drawing Ghod Almighty, but the numbers given for
>Random and Ghod Awful sound too high. The Elo system theoretically can
They sound way too high, IMHO. I usually lose to opponents rated around
1400, near as I can tell. *If* 1000 were truly the mathematical lower
bound, this would probably be correct, but...
>extend from minus infinity to plus infinity. Any lower bound is a
>creation of convenience (i.e., we don't have anyone worse than this) or
>politics (e.g., the USCF rule that once over 1000, you can't go below
>1000).
>
>Here's a common sense look at Random and Ghod Awful: I once gave up
>chess because I was good enough to beat most casual non-tournament
>players without working, but got crushed by regular tournament players.
>Among the casual players I could regularly beat, some could regularly
>beat others. It makes sense that in this situation, I should have been
>at least 800 points better than Random. My established rating of that
>time was 1208.
Sounds like my situation -- I win consistently against the computer when
it's set on 800-level. So far, I get about 50/50 results against 1200,
and I could tell even the 800 player would have no problem against
random. (I tried one game using a random number generator, and it was a
quick massacre...) I have yet to try playing a game against "random" while
doing my best to lose. I think it could be done. The only barrier I see would
be avoiding draw by the 50-move rule. Then again, that has to be claimed by
one of the players, and if Random "wants" to win and I don't, why should
anyone claim a draw when I'm down to only my king and can't possibly win
outright?
>The only rated opponent I ever faced whose moves approached Random-ness
>was rated in the 500s. It is not inconceivable that Ghod Awful could
>have forced this player to apply mate. Psychology as well as chess might
>be involved. To this day, I don't know if the 500-player realized that
>there was a legal move out of check when she resigned.
Oh, my. Telling check from checkmate is not brain surgery... %-s
>Based on this experience, I like 400 as a very rough estimate of Random's
Seems to be about right. The chess programs I have don't go that low, though;
800 is about the lower bound for them. Not that anyone I've seen needs
anything weaker; it would just be an interesting experiment, IMHO.
>rating. As a caveat, I have noticed that Masters sometimes can't
>distinguish between strong E players' and weak C players' ability. I
>retired from tournament play with rating of 1789. It is possible that I
>might not be able to distinguish between 800-level ability and 400-level
>ability . . .
I think it would probably be easy. I certainly could, though I'm most
likely around 1200 or so myself. (I can kick Random's posterior any day
of the week, but lose to almost any decent chess program as yet.)
>Whatever Random's true rating, Ghod Awful has to be at least 400 points
>worse, unless He plays exclusively in Virginia prisons!
ROTFLOL!!! 8-) The shoe fits -- I started this thread with the question,
and I'm from Virginia! %-} (I'm not even rated, though, and definitely
don't play in prison tournaments!)
P.S. As to the needed clarification, I intended for the "Ghod Almighty"
persona to *not* try to cheapo their opponent. "Ghod" would stay in the
won part of the move tree if possible, then stay in the drawn part, and
only move to the lost part if this could not be avoided.
Wlodzimierz Holsztynski
>
>How do you get these numbers? If Kasparov played a 100 game
>match against Ghod Almighty, are you saying the score would
>be 100-0? This seems like a deep question about how well
>people play chess these days. I could believe Kasparov might
>get some draws with the white pieces.
Naeh... Almighty would play games with Gary's mind, would blur his
vision without even setting the board so that Kasparov would face
South--Almighty would simply move the Sun against Kasparov no matter
how Kasparov would move his board. Kasparov would have a bunch
of excuses why he had to lose 100-to-0 and he would be right.
I would play a match against Almighty, but not for money.
Wlod
Cyber Linguist
No, not any God -- just his little brother *Ghod* almighty. 8-) You know,
not-quite-a-god wannabe, but plays totally perfect chess...
Javhar
: ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
: >
: > What would be the estimated ELO ratings of:
: >
: > * "Ghod Almighty"
: Statistical mathematics and the way of working out the ELO says this:
:
: Ghod almighty: 400 ELO greater than the World Champion (eg 3200 or so)
That would mean that if the top 10 (or so) players in the world quit
playing chess tomorrow, Ghod's rating would suddenly decrease, even though
Ghod's playing strength would still be the same.
As long as you're introducing Ghod as a chess player, you might as well
throw in a hypothetical `ladder' of intermediate players stretching all
the way from Kasparov to Ghod, such that Hhis ELO could be established.
It would probable be much higher than 3200. Recall that it was shown that
Grandmasters' play was far from perfect in KQ-KR endgames, which is a
tremendously less complex domain than the entire game of chess itself.
Anyway, I posted an article some time ago in which I had a stab at
estimating Ghod's ELO. I think it was somewhere in the 10,000's or
20,000's or so. About 50 magnitudes above Garry, if you will.
Jack van Rijswijck
jav...@ib.com
Paul Rubin
>Chris Whittington (chr...@cpsoft.demon.co.uk) wrote:
>As long as you're introducing Ghod as a chess player, you might as well
>throw in a hypothetical `ladder' of intermediate players stretching all
>the way from Kasparov to Ghod, such that Hhis ELO could be established.
>It would probable be much higher than 3200. Recall that it was shown that
>Grandmasters' play was far from perfect in KQ-KR endgames, which is a
>tremendously less complex domain than the entire game of chess itself.
I'd be interested in hearing of a GM who lost the Q side of Q vs. R,
or failed to make steady progress toward winning. It's true that
they've been known to win in somewhat more than the minimal number
of moves, which becomes an issue because of the 50 move rule.
But how often do these positions come up in real chess?
>Anyway, I posted an article some time ago in which I had a stab at
>estimating Ghod's ELO. I think it was somewhere in the 10,000's or
>20,000's or so. About 50 magnitudes above Garry, if you will.
I'd be interested in seeing that article if you still have it.
It's difficult even to describe what strategy Ghod would use, if
playing against a human. The starting position is objectively drawn
and after most of the 1st moves anyone would play, it's still
objectively drawn. So out of many available moves with the same
objective evaluation, how does Ghod decide which one is most likely
to eventually make the human choose a losing move?
Chris Whittington
> >ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
> >>
> >> last night, and came up with the following questions:
> >>
> >>
> >> -- Wins if possible as quickly as possible,
> >> -- Draws if a win isn't possible,
> >> -- Loses in as many moves as possible if inevitable
> >>
> >>
> >>
> >>
> >
> >
> >Ghod almighty: 400 ELO greater than the World Champion (eg 3200 or so)
> >
> >
> >Wants to lose - tricky, not the same as lose by default because can't
> >move a piece, because doesn't know the rules - this would be 1000 ELO
> >Wants to lose won't ever win a game (by definition).
> >Might draw some via 'not enough material' or something
> >Will lose occasionally when random hits the right move.
> >So >1000 but <1400. Maybe 1200 or so ?
>
> match against Ghod Almighty, are you saying the score would
> be 100-0? This seems like a deep question about how well
> people play chess these days. I could believe Kasparov might
> get some draws with the white pieces.
Depends whether you believe chess is a win or a draw for white.
Probably the all knowing player would win most and draw some.
Since you get your opponents ELO + 400 for winning, and your opponents
ELO for drawing; the all-knowing would perform in the range 2800 -
3200 (where 2800 is Kasparov's grade).
I assumed closer to the 3200 end.
Chris Whittington
Chris Whittington
>
> Chris Whittington (chr...@cpsoft.demon.co.uk) wrote:
> : ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
> : > What would be the estimated ELO ratings of:
> : >
> : > * "Ghod Almighty"
>
> : Statistical mathematics and the way of working out the ELO says this:
> :
> : Ghod almighty: 400 ELO greater than the World Champion (eg 3200 or so)
>
> playing chess tomorrow, Ghod's rating would suddenly decrease, even though
> Ghod's playing strength would still be the same.
>
> throw in a hypothetical `ladder' of intermediate players stretching all
> the way from Kasparov to Ghod, such that Hhis ELO could be established.
> It would probable be much higher than 3200. Recall that it was shown that
> Grandmasters' play was far from perfect in KQ-KR endgames, which is a
> tremendously less complex domain than the entire game of chess itself.
>
> estimating Ghod's ELO. I think it was somewhere in the 10,000's or
> 20,000's or so. About 50 magnitudes above Garry, if you will.
>
>
> jav...@ib.com
Your critical assumption is the existence of the hypothetical ladder.
If it exists then Ghod could have an infinite grade, since he will
always beat the nearest player, who would always beat the nearest player
and so on.
But, we live in the real world, Kasparov has the highest grade we know,
statistically you get opponent grade + 400 for winning, so Ghod's
grade can't get above 2800 + 400 unless better than Kasparov comes along.
Chris Whittington
Chris Whittington
>
> In article <8298622...@cpsoft.demon.co.uk>,
> Chris Whittington <chr...@cpsoft.demon.co.uk> wrote:
>
> >
> >How this ? 1000 Elo is the base. How to be worse then the worst ?
> >
>
>
> --
> Kenneth Sloan sl...@cis.uab.edu
> Computer and Information Sciences (205) 934-2213
> University of Alabama at Birmingham FAX (205) 934-5473
> Birmingham, AL 35294-1170 http://www.cis.uab.edu/info/faculty/sloan/
My memory.
I seem to recollect that ELO is calculated by +400 for a win, -400
for a loss, opponents ELO for a draw, and averaging.
It needs to start somewhere, and gets 'based'. My recollection is that
the base is 1000.
Might be wrong though, I'm not a statistician. Maybe an ELO calculating
expert would like to put us right .... ?
Best regards
Chris Whittington
Robert Hyatt
-->In article <4lbptq$c...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
-->>Chris Whittington (chr...@cpsoft.demon.co.uk) wrote:
-->>As long as you're introducing Ghod as a chess player, you might as well
-->>throw in a hypothetical `ladder' of intermediate players stretching all
-->>the way from Kasparov to Ghod, such that Hhis ELO could be established.
-->>It would probable be much higher than 3200. Recall that it was shown that
-->>Grandmasters' play was far from perfect in KQ-KR endgames, which is a
-->>tremendously less complex domain than the entire game of chess itself.
-->
-->I'd be interested in hearing of a GM who lost the Q side of Q vs. R,
-->or failed to make steady progress toward winning. It's true that
-->they've been known to win in somewhat more than the minimal number
-->of moves, which becomes an issue because of the 50 move rule.
-->But how often do these positions come up in real chess?
-->
-->>Anyway, I posted an article some time ago in which I had a stab at
-->>estimating Ghod's ELO. I think it was somewhere in the 10,000's or
-->>20,000's or so. About 50 magnitudes above Garry, if you will.
-->
-->I'd be interested in seeing that article if you still have it.
-->
-->It's difficult even to describe what strategy Ghod would use, if
-->playing against a human. The starting position is objectively drawn
-->and after most of the 1st moves anyone would play, it's still
-->objectively drawn. So out of many available moves with the same
-->objective evaluation, how does Ghod decide which one is most likely
-->to eventually make the human choose a losing move?
Try GM Walter Browne against Belle. It was well-documented in the late
70's. He studied it and won the re-match, BTW. The "belle" defense
has come to be called "the great flying rook".
--
Robert Hyatt Computer and Information Sciences
hy...@cis.uab.edu University of Alabama at Birmingham
(205) 934-2213 115A Campbell Hall, UAB Station
(205) 934-5473 FAX Birmingham, AL 35294-1170
Javhar
: In article <4lbptq$c...@da.bausch.nl>, Javhar <I> wrote:
: >Recall that it was shown that
: >Grandmasters' play was far from perfect in KQ-KR endgames, which is a
: >tremendously less complex domain than the entire game of chess itself.
:
: I'd be interested in hearing of a GM who lost the Q side of Q vs. R,
: or failed to make steady progress toward winning. It's true that
: they've been known to win in somewhat more than the minimal number
: of moves, which becomes an issue because of the 50 move rule.
: But how often do these positions come up in real chess?
The example was just intended to show that GM's play is not perfect. I
often read claims about perfect chess being just a little bit above
Kasparov's level, and that Kasparov would be able to score draws against
Ghod if he (K) played carefully and didn't make any blunders. I think
this is an astronomically vast underestimate of the `depth' of chess.
: >Anyway, I posted an article some time ago in which I had a stab at
: >estimating Ghod's ELO. I think it was somewhere in the 10,000's or
: >20,000's or so. About 50 magnitudes above Garry, if you will.
:
: I'd be interested in seeing that article if you still have it.
Hmmm... I don't, but I'll try to reconstruct it. Suppose, for a while,
that chess is a theoretical draw. That means that Kasparov will never win
a game against Ghod, but he might achieve an occasional draw. Even
Rhandom could achieve a draw, merely by playing perfect moves by pure
luck. With a "perfect move", I mean a move that doesn't throw away the draw.
What are Rhandom's chances of actually getting a draw? Let:
p = the average number of perfect moves in any given position;
m = the average number of *available* moves in any given position
(about 35, AFAIK);
l = the average length of a drawn chess game. This is the number of moves
until the resulting endgame is so "easy" for both players that they
won't blunder away the draw anymore, so the game is effectively over.
Then Rhandom's chances of getting the draw are (p/m)^l . Kasparov's
chances are better, because there are many "obviously bad" (to him) moves
that he doesn't even consider. If he considers only about k moves, and p
of those are perfect, then his chances of achieving a draw are (p/k)^l .
When two players whose rating differs by r play against each other, the
expected result is something like 1 / (1 + 10^(-r/400)) . Put this equal
to (p/k)^l and it turns out that the rating difference between Kasparov
and Ghod is of the order of 400 l log(p/k) . Now plug in your favourite
values for l, p, and k, and see what happens. I get typical values of
about 10,000 or 20,000.
Comparing Ghod to Rhandom, we can get some sort of upper bound for Ghod's
rating. The worst case scenario would be that there is only one single
perfect move in every chess position, and that you have to labour for 200
moves or so until the draw is clear. (this would in fact be the *best
case* scenario from Ghod's point of view) This results in a rating
difference between Ghod and Rhandom of about 100,00 or so. If it's not as
bad as all that, then Ghod's rating must be well below 100,000.
Of course, you might object and throw in extra complications. Ghod may
play for "trap" positions: positions in which the optimal move(s) is not
at all obvious, and none of the moves which Kasparov considers are
perfect. Heck, lots of moves that Kasparov plays, I wouldn't even have
considered. (: Chess might not even be a theoretical draw. Let's say
it's a win for white, then Ghod always wins with white and Kasparov may
sometimes win or draw with white. If he makes one minor error, he throws
away half a point. If he makes two minor errors or one major error, he
throws away a full point.
But all this doesn't alter the order of magnitude of Ghod's estimated
rating. I think it is definitely far bigger than 3200, probably bigger
than 10,000, and probably less than 100,000.
: It's difficult even to describe what strategy Ghod would use, if
: playing against a human. The starting position is objectively drawn
: and after most of the 1st moves anyone would play, it's still
: objectively drawn. So out of many available moves with the same
: objective evaluation, how does Ghod decide which one is most likely
: to eventually make the human choose a losing move?
Well, quite. The Dhevil can get better results than Ghod by playing
Afor positions in which he knows that Kasparov is likely to make a
mistake, or even take chances and play sacrifices that turn out [Ato be
incorrect but only if Kasparov finds the single non-obvious reply for the
next 20 moves. This will change a drawn position into a winning one most
of the time, and sometimes the Dhevil will get punished if Kasparov does
happen to find the correct defense, but the Dhevil will score more points
on average than Ghod does. The Dhevil should even study Kasparov's
playing style and learn to predict Garry's responses, so he can play for
positions in which he already knows that Garry is going to blunder.
Games between Dhevil and Ghod will always end in a draw (or always in a
win for white), so Ghod and Dhevil will always be tied at the end of a
match. Dhevil will get more points against non-perfect opposition, but
the rating differences between the two of them and mere mortals is so
vast that Dhevil's rating would not be much greater than Ghod's.
fWK#Y)ugr
Javhar
: [...]
: Dhevil's rating would not be much greater than Ghod's.
: fWK#Y)ugr
Apparently, that comment insulted at least one of the two players
mentioned, because that's where my modem mysteriously hung up. Anyway, I
just wanted to add that the theoretical rating of Rhandom seems to be
greatly *over*estimated. Any chess strategy whatsoever will beat random.
There have been experiments in which a computer chess program was supplied
with a random evaluation function, ie. one that returns a random value,
and its playing strength actually increased with a bigger search depth.
(that was because, effectively, the program would play for positions with
lots of available moves, ie for mobility). This program, set to a search
depth of 0 ply, would emulate Rhandom. As the program's rating increased
with its search depth, and the playing strength would still be awful, it
seems that Rhandom play is really far far weaker than 1000. Nevermind that
this is the official `ground level' of human play. Rhandom's rating should
be way below zero. Rating is not an `absolute' but a `relative' scale;
only rating *differences* matter.
Jack van Rijswijck
jav...@ib.com
vania
criticize, but to ask a question about something that puzzles me.
The ELO formula appears to be taken for granted in this whole discussion,
apparently forgetting that it is a *fit* that tries to force "new" data (data
coming from new games) under a bell curve. In a document on the net I have
found that Elo's assumption was to fix the mean at 1,500 points. Possibly the
400 one sees in the formula is simply related to the standard deviation Elo
calculated out of statistical info he had available. Also, the infamous
"Deltas" (32 for ratings below 2,100, 24 for 2,100 to 2,400, etc.) have all the
look of a statistical a-priori approach. Now, apparently one of the rules about
the Elo system is that there is NO established rating below 1,000, which again
looks as an attempt to "truncate" the bell curve in order to make the
statistical approach more fitting. Of course, there is some trouble there,
because one would expect a similar truncation for high ELOs, if it weren't for
the fact that the actual ELO distribution is NOT symmetric around the mean.
In fact, even if the assumption of the ELO system is that the mean is, say,
1,500, the USCF apparently sports an average ELO below 1,300.
It is difficult to see a way out, as the only truly reliable rating system
should be based on periodical and comprehensive statistical surveys of all
games played, which would entail a periodic readjustment of the constants (such
as 1,500, 400, 32, 24, etc. as above mentioned).
So, I am asking if some of the data I have quoted above are just wrong, or if
my suspicion stands, that the ELO approach to the analysis of extreme
"theological" cases would be inappropriate because of its very nature (that is,
nature of a formula meant to to handle "average" situations).
Thanks,
Vania.
Kenneth Sloan
vania <va...@uts.cc.utexas.edu> wrote:
>This thread on Chess Theology is very entertaining and I am posting not to
>criticize, but to ask a question about something that puzzles me.
>
>The ELO formula appears to be taken for granted in this whole discussion,
>apparently forgetting that it is a *fit* that tries to force "new" data (data
>coming from new games) under a bell curve. In a document on the net I have
>found that Elo's assumption was to fix the mean at 1,500 points.
I strongly recommend that you use primary sources, and not depend too
heavily on anything you find "on the net". Both of the statements above
are wrong. But, don't take my word for it - read Elo's book.
>... Possibly the
>400 one sees in the formula is simply related to the standard deviation Elo
>calculated out of statistical info he had available.
Not calculated. Assumed.
>Also, the infamous
>"Deltas" (32 for ratings below 2,100, 24 for 2,100 to 2,400, etc.) have all the
>look of a statistical a-priori approach.
Closer to correct - but please read Elo. It's too long to type in (many
here know that I have tried...)
> Now, apparently one of the rules about
>the Elo system is that there is NO established rating below 1,000,
BZZZT - absolutely wrong.
>...
>So, I am asking if some of the data I have quoted above are just wrong,
just wrong.
Chris Whittington
>
> I (jav...@ib.com) wrote:
>
> : [...]
> : Dhevil's rating would not be much greater than Ghod's.
> : fWK#Y)ugr
>
By random, I assumed he meant 'select a move at random from the legal
move list' rather than 'apply a random evaluation to each node, and do
a search'.
Chris Whittington
Cyber Linguist
>I (jav...@ib.com) wrote:
>
>: [...]
>: Dhevil's rating would not be much greater than Ghod's.
>: fWK#Y)ugr
>
>Apparently, that comment insulted at least one of the two players
8-)
[snip]
>seems that Rhandom play is really far far weaker than 1000. Nevermind that
>this is the official `ground level' of human play. Rhandom's rating should
>be way below zero. Rating is not an `absolute' but a `relative' scale;
>only rating *differences* matter.
True. But what about Ghod Awful? Hhe would lose almost every single game
against Random, and every one period against Ghod or the "Dhevil". So his
rating would be far below Random's, right? How far? I've played Kasparov's
Gambit set at ELO 800, and it's *very* weak. If set 800 points *weaker*, could
it still beat Random 50% or more of the time? I don't know... %-s
I'd say my best guess so far at the three (Well, four now!) after reading
the various followups would be:
Ghod Almighty: >=3200, possibly as high as 20,000.
Random: ~200 or so, give or take.
Ghod Awful: ~-4000 (no-holds-barred, loser-wins chess -- "giveaway" rules)
Ghod Awful 2: ~-400 (playing against VERY weak players trying to win, and
limited to standard chess rules I.E. don't hang your King.)
The Dhevil: (Ghod's rating +/- a slight amount (10-20 points?), given that:
* He plays Ghod and always draws,
* He can win certain "drawn" games by trickery,
* This gambit pays off more often than not.
What about these folks playing the 7-board chess version I suggested in
the other post? (7 boards, White goes first, move one piece on one board per
move.) -- optimal strategy would include determining which board to move on,
deciding to hang some to win others. Okay:
* Ghod and the Dhevil would kick Random's ass 9999 times out of 10000, and
draw the other,
* Ghod Awful would probably *ALWAYS* manage to lose...
* Kasparov (and everyone else) would probably do WAY worse than optimal.
Any comments? (Stupid question -- of COURSE you have 'em!) 8-)
Cyber Linguist
>
>By random, I assumed he meant 'select a move at random from the legal
>move list' rather than 'apply a random evaluation to each node, and do
>a search'.
This was indeed what I meant. Say you have 20 possible starting moves.
* Number them 1 through 20.
* Roll a 20-sided die. (Yes, I'm also an avid role-player!)
* Find that move on the list
* Shrug and make it.
* Use an N-sided die for when the number of possible moves changes.
Another clarification (forget if I said this before...)
*"Ghod Almighty" would never "cheapo" an opponent at all. Hhe would make
moves which :
- Kept the move tree in the winning branch, for him, if possible,
- Failing that, go for the "drawn" subset of the move tree,
- Only do "cheapo" stuff when Hhe would otherwise lose.
...And Javhar suggested the "Dhevil", who I assume would:
* Always go for the best position by:
- Forcing a win as "Ghod" would, if he could.
- If that wasn't possible, trying to "cheapo" the opponent by steering
the game toward a nasty, complicated branch, trying to make the opponent
blunder, or even:
- "cheapoing" the opponent by playing a drawing (maybe even losing!) move
in the (probably statistically sound) hope the opponent wouldn't see the
(possibly 30-moves-down-the-road) refutation.
Ehnjoy! ;-)
Dan Thies
>There have been experiments in which a computer chess program was supplied
>with a random evaluation function, ie. one that returns a random value,
>and its playing strength actually increased with a bigger search depth.
>(that was because, effectively, the program would play for positions with
>lots of available moves, ie for mobility). This program, set to a search
>depth of 0 ply, would emulate Rhandom. As the program's rating increased
>with its search depth, and the playing strength would still be awful, it
>this is the official `ground level' of human play. Rhandom's rating should
>be way below zero. Rating is not an `absolute' but a `relative' scale;
>only rating *differences* matter.
I think we might be trying to get the ELO rating system to do
something it was never intended to do. It was designed to indicate
relative strengths of actual human players. Trying to come up with a
rating for a player who would lose to every other player (a random
mover) is a little like trying to guess how many goals my grandmother
would score if she started playing football for Manchester United.
Zero.
Dan
Ed Seedhouse
>The example was just intended to show that GM's play is not perfect. I
>often read claims about perfect chess being just a little bit above
>Kasparov's level, and that Kasparov would be able to score draws against
>Ghod if he (K) played carefully and didn't make any blunders. I think
>this is an astronomically vast underestimate of the `depth' of chess.
I doubt it. If we define a class as the difference in strength at
which one player gathers twice as many points as the other in the next
class down, there are about 16 classes in chess. Backgammon has, as I
recall, 14, and Go has something like 24.
Now, if chess were that much deeper than humans can deal with their
should be at least as many classes in chess as in go. But there
aren't. Therefore I conclude that it is very likely that the best
human players are within one or two classes of the "perfect" chess
player.
Javhar
: jav...@ib.com (Javhar) wrote:
: > There have been experiments in which a computer chess program was supplied
: > with a random evaluation function, ie. one that returns a random value,
: > and its playing strength actually increased with a bigger search depth.
: > (that was because, effectively, the program would play for positions with
: > lots of available moves, ie for mobility). This program, set to a search
: > depth of 0 ply, would emulate Rhandom.
: By random, I assumed he meant 'select a move at random from the legal
: move list' rather than 'apply a random evaluation to each node, and do
: a search'.
If you apply a random evaluation function and do a (full-width) one ply
search, then that's equivalent to choosing a random move.
Jack.
Benjamin J. Tilly
In article <4lfqft$1...@da.bausch.nl>
jav...@ib.com (Javhar) writes:
> I (jav...@ib.com) wrote:
>
> : [...]
> : Dhevil's rating would not be much greater than Ghod's.
> : fWK#Y)ugr
>
> Apparently, that comment insulted at least one of the two players
> mentioned, because that's where my modem mysteriously hung up. Anyway, I
> just wanted to add that the theoretical rating of Rhandom seems to be
> greatly *over*estimated. Any chess strategy whatsoever will beat random.
This is false. I recall a person who mentioned a while ago a program to
look for legal moves in chess. He stuck a random number lookup on it
and had random. It was horrible at chess. So he changed it, and had it
search for 1 move with the goal of having the largest number of
possible moves after one move of its. If multiple moves ones hit this
number, it chose randomly. What happened? It was substantially worse!
Let me offer you the start of an obvious example...
Joe Bloe-Computer
1.e4 e6
e6 opens up the Q and B, adding lots of moves, and leaves the pawn with
a possible move to e5. Nothing else is as good in its evaluation.
2.d4 Qg5
The Q on this square hits a *lot* of squares...
3.Bxg5 ...
It is not hard to simulate the follow-up by hand. If you have trouble
winning the game, then you should go back to tic-tac-toe. (I tried it
against a friend who is perhaps 1100...by the time that he got
checkmate he had lost 2 pawns. The "computer" had lost practically
every piece and a couple of pawns to boot.)
The moral is that a very simple algorithm which may even incorate a
useful principle can be worse than random. Given this, it is not
suprising that there are some real humans who play worse than random
does.
(Of course the same algorithm, modified to look more than 1 ply ahead,
would be substantially better.)
Ben Tilly
bar...@ouvaxa.cats.ohiou.edu
In article <4l9pfu$o...@emf.emf.net>, fr...@emf.net (Karl Juhnke) writes:
>Cyber Linguist (ca...@tigerlily.cs.odu.edu) wrote:
>: Was thinking about ELO ratings after having had way too much caffeine
>: last night, and came up with the following questions:
>
>: What would be the estimated ELO ratings of:
>
>: * "Ghod AllAwful" -- Same as "Ghod Almighty", but wants to LOSE, not win.
>
>I think distinctions would be tricky on the lower end. Anyone trying
>to lose should be able to succeed 100% of the time against even a beginner
>trying to win. And two players trying to lose to each other will draw
>every time. So how can any sensible rating be assigned?
>
>Maybe the only way someone trying to lose could even be connected to the
>normal rating scale is if their opponent was too clueless to avoid
>stalemate. Throw in some draws against a 400-rated, and then you've got a
>legitimate rating!
>
I don't know. I have a miniature chess device a relative picked up in a diome
store a few years back. It makes legal moves but cannot win. Even with two
queens against bare king it doesn't find mate within the thirty or forty moves
I've been willing to watch. How would you rate that thing?
>Peace,
>Fritz
Benjamin J. Tilly
In article <8300846...@cpsoft.demon.co.uk>
Chris Whittington <chr...@cpsoft.demon.co.uk> writes:
> jav...@ib.com (Javhar) wrote:
> >
> > Chris Whittington (chr...@cpsoft.demon.co.uk) wrote:
> > : ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
> > : >
> > : > What would be the estimated ELO ratings of:
> > : >
> > : > * "Ghod Almighty"
> >
> > : Statistical mathematics and the way of working out the ELO says this:
> > :
> > : Ghod almighty: 400 ELO greater than the World Champion (eg 3200 or so)
> >
> > That would mean that if the top 10 (or so) players in the world quit
> > playing chess tomorrow, Ghod's rating would suddenly decrease, even though
> > Ghod's playing strength would still be the same.
> >
> > As long as you're introducing Ghod as a chess player, you might as well
> > throw in a hypothetical `ladder' of intermediate players stretching all
> > the way from Kasparov to Ghod, such that Hhis ELO could be established.
> > It would probable be much higher than 3200. Recall that it was shown that
> > Grandmasters' play was far from perfect in KQ-KR endgames, which is a
> > tremendously less complex domain than the entire game of chess itself.
> >
> > Anyway, I posted an article some time ago in which I had a stab at
> > estimating Ghod's ELO. I think it was somewhere in the 10,000's or
> > 20,000's or so. About 50 magnitudes above Garry, if you will.
> >
> >
> > Jack van Rijswijck
> > jav...@ib.com
>
> Your critical assumption is the existence of the hypothetical ladder.
> If it exists then Ghod could have an infinite grade, since he will
> always beat the nearest player, who would always beat the nearest player
> and so on.
>
This is not true. An almost complete analysis of the tree would mean
that their performance should be almost identical. (I assume that the
worse player will learn over time.)
> But, we live in the real world, Kasparov has the highest grade we know,
> statistically you get opponent grade + 400 for winning, so Ghod's
> grade can't get above 2800 + 400 unless better than Kasparov comes along.
I thought that you could get 1 rating point for each tournament that
you won...so there is no upper limit.
BTW the estimate of 10,000 is actually fairly reasonable in some sense.
I remember hearing that for each ply that you add to a computer
program, its rating improves by about 200 points. If we assume that a
10 ply search gives a 2000 rating or thereabouts, and think of a 60 ply
program, then, assuming that the rule remains roughly right, we would
predict a rating in the neighbourhood of 10,200. 60-ply is about 30
moves, which is the length of many games, so a figure on the order of
10,000-20,000 is reasonable. (Of course it depends upon extrapolations
that are only justified in our wildest imaginations...)
Ben Tilly
Cyber Linguist
>I think we might be trying to get the ELO rating system to do
>something it was never intended to do. It was designed to indicate
>relative strengths of actual human players. Trying to come up with a
>rating for a player who would lose to every other player (a random
>mover) is a little like trying to guess how many goals my grandmother
>would score if she started playing football for Manchester United.
>Zero.
But if she started playing football with the local kiddies, she might
get a goal every so often. Likewise, it's not inconceivable that Random
could beat a player with a legit (albeit very poor) rating of ELO 50 or so.
Check the ratings -- these folks do exist. Therefore, Random, which wouldn't
play much worse than them, should have a rating as well, right? Ghod Awful
would lose (nearly?) every single game, but Random should be rateable...
Matt Guthrie
>From: ca...@tigerlily.cs.odu.edu (Cyber Linguist)
>Subject: Re: Theoretical chess rating question...
>Date: 23 Apr 1996 15:20:08 GMT
>In article <4lhs2e$n...@news.accessone.com> rt...@accessone.com (Dan Thies)
>writes:
> Likewise, it's not inconceivable that Random
>could beat a player with a legit (albeit very poor) rating of ELO 50 or so.
>Check the ratings -- these folks do exist. Therefore, Random, which wouldn't
>play much worse than them, should have a rating as well, right? Ghod Awful
>would lose (nearly?) every single game, but Random should be rateable...
>--
> Eric Carr <ca...@cs.odu.edu> | http://www.cs.odu.edu/~carr
>----------------------------------------------------------------------------
>GAT d- s+:+ g++ a23 w C+++ US++ P L+ 3 E--- N+++ K- W M-- V-- t+ 5 R+(*) G++
>tv-- b++++ D--- B---- e>++ O++ PS+ PE- Y+ PGP X- DI++ h+ r-- n---- !y>+
Two comments:
1:Rhandom would win VERY few games, but would draw many. Why? Stalemate due
to opponent incompetence. In the nether reaches of the rating pool (<750)
many players have absolutely no idea how to mate. I would estimate a 5-10%
draw rate based mainly upon stalemate but occasionally by 50 move rule because
of not knowing eg KQ v. K. A recent unscientific example: Regional
Championship, primary (grades K-3) division: My team has 22 players entered,
all rated <1200. 5 rounds x 22 players = 110 games. Approximately 10 noshow
forfeits = 100 played games. 5 stalemates (2 by my team, 3 by opponents).
And believe me, this is typical of scholastic chess, in fact maybe better than
the norm (seeing that my team won both the regional and State Championships.)
2:Ghodawful is actually a selfmate machine. Chernev once published a postal
game between (I think) Paris and Marseilles where W gave Q odds and B had to
force selfmate. B won.
Matt Guthrie
Hark, now hear the sailors cry
Smell the sea and feel the sky
Let your soul and spirit fly into the mystic. (Thanks, Van)
Chris Whittington
>
snip-snip
> True. But what about Ghod Awful? Hhe would lose almost every single game
> against Random, and every one period against Ghod or the "Dhevil". So his
> rating would be far below Random's, right? How far? I've played Kasparov's
> Gambit set at ELO 800, and it's *very* weak.
This is about as good a benchmark as '... insert your own metaphor
here ....'
Chris Whittington
> Eric Carr <ca...@cs.odu.edu>
Javhar
: jav...@ib.com (Javhar) wrote:
: >The example was just intended to show that GM's play is not perfect. I
: >often read claims about perfect chess being just a little bit above
: >Kasparov's level, and that Kasparov would be able to score draws against
: >Ghod if he (K) played carefully and didn't make any blunders. I think
: >this is an astronomically vast underestimate of the `depth' of chess.
: I doubt it. If we define a class as the difference in strength at
: which one player gathers twice as many points as the other in the next
: class down, there are about 16 classes in chess. Backgammon has, as I
: recall, 14, and Go has something like 24.
This is essentially Bill Robertie's "skill level difference". His
definition of one SKD is such that the stronger player beats the weaker
player 75% of the time. The "difficulty" of a game is the SKD between the
world champion and a beginner. The difficulties of some well-known board
games are approximately:
Roulette 0
Blackjack 2
Checkers 8
Beckgammon 8
Scrabble 10
Poker 10
Bridge 10
Chess 11
Go 40
(see also R. Keene & B. Jacobs: "Man vs. Machine", 1996).
: Now, if chess were that much deeper than humans can deal with their
: should be at least as many classes in chess as in go. But there
: aren't.
I take it that you mean that the difficulty of Go shows that the human
mind can span at least 40 SKD levels, and as chess only seems to span 11
SKD levels, its depth must be within reach of the human mind. Well, not
necessarily, of course. A skill level in Go might be a much smaller
fraction of the "human mind span" than in chess.
First of all, the draw margin in Go is much smaller. In checkers it takes
a lot more superiority over another player in order to actually beat them,
than it does in chess. In Go, the stronger player is almost certain to
beat the weaker player; in fact it is not *whether or not* you beat your
opponent that counts in Go, but it's the margin (number of stones) with
which you beat them.
Second of all, Go relatively relies much much more on "intuition" and less
on "calculation" than chess does. Checkers, on the other hand, is
relatively more calculation and less intuition than chess. This might
explain a lot of the differences in difficulty between checkers, chess,
and Go. Apparently the human mind can be trained far more on intuition
than on calculation, so there is much more progress to make for a
beginner in Go than in checkers. I think that it is this that accounts
for the difference in complexity between chess and go.
: Therefore I conclude that it is very likely that the best
: human players are within one or two classes of the "perfect" chess
: player.
Then it seems strange that humans can't seem to conquer those last two
skill levels between Kasparov and Ghod, whereas they can reach as far as
40 skill levels in Go.
Returning to my example involving endgame databases: I've watched in
amazement as my computer played through the 223 moves of the maximin
variant of the KRB-KNN endgame. If KQ-KR, with a maximim of `only' about
30 (?), is already so difficult that even grandmasters can barely win it
at all against a database, then I'm willing to bet that Kasparov could
never win the KRB-KNN endgame. And this is a sub-class of chess with
only 6 pieces on the board. Nevermind that this particular endgame might
not occur all that often, it shows IMHO that there are *lots* of skill
levels above Kasparov's.
Cheers,
Jack.
Jack van Rijswijck
jav...@ib.com
Javhar
: >seems that Rhandom play is really far far weaker than 1000. Nevermind that
: >this is the official `ground level' of human play. Rhandom's rating should
: >be way below zero. Rating is not an `absolute' but a `relative' scale;
: >only rating *differences* matter.
: True. But what about Ghod Awful? Hhe would lose almost every single game
: against Random, and every one period against Ghod or the "Dhevil". So his
: rating would be far below Random's, right? How far?
Tricky question... If someone who wants to lose plays against someone who
wants to win, then it would be amazing if they didn't both get what they
want. In fact it's not a `zero sum game' anymore. Perhaps only Rhandom
could ever hope to *not* win a game against Ghod-Awful. In that case,
Ghod-Awful's rating would be awfully close to minus infinite.
It's a different story when two players who *both* want to lose play each
other. If both of them refuse to checkmate each other, then they'd have
to solve an incredibly complex "selfmate" problem. I've seen "selfmate"
problems (white to move, to result black checkmating white no matter what
black does), and they don't really look like the sort of position that
you might find yourself in in a regular game. So you'd expect to
masochist chess players to always draw, and therefore they'd all have the
same rating. But on the other hand, Ghod-Awful ought to be more Awful
than Rhandom-with-very-slight-masochistic-tendencies. Hmmm...
Jack van Rijswijck
jav...@ib.com
Javhar
: jav...@ib.com (Javhar) wrote:
: >[...] Rhandom play is really far far weaker than 1000. Nevermind that
: >this is the official `ground level' of human play. Rhandom's rating should
: >be way below zero. Rating is not an `absolute' but a `relative' scale;
: >only rating *differences* matter.
: I think we might be trying to get the ELO rating system to do
: something it was never intended to do. It was designed to indicate
: relative strengths of actual human players.
Agreed. Using `ELO-ratings' in these discussions might be a bit out of
place, but I think the spirit of the original question was to wonder what
the differences in playing levels between Ghod, Khasparov, Rhandom, etc,
are. I do think that something meaningful can be said about, at least,
Ghod, Dhevil, and Rhandom.
Jack van Rijswijck
jav...@ib.com
Santa Claus
>What are Rhandom's chances of actually getting a draw? Let:
>
>p = the average number of perfect moves in any given position;
>m = the average number of *available* moves in any given position
> (about 35, AFAIK);
>l = the average length of a drawn chess game. This is the number of moves
> until the resulting endgame is so "easy" for both players that they
> won't blunder away the draw anymore, so the game is effectively over.
>
>Then Rhandom's chances of getting the draw are (p/m)^l . Kasparov's
>chances are better, because there are many "obviously bad" (to him) moves
>that he doesn't even consider. If he considers only about k moves, and p
>of those are perfect, then his chances of achieving a draw are (p/k)^l .
>
>When two players whose rating differs by r play against each other, the
>expected result is something like 1 / (1 + 10^(-r/400)) . Put this equal
>to (p/k)^l and it turns out that the rating difference between Kasparov
>and Ghod is of the order of 400 l log(p/k) . Now plug in your favourite
>values for l, p, and k, and see what happens. I get typical values of
>about 10,000 or 20,000.
m = average number of moves. The way you are using this number, raising
it to a high power, is equivalent to getting the number of moves available
at each of the positions reached in a "normal" game, then multiplying them
all. The average you want for this is the GEOMETRIC mean, not the arithmetic
mean. So it's going to be less than 35: geometric means tend to be smaller.
*** QUESTION *** Can anyone out there with a database of games calculate
the geometric mean of the number of legal moves?
Yes, you're using the logistic distribution, which has minor differences to the
normal distribution, upon which Elo based his formulae. Most of the differences
are in larger "tails" ie for the logistic distribution, there are more
occurrences of things a long way from the mean. Hence you need at least 10,000
points to calculate the correct probability. Using the logistic distribution,
I calculated (I think) 16,000 points, which lies comfortably in
the range you say: 10,000 to 20,000. I posted here some theory based on
the normal distribution, using the same method to answer the same question, and
I got the answer: 3,700 points. This is because I used the normal distribution
instead of the logistic distribution. Since the normal distribution has smaller
"tails" (fewer occurrences of things far from the mean), it means more unlikely
events (like for example, Rhandom getting the draw)
need a smaller number of points. This means that Ghod's rating, calculated
from the normal distribution, gives a smaller number of points than if calculated
from the logistic distribution.
Ghod's rating from normal distribution: 3,700
Ghod's rating from logistic distribution: 10,000 - 20,000
To get that 3,700 points, I used a geometric mean of 20 legal moves, and a
number of perfect moves 2. (p=2, m=20)
> [ ... even longer long long games imply more points for a rating ...]
>difference between Ghod and Rhandom of about 100,000
I haven't tried calculating ratings for 200-move games using the normal
distribution.
This all raises the question of whether the logistic distribution is
better than the normal distribution. I think that the logistic distribution
describes humans, since humans can blunder. Generally, a human
plays at his or her skill level, but there are "bad days" and also occasional
downright blunders, which I feel explain why humans are a bit more variable
than the normal distribution suggests. I still think that the normal distri-
-bution would be better for a theoretical rating scale, though.
>But all this doesn't alter the order of magnitude of Ghod's estimated
>rating. I think it is definitely far bigger than 3200, probably bigger
>than 10,000, and probably less than 100,000.
I think I'll vote for the normal distribution, probably because I want a
rating scale that takes into account variations in skill while not taking
account of blunders. This means it would be useable for humans and
computers, which I think would probably play at a consistent skill level.
Simon
Paul Rubin
>Returning to my example involving endgame databases: I've watched in
>amazement as my computer played through the 223 moves of the maximin
>variant of the KRB-KNN endgame. If KQ-KR, with a maximim of `only' about
>30 (?), is already so difficult that even grandmasters can barely win it
>at all against a database, then I'm willing to bet that Kasparov could
>never win the KRB-KNN endgame. And this is a sub-class of chess with
>only 6 pieces on the board. Nevermind that this particular endgame might
>not occur all that often, it shows IMHO that there are *lots* of skill
>levels above Kasparov's.
I don't know that KQ-KR is that difficult. There are some positions
that need 40+ moves to win, and GM's have had difficulty winning them
in under 50 moves. However, it could be that no strong player would
have serious difficulty winning these positions using straightforward
methods, if they were allowed say 100 moves. It's finding the short
cuts to get it under 50 moves that is the hard part.
For more info, see "Secrets of Pawnless Endings", by John Nunn.
Komputer Korner
>
> In article <8298622...@cpsoft.demon.co.uk>,
> Chris Whittington <chr...@cpsoft.demon.co.uk> wrote:
>
> >
> >How this ? 1000 Elo is the base. How to be worse then the worst ?
> >
>
> Please cite a source for this claim.
>
> Kenneth Sloan sl...@cis.uab.edu
> Computer and Information Sciences (205) 934-2213
> University of Alabama at Birmingham FAX (205) 934-5473
> Birmingham, AL 35294-1170 http://www.cis.uab.edu/info/faculty/sloan/
It is possible to have a rating less than 1000. I have seen several, but with
participation points it becomes increasingly impossible to drop much below
800 even if the player loses every game he ever plays for the rest of his
life. I haven't worked out the math and every country has a different rating
formula, but there is a theoretical minimum which varies depending on the
specific formula if participation points are given. Without participation
points theoretically one could drop to 0, but it would take a long time and a
lot of losses. Komputer Korner
Cyber Linguist
>I don't know. I have a miniature chess device a relative picked up in a diome
>store a few years back. It makes legal moves but cannot win. Even with two
>queens against bare king it doesn't find mate within the thirty or forty moves
>I've been willing to watch. How would you rate that thing?
Awful. Simply awful. What's the brand? Even my GameBoy Chessmaster on the
wussiest setting possible would kick it around the board.
I've heard of programs that can't mate with two bishops. Many can't mate
with a bishop and a knight. But the village IDIOT should be able to mate
with two QUEENS!!! %-)
If it's truly as bad as you say, it may even be worse than Random. It's
at least in the same class! (I'd say around ELO 400 or so, maybe worse.)
At any rate, I know several 800-level computer chess "personalities"
that would have *no* problem putting it in its place!
Chris Whittington
No kidding .....
Yeah, sorry, skim read too fast and didn't note your 'set to 0 ply'.
Of course that's what you meant.
Chris Whittington
Michael Aigner
: with a bishop and a knight. But the village IDIOT should be able to mate
: with two QUEENS!!! %-)
: If it's truly as bad as you say, it may even be worse than Random. It's
: at least in the same class! (I'd say around ELO 400 or so, maybe worse.)
Actually, if you play "randomly" or do not have experience, MATING with
two queens can become a challenge, considering stalemate possibilities
increase substantially.
Michael
Benjamin J. Tilly
In article <4lh9js$3...@sanjuan.islandnet.com>
e...@islandnet.com (Ed Seedhouse) writes:
> jav...@ib.com (Javhar) wrote:
>
>
> >The example was just intended to show that GM's play is not perfect. I
> >often read claims about perfect chess being just a little bit above
> >Kasparov's level, and that Kasparov would be able to score draws against
> >Ghod if he (K) played carefully and didn't make any blunders. I think
> >this is an astronomically vast underestimate of the `depth' of chess.
>
> I doubt it. If we define a class as the difference in strength at
> which one player gathers twice as many points as the other in the next
> class down, there are about 16 classes in chess. Backgammon has, as I
> recall, 14, and Go has something like 24.
>
> Now, if chess were that much deeper than humans can deal with their
> should be at least as many classes in chess as in go. But there
> aren't. Therefore I conclude that it is very likely that the best
> human players are within one or two classes of the "perfect" chess
> player.
Judging by the present performance from computers, and the amount of
strength that they gain per extra ply that they are able to search, a
computer using present algorithms that was able to search 20 ply in a
middle-game position would be able to slaughter Kasparov repeatedly.
(He found 14 ply to be a reasonable game. And the gain is, if I recall
correctly, about 200 points per extra ply that you add. Obviously the
extrapolation will fail somewhere, but I do not think that we are going
to get such a drastic change that a computer with enough ply will not
be substantially better than Kasparov.) And, unless the situation
changes, said computer is going to be nowhere near a perfect player.
I am always astonished at how attached people are to the idea that the
top people are nearly perfect when they are aware that
1) Chess is so hard that no human can come close to perfectly
understanding it, and
2) Grandmasters, even top grandmasters, have their theories about how
to play the opening being constantly revised as people find busts to
lines and improvements to others. If the theory about a given position
(the start) is so difficult that we cannot trust the considerable
effort and energy put out by all of the top players to give the proper
evaluation of the best lines to play out to 20-40 ply (10-20 moves),
then how can we expect a single human to manage to better that analysis
in the middle-game positions that will arise later?
I would personally be astonished were it to turn out that people are
able to play anywhere near perfectly at chess. In fact I would be
unsuprised if the theoretically optimal opening lines diverges rapidly
from what opening theory today claims.
(Incidentally, I think that we are probably farther from the perfect
game of Go than we are from the perfect game of chess. But we are
nowhere near either.)
Ben Tilly
Ed Seedhouse
jav...@ib.com (Javhar) wrote:
>This is essentially Bill Robertie's "skill level difference". His
>definition of one SKD is such that the stronger player beats the weaker
>player 75% of the time. The "difficulty" of a game is the SKD between the
>world champion and a beginner. The difficulties of some well-known board
>games are approximately:
>Roulette 0
>Blackjack 2
>Checkers 8
>Beckgammon 8
>Scrabble 10
>Poker 10
>Bridge 10
>Chess 11
>Go 40
>(see also R. Keene & B. Jacobs: "Man vs. Machine", 1996).
Thanks for the correction. I was going from memory.
>: Now, if chess were that much deeper than humans can deal with their
>: should be at least as many classes in chess as in go. But there
>: aren't.
>I take it that you mean that the difficulty of Go shows that the human
>mind can span at least 40 SKD levels, and as chess only seems to span 11
>SKD levels, its depth must be within reach of the human mind. Well, not
>necessarily, of course. A skill level in Go might be a much smaller
>fraction of the "human mind span" than in chess.
I think my conclusion is still reasonable even given this.
>First of all, the draw margin in Go is much smaller. In checkers it takes
>a lot more superiority over another player in order to actually beat them,
>than it does in chess. In Go, the stronger player is almost certain to
>beat the weaker player; in fact it is not *whether or not* you beat your
>opponent that counts in Go, but it's the margin (number of stones) with
>which you beat them.
If the higher class player is the one who gains 75% of the available
"points" when matched against the next class down I don't see how this
would make a difference. You just go about gathering your points in a
different way with a rather coarser "grain", if you will, for chess.
>Second of all, Go relatively relies much much more on "intuition" and less
>on "calculation" than chess does.
I think that's just another way of saying it's a lot more complex than
chess, which is what I was trying to say. But both Go and Chess
involve both "calculation" and "intuition" when played by humans and
the fact that the proportions are different only reflects, so far as I
can see, the greater complexity of "Go". After all, what we call
"intuition" is presumably just some deeper level of abstraction that
humans call upon when faced with a problem too difficult to calculate.
>: Therefore I conclude that it is very likely that the best
>: human players are within one or two classes of the "perfect" chess
>: player.
>Then it seems strange that humans can't seem to conquer those last two
>skill levels between Kasparov and Ghod, whereas they can reach as far as
>40 skill levels in Go.
I don't see how that follows.
Ed Seedhouse
Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>> Now, if chess were that much deeper than humans can deal with their
>> should be at least as many classes in chess as in go. But there
>> aren't. Therefore I conclude that it is very likely that the best
>> human players are within one or two classes of the "perfect" chess
>> player.
>Judging by the present performance from computers, and the amount of
>strength that they gain per extra ply that they are able to search, a
>computer using present algorithms that was able to search 20 ply in a
>middle-game position would be able to slaughter Kasparov repeatedly.
This is based on an old linear extrapolation that has since been shown
to be wrong. By that extrapolation "Deep Blue" should, as I recall,
be rated around 3000.
>Obviously the
>extrapolation will fail somewhere, but I do not think that we are going
>to get such a drastic change that a computer with enough ply will not
>be substantially better than Kasparov.) And, unless the situation
>changes, said computer is going to be nowhere near a perfect player.
I think the current evidence is rather good that the extrapolation has
already failed.
>I am always astonished at how attached people are to the idea that the
>top people are nearly perfect when they are aware that
It's not an idea that I am "attached" to. If it turned out that it
isn't true it wouldn't bother me at all. It's just that on the
presently available evidence there is a good strong indication that it
is true, and no evidence at all that your position is true. When and
if the evidence changes I will be happy to change my position on the
matter.
Javhar
Santa Claus (Sa...@North.Pole) wrote:
: Ghod's rating from normal distribution: 3,700
: Ghod's rating from logistic distribution: 10,000 - 20,000
: To get that 3,700 points, I used a geometric mean of 20 legal moves, and a
: number of perfect moves 2. (p=2, m=20)
Granted, the logistic distribution is O(exp(x)) and the normal
distribution is of the order O(exp(x^2)) for large negative values of x.
Both estimates you give really mean the same thing: Kasparov's average
score against Ghod would be 1 point out of 10^40 (or whatever) games.
: This all raises the question of whether the logistic distribution is
: better than the normal distribution.
Actually, I think that as long as we're trying to estimate Ghod's playing
strength, the `skill level difference' would be a good measure. Ideally,
we would like the numbers to give us some idea of how much stronger Ghod
is than Kasparov, as compared to how much stronger Kasparov is than, say,
an average IM. The SKD measure is compatible with the imaginary ladder of
chess players between Kasparov and Ghod. The SKD is basically equivalent
to the logistic distribution, as it's also of the order O(exp(x)).
(the normal distribution is not compatible with such a ladder, as it
gives different results when you calculate Ghod's rating directly from
Hhis results against Kasparov, or when you calculate Hhis rating based on
the results of all the players in the ladder. that's probably why the ELO
rating is not considered `meaningful' if the difference in playing
strength is greater than 400 pts)
If you set one SKD at 75%, then it's equivalent to an ELO rating
difference of 200. To fix the ideas somewhat, let's take 600 ELO as the
ground level:
absolute beginner -- skill level 0
social player: 4
club player: 6
international strength player: 8
IM: 9
average IGM: 9.5
strong IGM: 10
world class IGM: 10.5
Kasparov: 11
And I'd say:
Ghod: 50-100.
All this does of course rest on the assumption that if 1 SKD means the
weaker player is going to score 25% of the points, then n SKD means he's
going to score (0.25^n) of the points. Anyway, I do think that this is a
reasonable result. ObWeirdSaying: An elephant is much bigger than a
mosquito, but neither one can make the ocean overflow when they bathe in it.
Jack van Rijswijck
jav...@ib.com
Javhar
Ed Seedhouse (e...@islandnet.com) wrote:
> >First of all, the draw margin in Go is much smaller. In
> >checkers it takes a lot more superiority over another player
> >in order to actually beat them, than it does in chess. In Go,
> >the stronger player is almost certain to beat the weaker
> >player; in fact it is not *whether or not* you beat your
> >opponent that counts in Go, but it's the margin (number of
> >stones) with which you beat them.
>
> If the higher class player is the one who gains 75% of the
> available "points" when matched against the next class down I
> don't see how this would make a difference. You just go about
> gathering your points in a different way with a rather coarser
> "grain", if you will, for chess.
If a skill level in Go is defined as the strength difference at
which the stronger player wins 75% of the games, it does make
that difference. If it is defined as the level at which the
stronger player gets 75% of the available points, then you're
right, it doesn't. I don't know which one of the two definitions
was used to determine the SKD of 40 for Go -- anyone?
But doesn't getting 75% of the available points at Go mean that
you would have to conquer 75% of the entire board? That's 180
stones difference -- a rather tall order! I suspect that the SKD
of 40 does refer to the definition where the stronger player wins
75% of the *games*, no matter by how many points. In that case
you'd have to win by just one stone, and that's a much smaller
margin of victory than a win in chess or checkers.
> >Second of all, Go relatively relies much much more on
> >"intuition" and less on "calculation" than chess does.
>
> I think that's just another way of saying it's a lot more
> complex than chess, which is what I was trying to say. But
> both Go and Chess involve both "calculation" and "intuition"
> when played by humans and the fact that the proportions are
> different only reflects, so far as I can see, the greater
> complexity of "Go".
From Ghod's points of view, all these games rely on *nothing but*
calculation. Go definitely is more complex than chess, but that
doesn't mean that top human chess players are close to `perfect'
chess.
> >: Therefore I conclude that it is very likely that the best
> >: human players are within one or two classes of the "perfect"
> >: chess player.
>
> >Then it seems strange that humans can't seem to conquer those
> >last two skill levels between Kasparov and Ghod, whereas they
> >can reach as far as 40 skill levels in Go.
>
> I don't see how that follows.
If a beginner's skill level is set at 0, then Kasparov's skill
level is about 12. What you are saying is that Ghod's level would
be about 14. You derive that from the fact that the human mind
spans 40 skill levels in Go and only 12 in chess. But if you can
get up to level 40 in Go, then level 14 in chess ought to be
incredibly easy to achieve. So then how come humans can get as
far as skill level 12 in chess, *but NOT* level 14? What is so
`special' about those levels 13 and 14?
Jack van Rijswijck
jav...@ib.com
Ed Seedhouse
jav...@ib.com (Javhar) wrote:
>But doesn't getting 75% of the available points at Go mean that
>you would have to conquer 75% of the entire board? That's 180
>stones difference -- a rather tall order!
Impossible really, and not what I meant. I meant that for every point
the lower class person gets the person in the next class gets three
points, however points are defined. Supposing in an extended match
the stronger players cumulative winning stones is 75, then the weaker
one has wins totalling 25 stones.
>> >Second of all, Go relatively relies much much more on
>> >"intuition" and less on "calculation" than chess does.
>>
>> I think that's just another way of saying it's a lot more
>> complex than chess, which is what I was trying to say. But
>> both Go and Chess involve both "calculation" and "intuition"
>> when played by humans and the fact that the proportions are
>> different only reflects, so far as I can see, the greater
>> complexity of "Go".
>
>From Ghod's points of view, all these games rely on *nothing but*
>calculation.
Agreed.
> Go definitely is more complex than chess, but that
>doesn't mean that top human chess players are close to `perfect'
>chess.
It doesn't prove it, I'll agree. However I think it gives us a fair
amount of pretty good evidence.
>> >Then it seems strange that humans can't seem to conquer those
>> >last two skill levels between Kasparov and Ghod, whereas they
>> >can reach as far as 40 skill levels in Go.
>>
>> I don't see how that follows.
>If a beginner's skill level is set at 0, then Kasparov's skill
>level is about 12. What you are saying is that Ghod's level would
>be about 14. You derive that from the fact that the human mind
>spans 40 skill levels in Go and only 12 in chess. But if you can
>get up to level 40 in Go, then level 14 in chess ought to be
>incredibly easy to achieve.
And the reason it isn't, it seems likely to me, is that it is very
nearly impossible to do so. Chess is a draw, I think, and I think the
best humans are good enough to force a draw against Ghod fairly often.
> So then how come humans can get as
>far as skill level 12 in chess, *but NOT* level 14? What is so
>`special' about those levels 13 and 14?
Well, comparing checkers and chess you could ask the same question.
Why is it so hard for checkers players to get to skill level 10 -
what's magic about 9 and 10? The answer is that unrestricted checkers
is less complex than chess and the best human checkers players can
play it pretty well perfectly. You can't get better than perfection.
If this is true for checkers why shouldn't it be true for chess? I
think the best human chess players are further away from "Ghod" than
the best human checkers players, but not as far away from "Ghod" as
the best go players.
I enjoyed answering this article - you've done some thinking and it
took me awhile to come up with a reply. But I still think you are
mistaken. :-)
Wlodzimierz Holsztynski
In article <4lum6d$i...@sanjuan.islandnet.com>,
Ed Seedhouse <e...@islandnet.com> wrote:
>jav...@ib.com (Javhar) wrote:
>
>>But doesn't getting 75% of the available points at Go mean that
>>you would have to conquer 75% of the entire board? That's 180
>>stones difference -- a rather tall order!
>
>Impossible really, and not what I meant. I meant that for every point
>the lower class person gets the person in the next class gets three
>points, however points are defined. Supposing in an extended match
>the stronger players cumulative winning stones is 75, then the weaker
>one has wins totalling 25 stones.
All this doesn't sound "GO-grammatical". First of all it is
the surrounded are which counts. The Japanese way of counting
points is to add to it the prisoners. The Chinese way is to
count your own live stones as the territory which you have
conquered. But that's a technical point. The main point is that
when the winner gets 50 points while the loser gets 0 then
it is as good, no better and no worse than when winner gets
75 points, and the loser gets 25. Nobody cares. It's the diff
that counts. (Well, there might be some psychological effect,
an embarrassement when you get 0; but not when your opponent
gets only, say, 10 points or less--such scores are however
quite improbable). Let me mention that during the counting
procedure, when done the Japanese way, players exchange their
prisoners for prisoners or for the surrounded points (by positioning
prisoners on points surrounded by the opponent). As you see,
nobody pays attention to how many points were scored by each
player--only the difference is the object of the game and the measure
of the players' skills.
>>From Ghod's points of view, all these games rely on *nothing but*
>>calculation.
>
>Agreed.
The notion of Ghod obscures at this moment this discussion.
When a game is very complex (maybe GO, most certainly GO played
on a 31 by 31 board instead of 19 by 19) then the mathematical
theorem about its finiteness becames irrelevant.
>And the reason it isn't, it seems likely to me, is that it is very
>nearly impossible to do so. Chess is a draw, I think, and I think the
>best humans are good enough to force a draw against Ghod fairly often.
Or best computers of the year 2010.
>> So then how come humans can get as
>>far as skill level 12 in chess, *but NOT* level 14? What is so
>>`special' about those levels 13 and 14?
You need a computer like endurance.
>I enjoyed answering this article - you've done some thinking and it
>took me awhile to come up with a reply. But I still think you are
>mistaken. :-)
>
>Ed Seedhouse
egards everybody,
Wlod
Jonathan Berry
Several sub-threads piqued my curiosity:
Rhandom:
Some programmer with insomnia may wish to give us this:
White plays randomly
White: Kc3
Black: Kh5
addsquares: a1 b2 a2 a3 b3 b1 c2 c1
suppress: 50-move draw rule
for m = knight to queen
for n = 1 to 8
put piece m on addsquare n
run 10000 times
play game to end
tabulate result: win, draw
{optionally divide draw into stalemate, insufficient
mating material, repetition of position}
rerun
next n
clear all addsquares of pieces
next m
post results to r.g.c.m
Ideal would be for Black to play "best moves" (such as to maximize the
possibility of a random stalemate), but if that is too much of a
programming challenge, Black might just play randomly.
Purpose: Reduce programmer's worry about insomnia.
Sub-purpose: Help us hhumans get a better idea of how crummy a random
player really would be.
Sub-sub-purpose: Possibility of surprising results (? more likely to win
with 8 knights than 8 queens ???)
>jav...@ib.com (Javhar) wrote:
>
>This is essentially Bill Robertie's "skill level difference". His
>definition of one SKD is such that the stronger player beats the weaker
>player 75% of the time. The "difficulty" of a game is the SKD between the
>world champion and a beginner. The difficulties of some well-known board
>games are approximately:
>
>Roulette 0
>Blackjack 2
>Checkers 8
>Beckgammon 8
>Scrabble 10
>Poker 10
>Bridge 10
>Chess 11
>Go 40
>
>(see also R. Keene & B. Jacobs: "Man vs. Machine", 1996).
Interesting. Is there a pointer to the original study? The base conditions
may play a role in the results.
Interesting that so many different games could be in the 8-11 range,
regardless of whether randomness is a factor!
I do not think that Go having 40 classes has anything to do with the
putative chess rating of Ghod. No more than chess having 11 classes would
have on Ghod's dan at Go.
Hasn't the game Othello been busted? We must know the hhuman class range
for it, perhaps 7? What is the class of one of the computers that can play
it perfectly? Assuming that it plays not only perfectly, but in a Ghodly
manner.
Jonathan Berry
Javhar
Ed Seedhouse (e...@islandnet.com) wrote:
> >Judging by the present performance from computers, and the
> >amount of strength that they gain per extra ply that they are
> >able to search, a computer using present algorithms that was
> >able to search 20 ply in a middle-game position would be able
> >to slaughter Kasparov repeatedly.
>
> This is based on an old linear extrapolation that has since
> been shown to be wrong. By that extrapolation "Deep Blue"
> should, as I recall, be rated around 3000.
During the match, Kasparov Hhimself stated that if Deep Blue
would search a couple more plies, it would outplay him. He also
said that Deep Blue did in fact play like a 3000 rated player
"in certain positions". Kasparov would rate Deep Blue as a top-20
player, and the 4-2 result of the match is consistent with that.
It's no surprise that this issue has been raised in a thread
about perfect chess. The viewpoints seem rather similar:
top human players are <---> top human players are
close to perfection nowhere close to perfection
computers will never <---> computers will eventually
beat Kasparov beat Kasparov consistently
So this thread runs the risk of turning into another "computers
will never beat Kasparov" thread. No points for guessing what I
think about the potential of computer chess...
> >Obviously the extrapolation will fail somewhere, but I do not
> >think that we are going to get such a drastic change that a
> >computer with enough ply will not be substantially better
> >than Kasparov.) And, unless the situation changes, said
> >computer is going to be nowhere near a perfect player.
>
> I think the current evidence is rather good that the
> extrapolation has already failed.
Computer chess researchers stated as far back as the 1950s that
computer would eventually beat the human world champion. Chess
players said that computers would never beat *anyone*. It did
happen though, in the late 60s. OK, but computers would never
beat anyone who can play a decent game of chess. They did in the
early 70s. Granted, but they would never beat expert players.
They did in the late 70s.
Well OK, but IMs were a different ball game. However, computers
started beating them, too, in the early 80s. But IGMs were a
totally different ball game, they would never lose against
computers. Alas, computers started beating IGMs in the last 80s.
But Kasparov was a completely different ball game, he would never
ever lose against computers. Yet, he did, in 1993. Yes but that
was at rapid chess; tournament chess was a different ball game
altogether. Kasparov will never lose a 40/2 game against a
computer. Enter Deep Blue. Ah, but Deep Blue didn't win the
match. Kasparov will never ever lose an entire match against a
computer.
Why suppose that this entire development will stop right here?
Would it not be strange if the theoretical limit of computer
chess capability happens to be *extremely* close to, but still
just slightly below, the limit of human chess capability?
Unless, of course, humans can play chess almost perfectly. But
then, in turn, it would still be surprising if perfect chess
level happens to be within human grasp, but *barely*. At least
99,9999% of all chess playing humans are far from perfect,
because Kasparov is clearly better than them. That would mean
that the limit of the chess playing capability of the human brain
is close to perfection within 0,0001%. Astonishing!
> >I am always astonished at how attached people are to the idea
> >that the top people are nearly perfect
>
> It's not an idea that I am "attached" to. If it turned out
> that it isn't true it wouldn't bother me at all. It's just
> that on the presently available evidence there is a good strong
> indication that it is true
There is? Naah... (:
Jack van Rijswijck
jav...@ib.com
Javhar
Ed Seedhouse (e...@islandnet.com) wrote:
> >But doesn't getting 75% of the available points at Go mean
> >that you would have to conquer 75% of the entire board?
> >That's 180 stones difference -- a rather tall order!
>
> Impossible really, and not what I meant. I meant that for
> every point the lower class person gets the person in the next
> class gets three points, however points are defined. Supposing
> in an extended match the stronger players cumulative winning
> stones is 75, then the weaker one has wins totalling 25 stones.
The Japanese scoring method is pretty much equivalent to the
Chinese method, which only counts the amount of territory you
conquered (I believe). Anyway, you're not talking about
`available' points. If the result is 75-25 stones after one
million games, I'd say that the players are pretty much equally
strong. That result would be statistically insignificant.
So I do think that a skill level in Go was defined as winning
75% of the *games*. And again, the draw margin in Go is
substantially lower than in chess or checkers. It's like the
difference between football (soccer that is) and basketball. One
single goal often decides a football match, but one single point
only decides a basketball match if the teams are rather evenly
matched. It's relatively more common if a weaker team gets a draw
or a win in football than it is in basketball. Does that mean
that Ajax are close to perfection and the Lakers aren't?
> > Go definitely is more complex than chess, but that doesn't
> > mean that top human chess players are close to `perfect'
> > chess.
>
> It doesn't prove it, I'll agree. However I think it gives us a
> fair amount of pretty good evidence.
Go on a 25x25 board is much more complex than standard Go. So, by
that reasoning, humans should be pretty close to perfection at
19x19 Go. Or indeed at any game whatsoever, because any game is
easier than NxN Go, for sufficiently large values of N.
> >If a beginner's skill level is set at 0, then Kasparov's skill
> >level is about 12. What you are saying is that Ghod's level
> >would be about 14. You derive that from the fact that the
> >human mind spans 40 skill levels in Go and only 12 in chess.
> >But if you can get up to level 40 in Go, then level 14 in
> >chess ought to be incredibly easy to achieve.
>
> And the reason it isn't, it seems likely to me, is that it is
> very nearly impossible to do so.
Which is just another way of saying that it's very difficult to
do so. You won't be surprised to hear that according to me, the
reason is that those last two levels are really about 50 levels.
The whole point of introducing these `skill levels' was that the
difference between consecutive skill levels is always the same.
If the difference between Ghod and Kasparov is that much bigger
than the difference between Kasparov and Short, then that by
definition implies that there are more skill levels between them.
> Chess is a draw, I think, and I think the best humans are good
> enough to force a draw against Ghod fairly often.
That seems to be a matter of opinion. (:
Let's look at the KRB-KNN endgame I mentioned earlier. The
maximin is 223 moves until conversion into a won KR-KN endgame.
The fact that it takes that much manoevering indicates that the
draw must be `very close'. What do you think would Kasparov's
chances be to win one of those 200+ moves positions, and what
would his chances be to successfully defend a drawn position with
the knights? [Is John Nunn reading this thread?]
The reason why the endgame takes so many moves is that KR-KN is
fairly often a draw. It's a very delicate affair to get black
into an `allow mate or conversion into a *lost* KR-KN endgame'
position. You have to master KR-KN first, before you can have a
go at achieving perfection in KRB-KNN. KRB-KNN is astronomically
more difficult. It contains KR-KN as tiny subset. Imagine how
much more difficult KRBP-KNNP must be. Imagine, then, how much
more difficult KQRRBBNNPPPPPPPP-KQRRBBNNPPPPPPPP must be.
Perhaps ACM, in the interest of science, should pay Kasparov to
play a match against endgame databases... (:
> >So then how come humans can get as far as skill level 12 in
> >chess, *but NOT* level 14? What is so `special' about those
> >levels 13 and 14?
>
> Well, comparing checkers and chess you could ask the same
> question. Why is it so hard for checkers players to get to
> skill level 10 - what's magic about 9 and 10? The answer is
> that unrestricted checkers is less complex than chess and the
> best human checkers players can play it pretty well perfectly.
Either that, or skill levels are farther apart in checkers than
they are in chess. Larger draw margin, and accent on different
capabilities (strategy/tactics).
> You can't get better than perfection. If this is true for
> checkers why shouldn't it be true for chess? I think the best
> human chess players are further away from "Ghod" than the best
> human checkers players, but not as far away from "Ghod" as the
> best go players.
I agree, but I'd add that all of them are still very *far* away
from Ghod.
> I enjoyed answering this article - you've done some thinking
> and it took me awhile to come up with a reply. But I still
> think you are mistaken. :-)
Why...!? (:
I think I'm not, actually...
Jack.
Paul Rubin
In article <4m0fom$d...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
>Let's look at the KRB-KNN endgame I mentioned earlier. The
>maximin is 223 moves until conversion into a won KR-KN endgame.
>The fact that it takes that much manoevering indicates that the
>draw must be `very close'. What do you think would Kasparov's
>chances be to win one of those 200+ moves positions, and what
>would his chances be to successfully defend a drawn position with
>the knights? [Is John Nunn reading this thread?]
>
>The reason why the endgame takes so many moves is that KR-KN is
>fairly often a draw. It's a very delicate affair to get black
>into an `allow mate or conversion into a *lost* KR-KN endgame'
>position. You have to master KR-KN first, before you can have a
>go at achieving perfection in KRB-KNN. KRB-KNN is astronomically
>more difficult. It contains KR-KN as tiny subset. Imagine how
>much more difficult KRBP-KNNP must be. Imagine, then, how much
>more difficult KQRRBBNNPPPPPPPP-KQRRBBNNPPPPPPPP must be.
>
>Perhaps ACM, in the interest of science, should pay Kasparov to
>play a match against endgame databases... (:
You're saying here that it is incredibly difficult to *win* KRB-KNN,
because the position teeters on the edge of being a draw. If
White messes up, a drawn instead of won KR-KN ending can result.
This doesn't show that the side trying *draw* necessarily has such
a hard time. Pushing a drawn position back "up" into a winning
one may take a bigger mistake on the defender's part than "falling"
from a won position to a drawn one.
Nor does it show that these endings are necessarily
reachable from KQRRBBNNPPPPPPPP-KQRRBBNNPPPPPPPP by force.
Maybe White can force some kind of perpetual check by the 20th
move with most of the pieces still on the board.
Paul Rubin
In article <4llgf9$g...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
>This is essentially Bill Robertie's "skill level difference". His
>definition of one SKD is such that the stronger player beats the weaker
>player 75% of the time. The "difficulty" of a game is the SKD between the
>world champion and a beginner. The difficulties of some well-known board
>games are approximately:
>
>Roulette 0
>Blackjack 2
>Checkers 8
>Beckgammon 8
>Scrabble 10
>Poker 10
>Bridge 10
>Chess 11
>Go 40
What does it mean for a strong player to beat a weak player 75% of
the time in a game like blackjack? Blackjack is usually an "iterated"
game, i.e. you play a large number of hands and if you have a 1%
edge over the other person, you will eventually bust him. But
there's no way to have a 75% chance of winning a single hand, because
of the randomness involved.
Suppose we invent the following game: we spin a roulette wheel.
If a red number comes up, you win. If a black number comes up, I win.
If 0 or 00 comes up, we play a game of chess to determine the winner.
Whichever one of us is a stronger chess player will win more "games"
in the long run. But what is the SKD?
Anders Thulin
>
>This is essentially Bill Robertie's "skill level difference". His
>definition of one SKD is such that the stronger player beats the weaker
>player 75% of the time. The "difficulty" of a game is the SKD between the
>world champion and a beginner. The difficulties of some well-known board
>games are approximately:
>
>Roulette 0
Don't confuse the players here: one side in roulette is the ordinary
players, the other side is the bank. Since the bank usually wins,
roulette should definitely have a non-zero classification.
--
Anders Thulin Anders...@lejonet.se 013 - 23 55 32
Telia Research AB, Teknikringen 2B, S-583 30 Linkoping, Sweden
Benjamin J. Tilly
In article <4lsc5i$5...@sanjuan.islandnet.com>
e...@islandnet.com (Ed Seedhouse) writes:
> Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>
> >> Now, if chess were that much deeper than humans can deal with their
> >> should be at least as many classes in chess as in go. But there
> >> aren't. Therefore I conclude that it is very likely that the best
> >> human players are within one or two classes of the "perfect" chess
> >> player.
>
> >Judging by the present performance from computers, and the amount of
> >strength that they gain per extra ply that they are able to search, a
> >computer using present algorithms that was able to search 20 ply in a
> >middle-game position would be able to slaughter Kasparov repeatedly.
>
> This is based on an old linear extrapolation that has since been shown
> to be wrong. By that extrapolation "Deep Blue" should, as I recall,
> be rated around 3000.
>
It is hardly news that basically EVERY linear extrapolation is false.
Furthermore the validity of any particular linear extrapolation is
limited by the number and quality of the data points that you have. (I
had thought that the extrapolation would actually put Deep Blue just
around Kasparov, I can check that later though.)
In the case of chess there are obvious reasons to believe that you
should get diminishing returns with additional ply on your search.
However experience has so far suggested that additional ply do add to
the quality of the program by a fairly predictable amount. (And indeed,
Deep Blue did give Kasparov a run for his money.) Now unless you can
suggest a solid reason for a dramatic change in the returns from each
ply between 14 ply (that is 7 moves ahead) and 18 ply (which is looking
9 moves ahead), there is extremely good reason to believe that a
computer using current algorithms and searching 18 ply would be
substantially better than Kasparov is. And there is still no reason to
believe that said computer is approaching perfection.
> >Obviously the
> >extrapolation will fail somewhere, but I do not think that we are going
> >to get such a drastic change that a computer with enough ply will not
> >be substantially better than Kasparov.) And, unless the situation
> >changes, said computer is going to be nowhere near a perfect player.
>
> I think the current evidence is rather good that the extrapolation has
> already failed.
>
It has failed to be a perfect predictor, but then nobody with any
experience in math and science would have expected it to be so. It has
been fairly accurate though, and there is no reason that I am aware of
for why its basic prediction of improvement in numbers of ply leading
to a roughly linear improvement in the playing strength for at least
several more ply. With diminishing returns that improved strength/ply
will be down a bit from what holds at the start of the trend, but it
should be substantial.
And it does not take much improvement between 14 ply (on a computer
without all of the bugs worked out) and 30 ply (with a good computer)
for the latter to slaughter Kasparov.
> >I am always astonished at how attached people are to the idea that the
> >top people are nearly perfect when they are aware that
>
> It's not an idea that I am "attached" to. If it turned out that it
> isn't true it wouldn't bother me at all. It's just that on the
> presently available evidence there is a good strong indication that it
> is true, and no evidence at all that your position is true. When and
> if the evidence changes I will be happy to change my position on the
> matter.
What evidence? I have given numbers, and I have given a variety of
reasons to believe that humans are just not that good at chess.
You have just claimed that humans are and have given no reasons.
Can you give me a solid reason for believing that it is possible to get
an almost perfect understanding of the game despite our being able to
actually think more than a few moves in advance? Or for why it is that
you think that Kasparov has actually achieved this?
For the record let me say that I am not putting people down. It is
truly astounding how well people can play and understand such a complex
game given our limitations. It is just that human limitations are such
that it seems impossible for us to play it very well. And every line of
evidence that I can think of (the history of opening theory, what
happens when we compare our performance to perfection in simple
endgames, and simple extrapolations from computer performance) supports
the reasonable conclusion.
Ben Tilly
Benjamin J. Tilly
In article <phrDqE...@netcom.com>
p...@netcom.com (Paul Rubin) writes:
> In article <4llgf9$g...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
As I recall, it was trying to get past the "flying rook" that was the
problem.
ie Many GMs then, and probably today, are unable to make progress in
the R vs Q game beyond a certain point.
Ben Tilly
Ed Seedhouse
jav...@ib.com (Javhar) wrote:
>Ed Seedhouse (e...@islandnet.com) wrote:
>> This is based on an old linear extrapolation that has since
>> been shown to be wrong. By that extrapolation "Deep Blue"
>> should, as I recall, be rated around 3000.
>During the match, Kasparov Hhimself stated that if Deep Blue
>would search a couple more plies, it would outplay him.
Beside the point which is that by the extrapolation postulated Deep
Blue should be much better than Kasparov *now*.
And don't forget that a "couple more ply" is one *heck* of a lot of
computer power.
>He also
>said that Deep Blue did in fact play like a 3000 rated player
>"in certain positions".
Even if true this is also beside the point since the claim was not
made about how the computer will play in "certain positions". Heck I
can play K+Q vs. Rook perfectly myself. Does that give me a 3000
rating?
(1)
>top human players are <---> top human players are
>close to perfection nowhere close to perfection
(2)
>computers will never <---> computers will eventually
>beat Kasparov beat Kasparov consistently
You seem to be saying that since certain respected thinkers were wrong
about (1) then I must be wrong about (2). For what it's worth I have
thought for the past 20 years or so that computers would eventually be
stronger than the best humans. I still think so, and fairly soon at
that.
But better than the best humans does not mean perfect. And the
argument is about what the rating of a perfect chess player would be.
>> It's not an idea that I am "attached" to. If it turned out
>> that it isn't true it wouldn't bother me at all. It's just
>> that on the presently available evidence there is a good strong
>> indication that it is true
>There is? Naah... (:
I have at least provided some evidence, however flawed. You however
have produced here nothing in the way of evidence, merely an invalid
argument by analogy. If you want to change my mind (for whatever
strange reason you might want to do that) you're going to have to
provide some actual evidence I'm afraid.
>Jack van Rijswijck
>jav...@ib.com
Paul Rubin
In article <4m0fav$d...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
>Ed Seedhouse (e...@islandnet.com) wrote:
>During the match, Kasparov Hhimself stated that if Deep Blue
>said that Deep Blue did in fact play like a 3000 rated player
>player, and the 4-2 result of the match is consistent with that.
>It's no surprise that this issue has been raised in a thread
>about perfect chess. The viewpoints seem rather similar:
The match was not long enough to give a meaningful rating for
Deep Blue. If it was stopped after the first game, that would
have given a rating of 3200. By the 5th and 6th games Kasparov
had taken DB's measure and was beating it in consistent style.
I believe that if the match had gone to 12 games, the score would
have been 8-4 or better. That does not indicate a top 20 player,
though top 100 is possible.
>top human players are <---> top human players are
>close to perfection nowhere close to perfection
>
>computers will never <---> computers will eventually
>beat Kasparov beat Kasparov consistently
>
>So this thread runs the risk of turning into another "computers
>will never beat Kasparov" thread. No points for guessing what I
>think about the potential of computer chess...
I don't think anyone here is saying computers will never beat Kasparov.
I do believe that if and when computers beat Kasparov, it will be
through better strategy (evaluation and search extension heuristics),
not by adding 1 or 2 more ply of full-width search speed and no
additional intelligence to the DB that played Kasparov.
>Unless, of course, humans can play chess almost perfectly. But
>then, in turn, it would still be surprising if perfect chess
>level happens to be within human grasp, but *barely*. At least
>99,9999% of all chess playing humans are far from perfect,
>because Kasparov is clearly better than them. That would mean
>that the limit of the chess playing capability of the human brain
>is close to perfection within 0,0001%. Astonishing!
What is so astonishing about it? Look at checkers.
When the top players are allowed to choose their own openings,
draws almost always result. They play so close to perfectly
that they are required to play randomly chosen openings in
order to make competitive events interesting.
Also, there's no claim that Kasparov plays perfectly, only that
he's (maybe) able to keep a game within the drawn portion of
the game tree against perfect play some of the time. Chess is
just glorified tic-tac-toe, and can (probably) only be won
if the opponent makes a sufficiently large mistake. That
Kasparov is better than anyone else just means that in a 100-game
match against Ghod, Kasparov might get 20 draws while Karpov
would get 18 and a generic IM might get 2 or 3. This would
be consistent with a rating in the low 3000's for Ghod.
Chris Whittington
> > >amount of strength that they gain per extra ply that they are
> > >able to search, a computer using present algorithms that was
> > >able to search 20 ply in a middle-game position would be able
> > >to slaughter Kasparov repeatedly.
> >
> > been shown to be wrong. By that extrapolation "Deep Blue"
> > should, as I recall, be rated around 3000.
>
> would search a couple more plies, it would outplay him. He also
> said that Deep Blue did in fact play like a 3000 rated player
> "in certain positions". Kasparov would rate Deep Blue as a top-20
> player, and the 4-2 result of the match is consistent with that.
> It's no surprise that this issue has been raised in a thread
> about perfect chess. The viewpoints seem rather similar:
>
> close to perfection nowhere close to perfection
>
> computers will never <---> computers will eventually
> beat Kasparov beat Kasparov consistently
>
> So this thread runs the risk of turning into another "computers
> will never beat Kasparov" thread. No points for guessing what I
> think about the potential of computer chess...
>
> > >think that we are going to get such a drastic change that a
> > >computer with enough ply will not be substantially better
> > >than Kasparov.) And, unless the situation changes, said
> > >computer is going to be nowhere near a perfect player.
> >
> > I think the current evidence is rather good that the
> > extrapolation has already failed.
>
> computer would eventually beat the human world champion. Chess
> players said that computers would never beat *anyone*. It did
> happen though, in the late 60s. OK, but computers would never
> beat anyone who can play a decent game of chess. They did in the
> early 70s. Granted, but they would never beat expert players.
> They did in the late 70s.
>
> Well OK, but IMs were a different ball game. However, computers
> started beating them, too, in the early 80s. But IGMs were a
> totally different ball game, they would never lose against
> computers. Alas, computers started beating IGMs in the last 80s.
> But Kasparov was a completely different ball game, he would never
> ever lose against computers. Yet, he did, in 1993. Yes but that
> was at rapid chess; tournament chess was a different ball game
> altogether. Kasparov will never lose a 40/2 game against a
> computer. Enter Deep Blue. Ah, but Deep Blue didn't win the
> match. Kasparov will never ever lose an entire match against a
> computer.
>
> Why suppose that this entire development will stop right here?
> Would it not be strange if the theoretical limit of computer
> chess capability happens to be *extremely* close to, but still
> just slightly below, the limit of human chess capability?
>
> then, in turn, it would still be surprising if perfect chess
> level happens to be within human grasp, but *barely*. At least
> 99,9999% of all chess playing humans are far from perfect,
> because Kasparov is clearly better than them. That would mean
> that the limit of the chess playing capability of the human brain
> is close to perfection within 0,0001%. Astonishing!
>
> > >that the top people are nearly perfect
> >
> > that it isn't true it wouldn't bother me at all. It's just
> > that on the presently available evidence there is a good strong
> > indication that it is true
>
> There is? Naah... (:
>
>
> jav...@ib.com
Extrapolate - extrapolate - ....
Its very easy to get better quickly when starting from a low base.
Take a program with search and no knowledge - give it knowledge
about material - this might be worth 400 ELOs.
Then give it knowledge about pawn structure - maybe 100-200 ELOs,
Then give it mobility knowledge - 50 ELOs ?
Speed it up, get more search depth - this gives good results for 1 to 2
plies, good for 2 to 3, but falls off at 8-9, 9-10 and so on.
Maybe the figures aren't exact. but you get the drift, it gets
increasingly hard to improve.
More examples - it didn't take Karpov so long to get to 2000 ELO,
not so long to 2200 ELO, but now he's at 2700(?), how long to get another
another 10 ELO, or 20 ELO - is it possible in his lifetime ?
My guess is that there is an upper limit to strength as represented
by ELO figure and that Kasparoc is pretty close to it.
My guess is also that getting to this strength by computer software
is going to be a mighty difficult and lengthy process, maybe never
being achieved. All the nonsense talked about 'one more ply' won't do it.
'one more ply' plus material knowledge gives general chess knowledge
(know that Q > Nite, then at 3 ply know that fork N and K is good, at
5 ply know that threaten NK fork is good), (know backward pawn is bad,
add some ply search, and know about the minority attack).
So ply search creates knowledge, but only up to a point, after N ply
it just creates more plies.
No doubt someone can think of chess knowledge that can't emerge from
search + mtrl ..........
Chris Whittington
Javhar
Ed Seedhouse (e...@islandnet.com) wrote:
>>> This is based on an old linear extrapolation that has since
>>> been shown to be wrong. By that extrapolation "Deep Blue"
>>> should, as I recall, be rated around 3000.
>>
>>During the match, Kasparov Hhimself stated that if Deep Blue
>>would search a couple more plies, it would outplay him.
>
>Beside the point which is that by the extrapolation postulated
>Deep Blue should be much better than Kasparov *now*. And don't
>forget that a "couple more ply" is one *heck* of a lot of
>computer power.
*That* is in fact beside the point. We were talking about Ghod,
who has unlimited computer power. The point is that more
computing will get you past Kasparov, and after that there is a
long long way to go until you get to Ghod.
>>He also said that Deep Blue did in fact play like a 3000 rated
>>player "in certain positions".
>
>Even if true this is also beside the point since the claim was
>not made about how the computer will play in "certain
>positions". Heck I can play K+Q vs. Rook perfectly myself.
>Does that give me a 3000 rating?
I would be quite happy if Kasparov told me that I played like a
3000 player in *any* position. He also said `but in other
positions it plays like a 2300 player' -- heck, I'd be happy with
that, too! Anyway, I can play KQ-K perfectly, but I doubt that
Kasparov would say that I play like a 3000 player in that
endgame, because it doesn't take a 3000 player to do that
(evidently!).
I'm not saying that Deep Blue is a 3000 player all round, but DB
is certainly up there at top GM level.
>>(1)
>>top human players are <---> top human players are
>>close to perfection nowhere close to perfection
>>(2)
>>computers will never <---> computers will eventually
>>beat Kasparov beat Kasparov consistently
>
>You seem to be saying that since certain respected thinkers were
>wrong about (1) then I must be wrong about (2).
No, I'm just saying that the viewpoints seem to be similar, quite
apart from whether or not they're wrong. Therefore it was only a
matter of time until the Ghod thread turned into the Deep Blue
thread.
>For what it's worth I have thought for the past 20 years or so
>that computers would eventually be stronger than the best
>humans. I still think so, and fairly soon at that.
That does surprise me. How much stronger than Kasparov do you
think computers will get?
>But better than the best humans does not mean perfect. And the
>argument is about what the rating of a perfect chess player
>would be.
That is what Ben Tilly and I have been saying. If DB's 14 ply (or
whatever it is) is IGM level, then 20 ply is better than Kasparov,
but you need some 100 ply at least to approach perfect chess. You
seem to be arguing against yourself here, for if Kasparov is
nearly perfect then `better than Kasparov' ought to be pretty
much equal to Ghod. Unless of course there's a lot of ground to
cover between Kasparov and Ghod, but then that is what my point
has been all along.
>>> It's not an idea that I am "attached" to. If it turned out
>>> that it isn't true it wouldn't bother me at all. It's just
>>> that on the presently available evidence there is a good
>>> strong indication that it is true
>>
>>There is? Naah... (:
>
>I have at least provided some evidence, however flawed. You
>however have produced here nothing in the way of evidence,
>merely an invalid argument by analogy. If you want to change my
>mind (for whatever strange reason you might want to do that)
>you're going to have to provide some actual evidence I'm afraid.
Here's what I produced: an actual estimate based on a computation
I've explained in detail, the endgame database example, and `the
DB search argument' (Ben Tilly). None of those arguments have
been disproved.
You came up with the SKD argument, of which I explained why I think
it's invalid, and a couple of invalid analogies: Go is more complex
than chess, computers get diminished returns at higher search depths.
Other than that, you basically maintain that humans are fairly close
to perfect chess, because Kasparov can probably draw against Ghod
every now and then. That's a circular argument.
I still think we should get John Nunn's opinion, as he appears to
have some knowledge about chess and has actually *played* against
Ghod (in rather restricted chess domains).
Jack.
Robert Hyatt
In article <83086770...@cpsoft.demon.co.uk>,
Chris Whittington <chr...@cpsoft.demon.co.uk> wrote:
-->jav...@ib.com (Javhar) wrote:
-->>
-->> Ed Seedhouse (e...@islandnet.com) wrote:
-->>
-->> > >Judging by the present performance from computers, and the
-->> > >amount of strength that they gain per extra ply that they are
-->> > >able to search, a computer using present algorithms that was
-->> > >able to search 20 ply in a middle-game position would be able
-->> > >to slaughter Kasparov repeatedly.
-->> >
-->> > This is based on an old linear extrapolation that has since
-->> > been shown to be wrong. By that extrapolation "Deep Blue"
-->> > should, as I recall, be rated around 3000.
-->>
-->> During the match, Kasparov Hhimself stated that if Deep Blue
-->> would search a couple more plies, it would outplay him. He also
-->> said that Deep Blue did in fact play like a 3000 rated player
-->> "in certain positions". Kasparov would rate Deep Blue as a top-20
-->> player, and the 4-2 result of the match is consistent with that.
-->> It's no surprise that this issue has been raised in a thread
-->> about perfect chess. The viewpoints seem rather similar:
-->>
-->> top human players are <---> top human players are
-->> close to perfection nowhere close to perfection
-->>
-->> computers will never <---> computers will eventually
-->> beat Kasparov beat Kasparov consistently
-->>
-->> So this thread runs the risk of turning into another "computers
-->> will never beat Kasparov" thread. No points for guessing what I
-->> think about the potential of computer chess...
-->>
-->> > >Obviously the extrapolation will fail somewhere, but I do not
-->> > >think that we are going to get such a drastic change that a
-->> > >computer with enough ply will not be substantially better
-->> > >than Kasparov.) And, unless the situation changes, said
-->> > >computer is going to be nowhere near a perfect player.
-->> >
-->> > I think the current evidence is rather good that the
-->> > extrapolation has already failed.
-->>
-->> Computer chess researchers stated as far back as the 1950s that
-->> computer would eventually beat the human world champion. Chess
-->> players said that computers would never beat *anyone*. It did
-->> happen though, in the late 60s. OK, but computers would never
-->> beat anyone who can play a decent game of chess. They did in the
-->> early 70s. Granted, but they would never beat expert players.
-->> They did in the late 70s.
-->>
-->> Well OK, but IMs were a different ball game. However, computers
-->> started beating them, too, in the early 80s. But IGMs were a
-->> totally different ball game, they would never lose against
-->> computers. Alas, computers started beating IGMs in the last 80s.
-->> But Kasparov was a completely different ball game, he would never
-->> ever lose against computers. Yet, he did, in 1993. Yes but that
-->> was at rapid chess; tournament chess was a different ball game
-->> altogether. Kasparov will never lose a 40/2 game against a
-->> computer. Enter Deep Blue. Ah, but Deep Blue didn't win the
-->> match. Kasparov will never ever lose an entire match against a
-->> computer.
-->>
-->> Why suppose that this entire development will stop right here?
-->> Would it not be strange if the theoretical limit of computer
-->> chess capability happens to be *extremely* close to, but still
-->> just slightly below, the limit of human chess capability?
-->>
-->> Unless, of course, humans can play chess almost perfectly. But
-->> then, in turn, it would still be surprising if perfect chess
-->> level happens to be within human grasp, but *barely*. At least
-->> 99,9999% of all chess playing humans are far from perfect,
-->> because Kasparov is clearly better than them. That would mean
-->> that the limit of the chess playing capability of the human brain
-->> is close to perfection within 0,0001%. Astonishing!
-->>
-->> > >I am always astonished at how attached people are to the idea
-->> > >that the top people are nearly perfect
-->> >
-->> > It's not an idea that I am "attached" to. If it turned out
-->> > that it isn't true it wouldn't bother me at all. It's just
-->> > that on the presently available evidence there is a good strong
-->> > indication that it is true
-->>
-->> There is? Naah... (:
-->>
-->>
-->> Jack van Rijswijck
-->> jav...@ib.com
-->
-->
-->Extrapolate - extrapolate - ....
-->
-->Its very easy to get better quickly when starting from a low base.
-->
-->Take a program with search and no knowledge - give it knowledge
-->about material - this might be worth 400 ELOs.
-->Then give it knowledge about pawn structure - maybe 100-200 ELOs,
-->
-->Then give it mobility knowledge - 50 ELOs ?
-->
-->Speed it up, get more search depth - this gives good results for 1 to 2
-->plies, good for 2 to 3, but falls off at 8-9, 9-10 and so on.
-->
-->Maybe the figures aren't exact. but you get the drift, it gets
-->increasingly hard to improve.
-->
-->More examples - it didn't take Karpov so long to get to 2000 ELO,
-->not so long to 2200 ELO, but now he's at 2700(?), how long to get another
-->another 10 ELO, or 20 ELO - is it possible in his lifetime ?
-->
-->My guess is that there is an upper limit to strength as represented
-->by ELO figure and that Kasparoc is pretty close to it.
-->
-->My guess is also that getting to this strength by computer software
-->is going to be a mighty difficult and lengthy process, maybe never
-->being achieved. All the nonsense talked about 'one more ply' won't do it.
-->
-->'one more ply' plus material knowledge gives general chess knowledge
-->(know that Q > Nite, then at 3 ply know that fork N and K is good, at
-->5 ply know that threaten NK fork is good), (know backward pawn is bad,
-->add some ply search, and know about the minority attack).
-->
-->So ply search creates knowledge, but only up to a point, after N ply
-->it just creates more plies.
-->
-->No doubt someone can think of chess knowledge that can't emerge from
-->search + mtrl ..........
-->
-->Chris Whittington
-->
I both agree and disagree. Firstly, I don't believe that there's an
absolute concept called positional chess. I firmly believe that
positional chess is nothing but very long-range tactics.
However, and this is the issue, some simple positional point like, say,
an isolated pawn, might only be understood by a 100 ply search. We know
the pawn is bad, because it's difficult to defend, and, as a result, we
simply don't create 'em. *IF* you could search deep enough, this doesn't
matter, because you can see all the way to the point where (a) it is lost;
(b) it is exchanged; (c) it promotes; or (d) it is unimportant because you
win or lose due to other reasons. Only in (a) is the term isolated pawn
important, yet even GM's consider them bad (as a rule) because they simply
can't see far enough to be certain of (b), (c) or (d).
Of course, this isn't ever going to be an issue in my lifetime, because
such search depths are a long way off. I won't ever say "never", but,
at age 47, even should I live another 100 years, I'm convinced that such
speeds won't be available within that time-frame.
Ergo, we are going to have to do more of what the GM does, supplant
search depth by useful knowledge that is an adequate replacement for
this unobtainable depth. This seems doable, while discussing truly
impossible search depths is not.
I personally have high hopes, and plenty of time to achieve 'em. But
they aren't based on searching 30 gadzillion nodes per second. :)
(plus or minus a googol-plex or two)
--
Robert Hyatt Computer and Information Sciences
hy...@cis.uab.edu University of Alabama at Birmingham
(205) 934-2213 115A Campbell Hall, UAB Station
(205) 934-5473 FAX Birmingham, AL 35294-1170
Ed Seedhouse
e...@islandnet.com (Ed Seedhouse) wrote:
>Even if true this is also beside the point since the claim was not
>made about how the computer will play in "certain positions". Heck I
>can play K+Q vs. Rook perfectly myself. Does that give me a 3000
>rating?
Er, I meant to say K and Q vs. K. Add a rook to the weak side and I
don't play anywhere near perfectly.
Ed Seedhouse
jav...@ib.com (Javhar) wrote:
>Ed Seedhouse (e...@islandnet.com) wrote:
>>>> This is based on an old linear extrapolation that has since
>>>> been shown to be wrong. By that extrapolation "Deep Blue"
>>>> should, as I recall, be rated around 3000.
>>>
>>>During the match, Kasparov Hhimself stated that if Deep Blue
>>>would search a couple more plies, it would outplay him.
>>
>>Beside the point which is that by the extrapolation postulated
>>Deep Blue should be much better than Kasparov *now*. And don't
>>forget that a "couple more ply" is one *heck* of a lot of
>>computer power.
>
>*That* is in fact beside the point. We were talking about Ghod,
>who has unlimited computer power. The point is that more
>computing will get you past Kasparov, and after that there is a
>long long way to go until you get to Ghod.
I don't see any evidence that there is. How do we know that a
computer that can calculate consistently 30 ply ahead won't play well
enough to draw against a computer that can calculate the entire game
tree? I think that the observed fact that there is a fairly large
draw margin in chess, and that this margin gets higher as human
player's chess increases until what, around 50% of games are drawn at
the top level in tournaments, and more than that in world championship
contests, argues fairly strongly that the best humans are already good
enough to draw a fairly large percentage of games even against "ghod".
>>You seem to be saying that since certain respected thinkers were
>>wrong about (1) then I must be wrong about (2).
>No, I'm just saying that the viewpoints seem to be similar, quite
>apart from whether or not they're wrong. Therefore it was only a
>matter of time until the Ghod thread turned into the Deep Blue
>thread.
If that's your point I don't see why you bothered making it.
>>For what it's worth I have thought for the past 20 years or so
>>that computers would eventually be stronger than the best
>>humans. I still think so, and fairly soon at that.
>
>That does surprise me. How much stronger than Kasparov do you
>think computers will get?
I think that computers will top out at around 200 to 300 points better
than the best humans. And I think "ghod" wouldn't be all that much
higher - say 400 points or 3200.
>That is what Ben Tilly and I have been saying. If DB's 14 ply (or
>whatever it is) is IGM level, then 20 ply is better than Kasparov,
>but you need some 100 ply at least to approach perfect chess. You
>seem to be arguing against yourself here, for if Kasparov is
>nearly perfect then `better than Kasparov' ought to be pretty
>much equal to Ghod.
I didn't say Kasparov is nearly perfect. I simply said that he's good
enough to get a fairly high number of draws against a perfect opponent
because there is a fairly large drawing margin in chess. You can make
mistakes and still draw the game. This isn't hard to understand.
Make me play tic-tac-toe against "ghod" and I will draw every game.
Give me K on e1 and p on e2 against K on e8 and p on e7 and I will
draw that one every time too, no matter how many ply "ghod" can
calculate.
>Here's what I produced: an actual estimate based on a computation
>I've explained in detail, the endgame database example, and `the
>DB search argument' (Ben Tilly). None of those arguments have
>been disproved.
But your "computation" so far as I can see, is based on flawed
premesis and thus proves nothing.
Ed Seedhouse
p...@netcom.com (Paul Rubin) wrote:
>In article <4m0fav$d...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
>>Ed Seedhouse (e...@islandnet.com) wrote:
>>During the match, Kasparov Hhimself stated that if Deep Blue
>>would search a couple more plies, it would outplay him. He also
>>said that Deep Blue did in fact play like a 3000 rated player
>>"in certain positions". Kasparov would rate Deep Blue as a top-20
>>player, and the 4-2 result of the match is consistent with that.
>>It's no surprise that this issue has been raised in a thread
>>about perfect chess. The viewpoints seem rather similar:
Actually I didn't write that. Javhar wrote it.
Ed Seedhouse
Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>In article <4lsc5i$5...@sanjuan.islandnet.com>
>e...@islandnet.com (Ed Seedhouse) writes:
>> Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>>
>> >> Now, if chess were that much deeper than humans can deal with their
>> >> should be at least as many classes in chess as in go. But there
>> >> aren't. Therefore I conclude that it is very likely that the best
>> >> human players are within one or two classes of the "perfect" chess
>> >> player.
>> >Judging by the present performance from computers, and the amount of
>> >strength that they gain per extra ply that they are able to search, a
>> >computer using present algorithms that was able to search 20 ply in a
>> >middle-game position would be able to slaughter Kasparov repeatedly.
>> This is based on an old linear extrapolation that has since been shown
>> to be wrong. By that extrapolation "Deep Blue" should, as I recall,
>> be rated around 3000.
>It is hardly news that basically EVERY linear extrapolation is false.
Of course it is hardly news. But I was countering an argument that
relied on the very extrapolation which you point out is undoubtably
false. If the extrapolation is invalid then so is the argument based
on it.
> there is extremely good reason to believe that a
>computer using current algorithms and searching 18 ply would be
>substantially better than Kasparov is.
Being substantially better than Kasparov is one thing, and perfectly
possible. Being thousands of rating points better than Kasparov is
another thing and there is reason to believe that even a perfect
computer will not achieve that distinction.
>And there is still no reason to
>believe that said computer is approaching perfection.
Even if this is so it does not constitute evidence that the computer
is not approaching perfection. Nor does it say anything about how
much better a perfect computer would be than Kasparov.
Because of the fairly large drawing margin in chess there is every
reason to suspect that the best human players are already good enough
to achieve a fairly high percentage of draws even against a perfect
chessplaying machine. As additional evidence we have the difference
in skill catagories between go and chess.
>> >I am always astonished at how attached people are to the idea that the
>> >top people are nearly perfect when they are aware that
>> It's not an idea that I am "attached" to. If it turned out that it
>> isn't true it wouldn't bother me at all. It's just that on the
>> presently available evidence there is a good strong indication that it
>> is true, and no evidence at all that your position is true. When and
>> if the evidence changes I will be happy to change my position on the
>> matter.
>What evidence? I have given numbers
Numbers are not necessarily evidence.
Simon Read
(newsgroups set to only rec.games.chess.computer)
Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>This is false. I recall a person who mentioned a while ago a program to
>look for legal moves in chess. He stuck a random number lookup on it
>and had random. It was horrible at chess. So he changed it, and had it
>search for 1 move with the goal of having the largest number of
>possible moves after one move of its. If multiple moves ones hit this
>number, it chose randomly. What happened? It was substantially worse!
>Let me offer you the start of an obvious example...
>
>Joe Bloe-Computer
>1.e4 e6 [ game snipped ]
>Ben Tilly
Your example shows Joe Bloe beating the computer which tried to maximise
its number of moves. Let's call this computer MS (mobility-seeker).
You've just shown Joe Bloe beating MS, but that still doesn't say
whether or not MS can beat random. You have to play MS against
random to find out which is better. This experiment shouldn't be
hard to carry out.
One thing that would be very useful here is a little more experimental
data. I appreciate that one person on this thread said that he had
simulated "Rhandom" and found that he could get it to beat him. He
mentioned that he could get it to promote a pawn (or several) which
would probably trap his king on his back rank, delivering mate. This
proves that there could be players (Ghod Awful etc.) who would not
just be slightly worse than Rhandom, but a _lot_ worse, as they would
lose almost every time.
This is interesting because it is not just kicking ideas around, someone
actually simulated Rhandom to find out how well it plays. It would be
very interesting to see any other experiments on this topic, like for
example gradually degrading some program's evaluation function to get it
to approach Rhandom's unique standard of play. I'm sure I've seen some
similar idea floated on this thread.
Yes, I am following my own advice. I have a chess program myself in
preparation, and I am going to generate ratings for various versions
of it, starting at Rhandom and working up to the full version. (That
isn't why I'm writing the program; I'm doing something more than
just calculating ratings.) This newsgroup will be the first to hear
of the results. There are problems with comparing chess programs of
different search depths, to try to calculate relative ratings, so
I'm not going to do that. The different versions of my program will
have identical depth of search, but greatly differing knowledge
(evaluation functions). Apparently, this also applies to humans,
which means that any ratings I generate will be useful to compare
with human performance.
Simon
Cyber Linguist
Several people have mentioned something to the effect of "higher-rated
players not seeing certain moves because they (the moves) are so dumb..."
This is a bit much, IMHO. I would bet "even" Kasparov 8-) could, if he
really wanted to, write a list of *all* the legal moves in any given
legal chess position, with either color to play. Heck, **I** can, and
I'm not even rated! (I'm probably around 1200 or so.)
If higher-rated players are truly having problems finding all the moves,
they should try:
* Make a list of your pieces.
* Ask yourself -- does this piece have a move?
* If so, add it.
* If not, go on to next piece.
* If you're still on the first piece, check for other moves.
* Go through all of your pieces this way.
If need be, you could take each piece andm for all the other 63 squares,
ask yourself if it would be legal for the piece to move there. Add
the "what could I promote this piece to?" question for pawn promotions,
and you have a way of finding *ALL* your options in any situation.
This isn't brain surgery...
Is this (check all other 63 squares) ridiculous? Yes.
Will it always work? Again, yes.
Any GM (or any decent player) can find all possible chess moves.
It may actually take them longer than for a beginner, but they can.
In the context of the original post: Ghod, GhodAwful, Random,
and now "Dhevil" and "Dhevilishly Bhad" should all be considered to at least
know about all possible moves. Random **has** to, to choose properly.
Oh, and Random wasn't spelled with an H... AFAIK, nobody worships any
deity with a similar name, and the spelling changes were to clearly show
I was talking about fictitious chessplaying "demigods." I don't need to
start a flame war. 8-)
--
Eric Carr <ca...@cs.odu.edu> | http://www.cs.odu.edu/~carr
----------------------------------------------------------------------------
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Benjamin J. Tilly
In article <4m5oio$t...@sanjuan.islandnet.com>
e...@islandnet.com (Ed Seedhouse) writes:
> Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>
> >In article <4lsc5i$5...@sanjuan.islandnet.com>
> >e...@islandnet.com (Ed Seedhouse) writes:
>
> >> Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
> >>
> >> >> Now, if chess were that much deeper than humans can deal with their
> >> >> should be at least as many classes in chess as in go. But there
> >> >> aren't. Therefore I conclude that it is very likely that the best
> >> >> human players are within one or two classes of the "perfect" chess
> >> >> player.
>
> >> >Judging by the present performance from computers, and the amount of
> >> >strength that they gain per extra ply that they are able to search, a
> >> >computer using present algorithms that was able to search 20 ply in a
> >> >middle-game position would be able to slaughter Kasparov repeatedly.
>
> >> This is based on an old linear extrapolation that has since been shown
> >> to be wrong. By that extrapolation "Deep Blue" should, as I recall,
> >> be rated around 3000.
>
> >It is hardly news that basically EVERY linear extrapolation is false.
>
> Of course it is hardly news. But I was countering an argument that
> relied on the very extrapolation which you point out is undoubtably
> false. If the extrapolation is invalid then so is the argument based
> on it.
>
There is a saying that science is about finding useful lies. What do we
mean by that? It means that science very often progresses by finding
useful approximations. We know that the approximations are false, but
they can let us get a good idea of what will happen.
Now the fact is that a simple extrapolation will almost always be false
in detail. However it frequently gives roughly the right ballpark.
Now the extrapolation that you are arguing against is false in detail,
we are all agreed upon that. But will you give me one reason to believe
that its basic ballpark predictions are not reasonably accurate? You
have not done so to date. The fact is that so far the principle of each
extra ply giving us roughly a fixed amount of improvement has held up
pretty well. And it does not take that many more ply, if more ply give
anything resembling the current amount of improvement (or even if it
only gives us 50-100, which is a lot less than we have been getting so
far), to get better than Kasparov. And it does not take that many more
ply after that to be able to beat Kasparov with extremely high odds.
(What happens when Kasparov plays a 2400 player?? What about a 2200
player???) And said computer will STILL have all of the basic
weaknesses of lacking a positional understanding, and I see no reason
that a perfect player would not be able to take it apart.
> > there is extremely good reason to believe that a
> >computer using current algorithms and searching 18 ply would be
> >substantially better than Kasparov is.
>
> Being substantially better than Kasparov is one thing, and perfectly
> possible. Being thousands of rating points better than Kasparov is
> another thing and there is reason to believe that even a perfect
> computer will not achieve that distinction.
>
"There is reason to believe" you claim, but you have not come up with a
solid reason yet that I have seen. In any case all that I am claiming
is that Kasparov would lose to a perfect player essentially every time.
He would not manage to get a substantial number of draws against it.
The "thousands of points" was just an extrapolation to come up with a
general ballpark of what could be possible. But the basic point is that
Kasparov would not have chances of drawing, no human so far would even
be close to that point.
The fact is that the more that we know about human performance, the
worse it seems to be when compared to any absolute standard. Take, for
an example that you have so far ignored, the many suprises about the
ending that the databases have found. If people could not on their own,
despite a tremendous amount of work and thought about endgames by many
of the top players, notice that they did not know how to win QKrk (just
2 pieces, with very unfair material odds) until computers showed them
the "flying rook" defense, why are we so convinced that humans can play
with more pieces any more accurately?
> >And there is still no reason to
> >believe that said computer is approaching perfection.
>
> Even if this is so it does not constitute evidence that the computer
> is not approaching perfection. Nor does it say anything about how
> much better a perfect computer would be than Kasparov.
>
I think that we can agree that a perfect computer would be better than
the computer that I just described.
And unless there is a sudden change in what extra ply do for us, it
would not take that many more ply to reduce Kasparov's drawing chances
to nearly nil.
> Because of the fairly large drawing margin in chess there is every
> reason to suspect that the best human players are already good enough
> to achieve a fairly high percentage of draws even against a perfect
> chessplaying machine. As additional evidence we have the difference
> in skill catagories between go and chess.
>
How large is the drawing margin? I am not convinced that it is that
large.
What reason do I have for that claim? The reason is that in endgames,
which are after all the only situations which we can analyze perfectly,
if you do not move very, very, precisely then a win quickly becomes a
draw, and a draw quickly becomes a loss. I see little reason to believe
that the situation is any different in "endgames" with more pieces,
however finding the correct way to exploit a mistake becomes much
harder because the situation is more complicated.
In any case it does not really matter that much, because I believe that
there is so much room for improvement on human play that people are
nowhere near drawing margin against a perfect player.
> >> >I am always astonished at how attached people are to the idea that the
> >> >top people are nearly perfect when they are aware that
>
> >> It's not an idea that I am "attached" to. If it turned out that it
> >> isn't true it wouldn't bother me at all. It's just that on the
> >> presently available evidence there is a good strong indication that it
> >> is true, and no evidence at all that your position is true. When and
> >> if the evidence changes I will be happy to change my position on the
> >> matter.
>
> >What evidence? I have given numbers
>
> Numbers are not necessarily evidence.
If you are going to edit what I say, then please indicate that. The
above sentence, truncated where it was, is VERY different from my
actual sentence of "What evidence? I have given numbers, and I have
given a variety of reasons to believe that humans are just not that
good at chess."
Now for the record, the numbers in question are indeed evidence unless
there is reason to believe that how strength scales with extra ply will
change very suddenly.
Furthermore I find it interesting that when I continue looking at what
you did NOT quote, with no indication that you left anything out, I
find the following paragraphs.
"Can you give me a solid reason for believing that it is possible to
get
an almost perfect understanding of the game despite our being able to
actually think more than a few moves in advance? Or for why it is that
you think that Kasparov has actually achieved this?"
"For the record let me say that I am not putting people down. It is
truly astounding how well people can play and understand such a complex
game given our limitations. It is just that human limitations are such
that it seems impossible for us to play it very well. And every line of
evidence that I can think of (the history of opening theory, what
happens when we compare our performance to perfection in simple
endgames, and simple extrapolations from computer performance) supports
the reasonable conclusion."
These points still seem solid to me. Would you care to address them
rather than ignoring them?
After all it seems to me that you are the one who is making the
stronger claim about how well we understand and play chess. After all I
am not trying to claim that we should be unable to extrapolate from
past performance of computers to give somewhat reasonable estimates of
future performance, nor am I trying to claim that an individual human
can analyze complex middle-game positions with more accuracy than the
entire chess community has been able to analyze "simple" endgames. And
I am definitely not claiming that in addition to this being possible,
Kasparov can manage it.
But I will make a claim, and a rather strong one at that. All of our
chess theory about positional play is designed to let people make the
best possible analysis of a position that we can make with the
limitation of only being able to analyze a very small number of moves.
I claim that this substitution of theory for analsis, while it is very
useful for a human to do, is bound to be far less effective than a
comprehensive analysis would be if it were possible for us to do it.
Ben Tilly
David Spencer
In article <4m5oiu$t...@sanjuan.islandnet.com>,
>
>>>>> This is based on an old linear extrapolation that has since
>>>>> been shown to be wrong. By that extrapolation "Deep Blue"
>>>>> should, as I recall, be rated around 3000.
>>>>
>>>>During the match, Kasparov Hhimself stated that if Deep Blue
>>>>would search a couple more plies, it would outplay him.
>>>
>>>Beside the point which is that by the extrapolation postulated
>>>Deep Blue should be much better than Kasparov *now*. And don't
>>>forget that a "couple more ply" is one *heck* of a lot of
>>>computer power.
>>
>>*That* is in fact beside the point. We were talking about Ghod,
>>who has unlimited computer power. The point is that more
>>computing will get you past Kasparov, and after that there is a
>>long long way to go until you get to Ghod.
>
>computer that can calculate consistently 30 ply ahead won't play well
>enough to draw against a computer that can calculate the entire game
>tree? I think that the observed fact that there is a fairly large
>draw margin in chess, and that this margin gets higher as human
>player's chess increases until what, around 50% of games are drawn at
>the top level in tournaments, and more than that in world championship
>contests, argues fairly strongly that the best humans are already good
>enough to draw a fairly large percentage of games even against "ghod".
I don't really think that it follows that just because the best humans
draw a lot it follows that they can draw a lot against perfect play.
To me you can't compare human performance vs. perfect performance based
only on how humans perform, as perfect performance could be "infinitely" better
than human performance.
Paul Rubin
In article <4mb0rn$q...@marvin.telops.com>,
David Spencer <dspe...@telops.com> wrote:
>I don't really think that it follows that just because the best
>humans draw a lot it follows that they can draw a lot against perfect
>play. To me you can't compare human performance vs. perfect
>performance based only on how humans perform, as perfect performance
>could be "infinitely" better than human performance.
Nobody seems to be claiming this, as far as I can tell. Some people
are claiming the opposite. Others are questioning the claim (of the
opposite). I.e. for the question "How would Kasparov do in a 100 game
match against Ghod", the two camps seem to be "Ghod wins 100-0" and
"who knows, maybe Kasparov can get some draws". The first camp
seems to not be supporting its claim with good evidence. The
second is looking around for evidence one way or the other, but
nothing conclusive has shown up.
Benjamin J. Tilly
In article <4m9d7v$6...@maui.cc.odu.edu>
ca...@tigerlily.cs.odu.edu (Cyber Linguist) writes:
> Several people have mentioned something to the effect of "higher-rated
> players not seeing certain moves because they (the moves) are so dumb..."
> This is a bit much, IMHO. I would bet "even" Kasparov 8-) could, if he
> really wanted to, write a list of *all* the legal moves in any given
> legal chess position, with either color to play. Heck, **I** can, and
> I'm not even rated! (I'm probably around 1200 or so.)
>
I think that you are confusing two different comments. The first is
that good players do not even *think* about certain moves because they
"know" that they are bad. (They may not be, but unless there is a
recognizable tactical pattern resulting, it is usually not wise to
throw away a queen, and it is not worth the effort to see if there is
some compensation.) The second is that no human can analyze the entire
set of possible moves more than a short distance in advance. This is
because of human limitations...
>
> If higher-rated players are truly having problems finding all the moves,
> they should try:
>
> * Make a list of your pieces.
> * Ask yourself -- does this piece have a move?
> * If so, add it.
> * If not, go on to next piece.
> * If you're still on the first piece, check for other moves.
> * Go through all of your pieces this way.
>
> If need be, you could take each piece andm for all the other 63 squares,
> ask yourself if it would be legal for the piece to move there. Add
> the "what could I promote this piece to?" question for pawn promotions,
> and you have a way of finding *ALL* your options in any situation.
> This isn't brain surgery...
>
And in a naive way we can, for instance, extend this to thinking about
all sequences of 5 moves. No human can actually do this and keep track
of it though.
> Is this (check all other 63 squares) ridiculous? Yes.
> Will it always work? Again, yes.
> Any GM (or any decent player) can find all possible chess moves.
> It may actually take them longer than for a beginner, but they can.
> In the context of the original post: Ghod, GhodAwful, Random,
> and now "Dhevil" and "Dhevilishly Bhad" should all be considered to at least
> know about all possible moves. Random **has** to, to choose properly.
>
In theory, given enough time and paper to record my thoughts on, I can
play perfectly. I am not about to do so for obvious reasons though.
> Oh, and Random wasn't spelled with an H... AFAIK, nobody worships any
> deity with a similar name, and the spelling changes were to clearly show
> I was talking about fictitious chessplaying "demigods." I don't need to
> start a flame war. 8-)
Are you insulting Lady Luck! All of her worshippers know that the holy
words are "It is Random" and you don't call her name in vain!!! :-)
Ben
Kevin Clinefelter
Cyber Linguist wrote:
>
> Several people have mentioned something to the effect of "higher-rated
> players not seeing certain moves because they (the moves) are so dumb..."
> This is a bit much, IMHO. I would bet "even" Kasparov 8-) could, if he
> really wanted to, write a list of *all* the legal moves in any given
> legal chess position, with either color to play. Heck, **I** can, and
> I'm not even rated! (I'm probably around 1200 or so.)
>
It's not that I _can't_ see the moves, it's that I have to count them in
the (snipped) manner you suggested. This is quite tedious, as it has to
be done each time Random is to move. Yes, it would be better to have a
computer do it. Unfortunately, I have no chess software that with a
Random personality and lack the expertise to write it myself.
One of these days, I gotta write a signature file . . .
Kevin Clinefelter
Paul Rubin
In article <4mapa0$s...@dartvax.dartmouth.edu>,
Benjamin J. Tilly <Benjamin...@dartmouth.edu> wrote:
>> >It is hardly news that basically EVERY linear extrapolation is false.
>>
>> Of course it is hardly news. But I was countering an argument that
>> relied on the very extrapolation which you point out is undoubtably
>> false. If the extrapolation is invalid then so is the argument based
>> on it.
>>
>There is a saying that science is about finding useful lies. What do we
>mean by that? It means that science very often progresses by finding
>useful approximations. We know that the approximations are false, but
>they can let us get a good idea of what will happen.
>
>Now the fact is that a simple extrapolation will almost always be false
>in detail. However it frequently gives roughly the right ballpark.
The central question to this thread is whether the linear approxmation
is useful or not at the level that computers now play at. Newtonian
physics works extremely well for computing motions of automobiles and
pretty good for planets, but it is useless near the speed of light.
The question then is whether the best human and computer players
today are playing near the "speed of light" in chess.
>> > there is extremely good reason to believe that a
>> >computer using current algorithms and searching 18 ply would be
>> >substantially better than Kasparov is.
Evidence?
>The fact is that the more that we know about human performance, the
>worse it seems to be when compared to any absolute standard. Take, for
>an example that you have so far ignored, the many suprises about the
>ending that the databases have found. If people could not on their own,
>despite a tremendous amount of work and thought about endgames by many
>of the top players, notice that they did not know how to win QKrk (just
>2 pieces, with very unfair material odds) until computers showed them
>the "flying rook" defense, why are we so convinced that humans can play
>with more pieces any more accurately?
The possibility exists that they don't NEED to play that accurately
and still be able to draw from the starting position.
>"Can you give me a solid reason for believing that it is possible to get
>an almost perfect understanding of the game despite our being able to
>actually think more than a few moves in advance? Or for why it is that
>you think that Kasparov has actually achieved this?"
Just subjective evidence given by the large number of draws in
grandmaster chess, where nobody has been able to find better moves
in post-game analysis. I haven't seen any really concrete evidence
one way or the other.
>"For the record let me say that I am not putting people down. It is
>truly astounding how well people can play and understand such a complex
>game given our limitations. It is just that human limitations are such
>that it seems impossible for us to play it very well. And every line of
>evidence that I can think of (the history of opening theory, what
>happens when we compare our performance to perfection in simple
>endgames, and simple extrapolations from computer performance) supports
>the reasonable conclusion."
>
>These points still seem solid to me. Would you care to address them
>rather than ignoring them?
It's certainly true that endgames exist where a draw can easily turn
into a loss, so a human getting into such an ending would probably
make a mistake and lose. You haven't shown however that it's so
difficult for people to avoid getting into such endings.
>But I will make a claim, and a rather strong one at that. All of our
>chess theory about positional play is designed to let people make the
>best possible analysis of a position that we can make with the
>limitation of only being able to analyze a very small number of moves.
>I claim that this substitution of theory for analsis, while it is very
>useful for a human to do, is bound to be far less effective than a
>comprehensive analysis would be if it were possible for us to do it.
If by "far less effective" you mean comprehensive analysis would
lead to 100% wins against today's best players (human or computer),
that's not impossible, but it is a rather strong claim that I haven't
seen any persuasive evidence for.
Cyber Linguist
In article <113.6692...@Th0r.foo.bar> kie...@spuddy.mew.co.uk (Kieron Dunbar) writes:
>Could someone tell me how the Dhevil plays? I seem to have missed the posting
>mentioning it. :(
The Dhevil would play as well as Ghod, but would "cheapo" his opponent in
drawn situations if the odds were he'd win. For example, if he were playing
Ghod, he would play perfectly, so as not to lose. But if he were playing
a mere mortal, and a drawn situation could turn into a win for him if only
the human missed a mate-in-30 combination, the Dhevil would at least
consider "cheapoing" the opponent, running a slight risk of a draw in
return for a more likely win. The interesting aspect to this is, though
he would never beat Ghod in play (unless there was a forced win), he would
end up with a slightly higher rating, due to more wins over weaker players.
Against GhodAwful, Random, or Ghod, the Dhevil would play like Ghod would,
but not so against players he thinks he can bamboozle...
...And Dhevilishly Bhad would be the "losing" correlary to GhodAwful.
"cheapoing" his opponents into a forced-mate situation against him...
Ed Seedhouse
Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>There is a saying that science is about finding useful lies.
If there such a saying that by itself doesn't make it a true saying.
>What do we
>mean by that? It means that science very often progresses by finding
>useful approximations. We know that the approximations are false, but
>they can let us get a good idea of what will happen.
The argument didn't base itself on this being merely a usefull
approximation. It based itself on this being an accurate linear
extrapolation. If you then admit that it isn't really accurate but
only approximate then any conclusion that is based upon it being
accurate becomes without ground.
>Now the extrapolation that you are arguing against is false in detail,
>we are all agreed upon that. But will you give me one reason to believe
>that its basic ballpark predictions are not reasonably accurate?
Well, since the original argument was based upon it's being, not
"approximate" or "false in detail" but on it's being accurate. Why
should the burden of proof rest on me to prove it's conclusion false
when you have already admitted that the premise it is based upon is
false? I think it's up to you to show that it is a correct
conclusion, not me to prove that it is incorrect.
>You
>have not done so to date. The fact is that so far the principle of each
>extra ply giving us roughly a fixed amount of improvement has held up
>pretty well.
The fact is that it hasn't, actually.
>> Being substantially better than Kasparov is one thing, and perfectly
>> possible. Being thousands of rating points better than Kasparov is
>> another thing and there is reason to believe that even a perfect
>> computer will not achieve that distinction.
>"There is reason to believe" you claim, but you have not come up with a
>solid reason yet that I have seen.
I've already given the argument and you haven't refuted it or shown
that it's premesis are invalid. Merely saying that it is invalid
doesn't make it so so far as I know.
> In any case all that I am claiming
>is that Kasparov would lose to a perfect player essentially every time.
>He would not manage to get a substantial number of draws against it.
>The "thousands of points" was just an extrapolation to come up with a
>general ballpark of what could be possible.
In other words you are shifting your ground and now defending a
different proposition, but without admitting that you are doing so.
In any event I see no reason to suppose that a perfect chess computer
would beat Kasparov all the time, and good reasons to suspect rather
that Kasparov would get a good percentage of draws against it.
Certainly we know beyond question that the very best checkers players
would draw a perfec checkers computer almost all the time. I think
the current evidence is that the best chess players will draw a
perfect computer quite often but not almost all the time because chess
is more complicated than checkers.
>> Even if this is so it does not constitute evidence that the computer
>> is not approaching perfection. Nor does it say anything about how
>> much better a perfect computer would be than Kasparov.
>I think that we can agree that a perfect computer would be better than
>the computer that I just described.
No, we can't.
>And unless there is a sudden change in what extra ply do for us, it
>would not take that many more ply to reduce Kasparov's drawing chances
>to nearly nil.
>> Because of the fairly large drawing margin in chess there is every
>> reason to suspect that the best human players are already good enough
>> to achieve a fairly high percentage of draws even against a perfect
>> chessplaying machine. As additional evidence we have the difference
>> in skill catagories between go and chess.
>How large is the drawing margin? I am not convinced that it is that
>large.
>In any case it does not really matter that much, because I believe that
>there is so much room for improvement on human play that people are
>nowhere near drawing margin against a perfect player.
Feel free to believe that, but I can't see any actual evidence to
support this belief. If you are going to claim that my position is
invalid because I can't give convincing evidence to back it up you can
hardly then claim that your position is valid when you yourself don't
have any evidence to back *it* up. At least you can't if you are
being reasonable.
>> >What evidence? I have given numbers
>>
>> Numbers are not necessarily evidence.
>If you are going to edit what I say, then please indicate that.
No, sorry. If you want to talk to me you are going to have to accept
that fact that I'm going to edit your replies. Otherwise our
correspondance will soon become so voluminous that no one will read
it, and I'm not interested in that. If you insist that all replies
quote every one of your golden words you are soon going to be left
with no one to talk to.
>But I will make a claim, and a rather strong one at that. All of our
>chess theory about positional play is designed to let people make the
>best possible analysis of a position that we can make with the
>limitation of only being able to analyze a very small number of moves.
>I claim that this substitution of theory for analsis, while it is very
>useful for a human to do, is bound to be far less effective than a
>comprehensive analysis would be if it were possible for us to do it.
Once again this claim, even if true, says nothing one way or the other
about whether the best humans will get a fair percentage of draws
against a perfect player.
Ed Seedhouse
dspe...@telops.com (David Spencer) wrote:
>I don't really think that it follows that just because the best humans
>draw a lot it follows that they can draw a lot against perfect play.
>To me you can't compare human performance vs. perfect performance based
>only on how humans perform, as perfect performance could be "infinitely" better
>than human performance.
There is no evidence that this is so, and pretty strong evidence that
suggests that it isn't so.
Javhar
>How do we know that a
>computer that can calculate consistently 30 ply ahead won't play well
>enough to draw against a computer that can calculate the entire game
>tree?
We can take a look, again, at the KRB-KNN endgame database. It takes 400+
plies in some positions to calculate the correct move(s). That strongly
suggests that at a `mere' 30 ply, a lot of moves that look winning or
drawish actually aren't. Either the computer has heuristics that can work
out the correct moves (such as the well-known KBN-K `trick', which is
suboptimal but still winning; but humans clearly don't have these
heuristics in many endgames, as has been shown by GM games analysis with
databases), or it has to compute the entire tree. Less computing won't do;
it will run into the horizon effect, and, inevitably, play wrong moves.
Moves that throw away wins and/or draws.
Compare the typical lengths of the maximin lines in various endgames. The
more pieces there are on the board, the `longer' the endgame gets. KRB-KNN
takes 223 moves or so, while the average 4 man endgame is a lot shorter.
This suggests that 7 man endgames take even longer, not to mention 8 man
endgames etc. It takes ever increasing computing power (more than
exponentially increasing) to keep up with Ghod in those endgames, and if
you don't have that computing power, you will lose. You will not draw.
Now, chess itself is a 32-man endgame. I do think there's a long long
way to go from Kasparov to Ghod.
Jack.
Kevin Clinefelter
Ed Seedhouse wrote:
>
> dspe...@telops.com (David Spencer) wrote:
>
> >To me you can't compare human performance vs. perfect performance based
> >only on how humans perform, as perfect performance could be "infinitely" better
> >than human performance.
>
> There is no evidence that this is so, and pretty strong evidence that
> suggests that it isn't so.
because chess is a finite game. This claim is like saying infinitely
more water flows over Niagara Falls than through my bathroom faucet; even
though the falls are a lot more impressive than the faucet, they aren't
infinite.
Another thread has discussed at length the number of valid board
positions. While there was no general agreement as to what that number
is, no one disputed the fact that it is finite. Given a finite number of
positions, there must be a finite number of games assuming only that we
keep the threefold repetition draw rule. If there are P possible
positions, after P+1 moves we have a repetition of positions and after
2P+1 moves we have a threefold repetition. So the longest possible game
has a finite number of moves. Computing power sufficient to analyze to
that depth would constitute perfect play.
Granted, we don't have that level of computing power today. I don't
think we will get that level of computing power any time soon, and it may
be theoretically impossible. But the solution to the opening position is
_not_ an infinite problem.
Ghod Almighty knows that the opening position is either a draw, a win for
White, or a win for Black. And Hhe isn't telling me which!
Cyber Linguist
Well, since this has transformed itself into a "Do humans play near-perfect
chess" thread, I figured I'd add some Random thoughts. 8-)
* Javhar seems to have a pretty convincing argument about endgames, IMHO.
The sheer number of games possible in chess would seem to indicate that
a program capable of calculating 100 ply would find incredibly subtle
schemes to defeat Kasparov, and would probably be playing cat-and-mouse
with Deep Blue in short order.
* With some of these, (as in some endgames) looking ahead 100+ moves would be
necessary to get a draw or a win. Any mistake could push the game out of the
"won" or "drawn" tree.
* I really don't fear the day when a computer beats the current world champion,
because humans *created* this machine, after all, and there are so many
things we can do better than it. My watch calculator can do 4-digit
multiplication faster and better than I can manually. I don't consider
this a "threat".
* I will keep rooting for the humans, though, just on general principles. 8-)
* As for evidence one way or the other, I doubt we'll know until we build
a computer that can calculate 100+ ply (or some other large number). If
Kasparov can still draw most games against this machine, perhaps current
GMs do indeed play near-perfect chess.
* Keep in mind, though, that a 100-ply machine could search 95 ply or so
almost instantly. Could Kasparov still draw most games, when each and every
move he made was met with an instant reply, taking away half of his thinking
time? I know **I** would play much worse given this condition...
* This is rec.games.chess.*, not alt.flame. 8-)
Paul Rubin
In article <4mfrv9$b...@maui.cc.odu.edu>,
Cyber Linguist <ca...@tigerlily.cs.odu.edu> wrote:
>Well, since this has transformed itself into a "Do humans play near-perfect
>chess" thread, I figured I'd add some Random thoughts. 8-)
>
>* Javhar seems to have a pretty convincing argument about endgames, IMHO.
> The sheer number of games possible in chess would seem to indicate that
> a program capable of calculating 100 ply would find incredibly subtle
> schemes to defeat Kasparov, and would probably be playing cat-and-mouse
> with Deep Blue in short order.
What is convincing about that argument?
The way I see it, the existence of those horrendously complicated
endings proves that the exact boundary between winning and drawing,
or between drawing and losing, has a very complicated shape and if
you get too close to the edge, you can fall in. But nothing I've
seen persuades me that staying well clear of that edge is necessarily
so difficult.
Look, say you want to cross a river and three methods are available.
#1, you can drive over the bridge, no problem. #2, you can take the
ferry boat, no problem. #3, you can walk a tightrope over the
waterfall, where dozens of angry alligators are waiting at the bottom
to devour your carcass if you make a misstep.
Now think of playing a chess game as being like crossing a river.
That "chess has a thick draw margin" is like saying routes like #1 and
#2 exist. That "there are horrendously complicated endings like
KRB-KNN" is like saying routes like #3 exist. That doesn't prove at
all that it is to draw at chess. You don't need to learn to walk the
tightrope, if you can avoid it and use the bridge or boat.
>* With some of these, (as in some endgames) looking ahead 100+ moves would be
> necessary to get a draw or a win. Any mistake could push the game out of the
> "won" or "drawn" tree.
Yes but you have to show that the opponent can force you into such an ending.
You haven't done that.
>* I will keep rooting for the humans, though, just on general principles. 8-)
Me too :)
>* As for evidence one way or the other, I doubt we'll know until we build
> a computer that can calculate 100+ ply (or some other large number). If
> Kasparov can still draw most games against this machine, perhaps current
> GMs do indeed play near-perfect chess.
In past decades, adding another search ply to a brute force program
was good for 50 or so rating points. With today's programs, the extra
ply is good for a lot less points. This decline may indicate that
a "speed of light" boundary is being approached.
Chris Whittington
"Positional is nothing but long range tactics" - great quote !
May I try some:
"The whole is just the sum of the parts"
"Bob Hyatt is just a random arrangement of carbon, hydrogen, oxygen"
OK, all these are true if you have enough time and space (like we could shake the
CHO for long enough and out you would pop ..!)
Only we don't have the time or the space - so in this field of cptr-chess,
we need to analyse the positional concepts which are not able to emerge
from the application of search on material/pawn structure type evaluations.
Or, and, which positional concepts are better placed in the evaluation function#
rather than allowed to emerge via search.
My worry is that all the talk and effort going into speed and efficient
coding kind of masks the non-study and non-implementation of positional
Chris Whittington
Robert Hyatt
In article <83139040...@cpsoft.demon.co.uk>,
Chris Whittington <chr...@cpsoft.demon.co.uk> wrote:
>
>"Positional is nothing but long range tactics" - great quote !
>
>May I try some:
>
>"The whole is just the sum of the parts"
>
>"Bob Hyatt is just a random arrangement of carbon, hydrogen, oxygen"
>
>OK, all these are true if you have enough time and space (like we could shake the
>CHO for long enough and out you would pop ..!)
>
>Only we don't have the time or the space - so in this field of cptr-chess,
>we need to analyse the positional concepts which are not able to emerge
>from the application of search on material/pawn structure type evaluations.
>
>Or, and, which positional concepts are better placed in the evaluation function#
>rather than allowed to emerge via search.
>
>My worry is that all the talk and effort going into speed and efficient
>coding kind of masks the non-study and non-implementation of positional
>
I hope not too, but I suspect it is. Speed's important, but here's the
"lesson" I try to preach to every aspiring programmer: Speed is only
better, if, to achieve it, you don't compromise the quality of the chess
knowledge or the search used to exploit this knowledge.
What does that mean? Simply, write the program the way you want it to
be, including any knowledge or search extension you think is important.
Then, if you can make it go faster without removing any of this, the
speed will help. However, to make it faster by removing knowledge that
is slow to compute, is making a trade-off that seems on the surface to
be wrong.
If you look at Crafty, I've jumped through a lot of hoops to make things
faster, like the rotated bitmap approach, etc., but never at the expense
of removing knowledge until that knowledge has been proven bad. As a
result, Crafty at 80K nps is better than Crafty at 40K nps. However,
were I to modify Crafty, and produce a Crafty' which is faster but
dumber, it would likely produce different results. How to compare
Crafty at 40K to Crafty' at 80K, when there are now two degrees of
freedom in the comparison, speed and knowledge.
Personally, I worry about speed, but only to the extent of "can I change
something to make it run faster without reducing its quality in the
process?" I don't mind letting technology sweep me along faster and
faster, because that's a "non-compromised" was of getting better. I'm
still firmly convinced that we already have enough speed. we just need
better "smarts". For those that are NPS-crazy, it's going to be very
tough to ever understand an isolated pawn. For those of us that evaluate
such things, it's not.
Be an interesting debate, this knowledge vs speed thing. I already see
phenomonal tactics from Crafty, and occasionally even GM-like games are
played by it (this as assessed by GM players, BTW, not by me.) However,
I also see silly games played where an important "hole" in its knowledge
takes the game down a path only an idiot would follow.
One interesting thing to watch is to find games where crafty thinks its
ahead until the eval suddenly drops significantly. Obviously, in that
position, its positional knowledge was deficient, because it was likely
losing and didn't know it or understand why. These deficiencies can be
cured over time, so long as I don't let the "nps" statistic control what
I do or when I do it.
Javhar
: >I don't really think that it follows that just because the best humans
: >draw a lot it follows that they can draw a lot against perfect play.
: >To me you can't compare human performance vs. perfect performance based
: >only on how humans perform, as perfect performance could be "infinitely" better
: >than human performance.
: There is no evidence that this is so, and pretty strong evidence that
: suggests that it isn't so.
I wouldn't say infinitely better, but I would say astronomically better.
In a debate about perfect play, perhaps we should not forget that we have
actually SEEN glimpses of perfect play. Things we learn from endgame
databases cannot be discarded as `no evidence'. On the other hand, the one
thing we have indeed seen no evidence for is the far stronger claim that
human chess play is nearly perfect.
Jack.
Javhar
First of all let me say that this entire thread has not produced
any PROOF at all. All we can possibly be talking about is whether
existing data INDICATES / SUGGESTS that human chess is close to
perfect chess or not. Let me also say that "I think `A' and you
have not shown any convincing evidence to believe `B'" is hardly
a valid argument in favour of A.
Paul Rubin (p...@netcom.com) wrote:
> >The fact is that the more that we know about human performance, the
> >worse it seems to be when compared to any absolute standard. Take, for
> >an example that you have so far ignored, the many suprises about the
> >ending that the databases have found. If people could not on their own,
> >despite a tremendous amount of work and thought about endgames by many
> >of the top players, notice that they did not know how to win QKrk (just
> >2 pieces, with very unfair material odds) until computers showed them
> >the "flying rook" defense, why are we so convinced that humans can play
> >with more pieces any more accurately?
>
> The possibility exists that they don't NEED to play that accurately
> and still be able to draw from the starting position.
Of course this possibility exists. The question is whether or not it is a
likely possibility, given the examples about solved endgames. Evidence
from 5 and 6 man endgame databases (and not just *some* of them), which
involve conversion into endgames with fewer pieces, is that you DO need to
play that accurately. That still doesn't mean that the 32 man endgame
doesn't have a large draw margin (which is what you are saying), but I
think that given the experiences with endgame databases it would be far
more surprising if it did than if it didn't.
> >"Can you give me a solid reason for believing that it is possible to get
> >an almost perfect understanding of the game despite our being able to
> >actually think more than a few moves in advance? Or for why it is that
> >you think that Kasparov has actually achieved this?"
>
> Just subjective evidence given by the large number of draws in
> grandmaster chess, where nobody has been able to find better moves
> in post-game analysis. I haven't seen any really concrete evidence
> one way or the other.
Evidence from grandmaster chess doesn't say anything about perfect chess.
Top athletes in any sport are almost equally fast (the average winning
margin in running races, for example, is less than one percent), but that
doesn't mean that any of them are getting near the speed of light.
In post-game analysis of `simple' endgames, it has been shown often enough
that grandmasters make mistakes which would cost them a win or a draw
against a database.
> It's certainly true that endgames exist where a draw can easily turn
> into a loss, so a human getting into such an ending would probably
> make a mistake and lose. You haven't shown however that it's so
> difficult for people to avoid getting into such endings.
And on the other hand, nobody has shown that it is NOT difficult (or even
impossible) for humans to avoid these endings. You haven't shown that it's
so difficult for Ghod to avoid getting into endings in which humans won't
make decisive mistakes. Whose is the burdon of proof here? Not just mine.
Evidence shows that the draw margin is narrow with few pieces on the
board, therefore the claim that the margin would be wide with many pieces
on the board needs at least as much justification, if not more.
> If by "far less effective" you mean comprehensive analysis would
> lead to 100% wins against today's best players (human or computer),
> that's not impossible, but it is a rather strong claim that I haven't
> seen any persuasive evidence for.
Maybe not persuasive (evidently), but at least fairly convincing to me. I
feel that "humans can achieve a fairly large draw percentage against
perfect play" is a FAR stronger claim, for which I haven't seen any
evidence whatsoever.
Jack.
Benjamin J. Tilly
In article <4meu85$l...@sanjuan.islandnet.com>
e...@islandnet.com (Ed Seedhouse) writes:
> Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
>
>
> >There is a saying that science is about finding useful lies.
>
> If there such a saying that by itself doesn't make it a true saying.
>
However in this case a passing understanding of several areas of
science will make it obvious that this one is a quite accurate
description of something real in science.
>
> >What do we
> >mean by that? It means that science very often progresses by finding
> >useful approximations. We know that the approximations are false, but
> >they can let us get a good idea of what will happen.
>
> The argument didn't base itself on this being merely a usefull
> approximation. It based itself on this being an accurate linear
> extrapolation. If you then admit that it isn't really accurate but
> only approximate then any conclusion that is based upon it being
> accurate becomes without ground.
>
The argument for what? For estimating "Ghod" as having a predicted
rating of over 10,000? That was a ballpark estimate of what it might
be, but I certainly am not ready to claim that it is that high. However
a far weaker claim, and therefore a far less accurate extrapolation, is
needed to get an opponent whose rating should be over 3500. Which is
quite enough to trash Kasparov repeatedly with little nonsense about
scoring lots of draws.
> >Now the extrapolation that you are arguing against is false in detail,
> >we are all agreed upon that. But will you give me one reason to believe
> >that its basic ballpark predictions are not reasonably accurate?
>
> Well, since the original argument was based upon it's being, not
> "approximate" or "false in detail" but on it's being accurate. Why
> should the burden of proof rest on me to prove it's conclusion false
> when you have already admitted that the premise it is based upon is
> false? I think it's up to you to show that it is a correct
> conclusion, not me to prove that it is incorrect.
>
Please demonstrate what accuracy the original argument needs to show
that it is possible in principle to play chess far better than
Kasparov. As the person who made that argument I am claiming that if
the extrapolation remains anywhere close to its present accuracy (ie
improvements of within a factor of 1/4 of the observed rate) for many
ply (let us say the next 10 ply) then a computer can be much better
than Kasparov. And even with similar diminished returns, it does not
take that much to get a computer that is so much better than Kasparov
that he would not even have a reasonable drawing chance.
If you wish to claim that my argument needs more accuracy than what I
claim, then it is up to you to show it. And if you wish to claim that
the extrapolation is unlikely to hold up, then it is up to you to give
solid reasons.
>
> >You
> >have not done so to date. The fact is that so far the principle of each
> >extra ply giving us roughly a fixed amount of improvement has held up
> >pretty well.
>
> The fact is that it hasn't, actually.
>
Would you care to demonstrate this?
> >> Being substantially better than Kasparov is one thing, and perfectly
> >> possible. Being thousands of rating points better than Kasparov is
> >> another thing and there is reason to believe that even a perfect
> >> computer will not achieve that distinction.
>
> >"There is reason to believe" you claim, but you have not come up with a
> >solid reason yet that I have seen.
>
> I've already given the argument and you haven't refuted it or shown
> that it's premesis are invalid. Merely saying that it is invalid
> doesn't make it so so far as I know.
>
Which one? The comparison with Go? The fact is that we have no way of
knowing how close we are to understanding the game of Go. Given that, a
comparison between chess and Go adds absolutely nothing to our
understanding of how well we play chess.
Claiming that it does does not make it so, as you point out.
Alternately you could be talking about your "wide drawing margin in
chess" claim. Fine, there may be a wide drawing margin. Yet when you
play an IM, I will bet that you will not manage to get a high
proportion of draws. The relative skill difference is just too great.
And you claim that the possible skill level between the top
grandmasters of today and perfection is so small that it is within this
drawing margin.
I think that it is worthwhile to remark that not so long ago the same
was said of the top chess grandmasters. It would be impossible to put
up impressive levels of wins against them. Then Bobby Fischer did it.
And we all know he was not perfect. Yet people today are back to making
the same claim about today's players with no more real evidence for
it...
>
> > In any case all that I am claiming
> >is that Kasparov would lose to a perfect player essentially every time.
> >He would not manage to get a substantial number of draws against it.
> >The "thousands of points" was just an extrapolation to come up with a
> >general ballpark of what could be possible.
>
> In other words you are shifting your ground and now defending a
> different proposition, but without admitting that you are doing so.
No. I challenge you to go back through my posts and find where I
"shifted". It has been my claim all along that Kasparov is nowhere near
perfect. I did make the claim that an estimate of a perfect player as
being around 10000 points was not an unreasonable estimate. However I
freely admit, and at the time I would have freely admitted (in that
post I believe that I did so admit) that there is no really solid way
to test this one way or the other.
And in our discussion all along I have taken the view that Kasparov
would lose and lose badly, while you have taken the position that
Kasparov would score a substantial proportion of draws against a
perfect player. Those have been our respective positions for some time
now. Do you deny it?
> In any event I see no reason to suppose that a perfect chess computer
> would beat Kasparov all the time, and good reasons to suspect rather
> that Kasparov would get a good percentage of draws against it.
> Certainly we know beyond question that the very best checkers players
> would draw a perfec checkers computer almost all the time. I think
> the current evidence is that the best chess players will draw a
> perfect computer quite often but not almost all the time because chess
> is more complicated than checkers.
>
And again I ask you what this evidence consists of. Please tell me.
>
> >> Even if this is so it does not constitute evidence that the computer
> >> is not approaching perfection. Nor does it say anything about how
> >> much better a perfect computer would be than Kasparov.
>
> >I think that we can agree that a perfect computer would be better than
> >the computer that I just described.
>
> No, we can't.
>
Yes we can. The computer that I had described (which only searched 20
ply I believe, that is under a dozen moves in the future) is by nature
imperfect. It only searched a limited portion of the possible search
tree, and then applied an evaluation function to it with known
weaknesses. (Known enough for humans to use them regularly.) Therefore
it is guarenteed that it will make mistakes and second-rate moves.
A perfect computer would search the entire search tree, and would
therefore be able to catch any mistakes. Since we are guarenteed of at
least occasional mistakes, the perfect computer would be better.
> >And unless there is a sudden change in what extra ply do for us, it
> >would not take that many more ply to reduce Kasparov's drawing chances
> >to nearly nil.
>
> >> Because of the fairly large drawing margin in chess there is every
> >> reason to suspect that the best human players are already good enough
> >> to achieve a fairly high percentage of draws even against a perfect
> >> chessplaying machine. As additional evidence we have the difference
> >> in skill catagories between go and chess.
>
> >How large is the drawing margin? I am not convinced that it is that
> >large.
>
> >In any case it does not really matter that much, because I believe that
> >there is so much room for improvement on human play that people are
> >nowhere near drawing margin against a perfect player.
>
> Feel free to believe that, but I can't see any actual evidence to
> support this belief. If you are going to claim that my position is
> invalid because I can't give convincing evidence to back it up you can
> hardly then claim that your position is valid when you yourself don't
> have any evidence to back *it* up. At least you can't if you are
> being reasonable.
>
You have given no evidence at all. I have given evidence. Beyond
claiming that my extrapolation is wrong in detail, and therefore any
argument based on it or any version of it is false (anybody who uses
approximations will see the flaw in this line of reasoning). On the
same "logic" you can throw out Newton's laws.
>
> >> >What evidence? I have given numbers
> >>
> >> Numbers are not necessarily evidence.
>
> >If you are going to edit what I say, then please indicate that.
>
> No, sorry. If you want to talk to me you are going to have to accept
> that fact that I'm going to edit your replies. Otherwise our
> correspondance will soon become so voluminous that no one will read
> it, and I'm not interested in that. If you insist that all replies
> quote every one of your golden words you are soon going to be left
> with no one to talk to.
>
(sigh)
On Usenet it is standard practice to indicate editing. The standard
ways of doing this are to write [...] or (snip) or some other
indicator.
The reason for this is that improper editing can distort what a person
says, so it is important to indicate where you have edited so that
readers can understand where the context shifts. You can find more on
this topic in news.announce.newusers.
(For example twice now you have edited out 2 of my lines of argument
without responding to them. The fact that you are doing this without
indicating it is dishonest, and I am therefore requesting that you
indicate editing in the standard way.
Incidentally do you wish to address my other two lines of argument?
(Incidentally after my request for you to indicate editing when you do
it, you edited out the next section without indicating it. I don't mind
the editing, although it is irritating to have 2/3 of my argument
ignored, but I do mind your pretending that there was nothing there.)
> >But I will make a claim, and a rather strong one at that. All of our
> >chess theory about positional play is designed to let people make the
> >best possible analysis of a position that we can make with the
> >limitation of only being able to analyze a very small number of moves.
> >I claim that this substitution of theory for analsis, while it is very
> >useful for a human to do, is bound to be far less effective than a
> >comprehensive analysis would be if it were possible for us to do it.
>
> Once again this claim, even if true, says nothing one way or the other
> about whether the best humans will get a fair percentage of draws
> against a perfect player.
When I say "far less effective" I mean that when faced with the real
thing it will fall apart and the human will lose.
Ben Tilly
Ed Seedhouse
jav...@ib.com (Javhar) wrote:
I've never claimed that human chess play is "nearly perfect", only
that because chess has a fairly large draw margin the best players are
good enough so that their mistakes are not enough to lose all the time
against a "perfect" chess machine.
You know all of your arguments could be applied pretty well unchanged
to unrestricted checkers, but if you tried to do that I don't think
many people would give you much credibility. Well, we observe as a
fact that among the best checkers players a decisive game is a rarity.
What explanation do we have for that other than that the very best
human players are pretty well perfect at checkers, or at least good
enough so that their mistakes are so small as to be important only in
the rarest of cases?
In chess too, at the highest levels, we see a large number of draws.
Not nearly as much as in checkers, but at the highest levels the draw
percentage is well over 50%. If chess is so little understood by
humans where does the rather high percentage of draws come from? If
the high percentage of draws in checkers is evidence that the best
humans play well enough not to lose against anyone except as a rare
exception why shouldn't the same evidence mean the same thing for
chess?
Personally I think that certainly since Capablanca and possibly since
Lasker there has always been at least one chess player alive who would
draw a fairly high percentage of games (> 40% anyway) against even a
perfect chess player. And I think the weight of the available
evidence supports this belief of mine.
Ed Seedhouse
Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
.. an amazingly long reply to what had already become an unnecesarily
long thread.
Sorry folks, I don't have time to deal with "argument by exhaustion"
so I'm not even going to try. I've also snipped the list of
newsgroups back to the one where I think it might be faintly
appropriate.
I think Ben is wrong and there's an end to it.
Ed Seedhouse
jav...@ib.com (Javhar) wrote:
>First of all let me say that this entire thread has not produced
>any PROOF at all.
Indeed it hasn't. Nor it seems has it produced much light for that
matter.
Brian J. Ritzel
Ed Seedhouse (e...@islandnet.com) wrote:
: Benjamin...@dartmouth.edu (Benjamin J. Tilly) wrote:
: .. an amazingly long reply to what had already become an unnecesarily
: long thread.
: Sorry folks, I don't have time to deal with "argument by exhaustion"
: so I'm not even going to try. I've also snipped the list of
: newsgroups back to the one where I think it might be faintly
: appropriate.
: I think Ben is wrong and there's an end to it.
: Ed Seedhouse
: President, Victoria Chess Club.
: CFC Rating: 2058
Wow, Ben!
It's seems as if Mr. Seedhouse has gone from creatively editting your
posts and ignoring your arguments to editting out the whole thing and
claiming victory!
Amazing!
-Bri
--
Brian Jay Ritzel
Urbana, IL USA
rit...@prairienet.org
M D. Grimminck
Let's trow in some maths on the problem...
If Ghod has a ELO rating G, and Kasparov K the expected
score p of Ghod against Kasparov is given by:
s=1/{1+10^[(K-G)/400]}, so G is given by
G=400*log(p/(1-p))+K
For simplicity, lets assume Ghod plays a lot
better than Kasparov, such that p about 1.
Furthermore let's assume chess is a draw.
(for simplicity!)
If an average game played by Ghod-Kasparov is 60 moves
before a draw is obvious, we can compute a relation
between Kasparovs typical error rate (the chanche he
moves from from draw to lose) per move and Ghod's rating:
p about 1-0.5*(1-e)^60.
error p Ghod's rating
rate
kasparov
1/1000 .53 2820
1/100 .87 3120
1/30 .94 3260
1/10 .999 4020
1/5 1 5130
1/2 1 10020
So now you only have to estimate Kasparov error rate.
Which is very hard ofcourse, but my personal estimate
is between 1/30 and 1/5, giving Ghod's rating
someware between 3260 to 5130.
Nb. if e is large (>.03) one can approximate
G=K-24000*log(1-e)
All logarithms mentioned are base 10.
--
Michel Grimminck, Computational Physics, University of Amsterdam.
draughts/checker page: http://carol.fwi.uva.nl/~grimmink/draughts.html
Bradlee Johnson
>Personally I think that certainly since Capablanca and possibly since
>Lasker there has always been at least one chess player alive who would
>draw a fairly high percentage of games (> 40% anyway) against even a
>perfect chess player. And I think the weight of the available
>evidence supports this belief of mine.
>
>
>President, Victoria Chess Club.
>CFC Rating: 2058
This is a rather fascinating discussion. It seems your arguments are
true and germaine as long as computers "see" the game in the same
fashion that humans do. It could be that the high number of draws at
the highest level of chess has to do with how human GMs use pattern
recognition to play the game. In other words, as we get to the top of
the human pile of players they tend to have certain kinds of
strengths and certain kinds of weaknesses. I think enough is known
about how GMs think to support this view to some extent. GMs tend to
have a high degree of pattern recognition, right brain
spatial/temporal knowledge and other characteristics that
differentiate them from lesser mortals. Computers may be able to
"think" about the game in such a radically different fashion that
they exploit certain human weaknesses. For instance, if you could
give a computer the pattern recognizing skills (through some sort of
AI device), that GMs possess AND give them tactical calculating
abilities of DeepThought, it may be that humans simply would not have
the mental firepower to draw with the machines.
Kasparov commented that in the first Game against The Machine he
sensed an intuitive grasp of the position in a pawn sacrifice made by
The Machine. Turns out, as we now know, that the machine had simply
calculated what the champ knew by intuition. Very different "kinds"
of skills.
Your statements would, I suppose, remain true of machine vs machine.
If, in fact, machines became so much better than humans, they would
enter into that same sort of high end drawing lock that GMs now find
themselves in. This is the first posting I've seen from this
particular thread so you may have already made this point. In fact,
that may be the gist of your point.
Gerry Quinn
The rating of Ghod would depend on whether he had opponents of similar
stature, and for how long he played. If he was 400 points above all others,
he would get only 1 point or so for a win (nothing for a draw). Each win
would take 6 hours. Playing two games a day, and winning both of them, he
would get from 3200 to 10000 in about 9 years, and keep rising.
If he took even a small percentage of draws, his rating would level off at a
much lower value. This would mean humans sometimes did not play badly enough
to lose.
If Dhemighod (ghodlike against humans, weaker than Ghod) is also playing,
he could get almost as high a rating against humans as Ghod. But Ghod might
then take extra points by doing well against him.
So its back to that question of how many distinguishable levels of chess
ability exist or might exist. No doubt the Ghnostic doctrines could be
invoked to identify various levels of ghodhood.
We could, however, estimate a minimum rating for Ghod by looking at all
Kasparov's games, changing each loss to at least a draw, and claiming every
missed win, and perhaps (this may be less sound) claiming every position
agreed to be practically unanalysable. Has anybody tried this approach?
----------------------------------------------------------
ger...@indigo.ie (Gerry Quinn)
----------------------------------------------------------
Benjamin J. Tilly
In article <4n5icd$j...@niamh.indigo.ie>
ger...@indigo.ie (Gerry Quinn) writes:
> The rating of Ghod would depend on whether he had opponents of similar
> stature, and for how long he played. If he was 400 points above all others,
> he would get only 1 point or so for a win (nothing for a draw). Each win
> would take 6 hours. Playing two games a day, and winning both of them, he
> would get from 3200 to 10000 in about 9 years, and keep rising.
>
> If he took even a small percentage of draws, his rating would level off at a
> much lower value. This would mean humans sometimes did not play badly enough
> to lose.
>
> If Dhemighod (ghodlike against humans, weaker than Ghod) is also playing,
> he could get almost as high a rating against humans as Ghod. But Ghod might
> then take extra points by doing well against him.
>
> So its back to that question of how many distinguishable levels of chess
> ability exist or might exist. No doubt the Ghnostic doctrines could be
> invoked to identify various levels of ghodhood.
>
> We could, however, estimate a minimum rating for Ghod by looking at all
> Kasparov's games, changing each loss to at least a draw, and claiming every
> missed win, and perhaps (this may be less sound) claiming every position
> agreed to be practically unanalysable. Has anybody tried this approach?
Each game reached the starting position. Despite a great amount of
effort, this position is practically not completely analyzable. Do we
then say that Ghod wins all games? :-)
Ben Tilly
Kevin Clinefelter
Benjamin J. Tilly wrote:
>
> In article <4n5icd$j...@niamh.indigo.ie>
> ger...@indigo.ie (Gerry Quinn) writes:
> > We could, however, estimate a minimum rating for Ghod by looking at all
> > Kasparov's games, changing each loss to at least a draw, and claiming every
> > missed win, and perhaps (this may be less sound) claiming every position
> > agreed to be practically unanalysable. Has anybody tried this approach?
>
> Each game reached the starting position. Despite a great amount of
> effort, this position is practically not completely analyzable. Do we
> then say that Ghod wins all games? :-)
>
As I understand the state of this discussion, that is the big question.
There have been some numbers tossed around for Ghod's rating if Hhe wins
all games, but there is no consensus that Hhe actually does score 100%
against the best human opposition.
The theoretical assumption underlying this thread appears to be that Ghod
_can_ analyze the opening position. If the opening position is a draw,
the question of Ghod's results vs. the best human players boils down to
how often can the humans in question avoid bad enough mistakes to turn
their drawn game into a loss. Gerry Quinn's method for estimating a
minimum rating for Ghod seems to assume that the opening position is a
draw given perfect play.
If the opening position is won for White or won for Black, it boils down
to how often the humans achieve the win or a draw with the winning color.
Ghod wins the games where Hhe has the winning color. If we believe that
the opening position is won for White (or won for Black), the
corresponding minimum estimate of Ghod's rating would claim the win for
all games with White (Black) and do a trickier analysis of Kasparov's
draws and losses with Black (White) to determine whether they should be
upgraded to wins or draws.
This sounds like a reasonable method of estimating a minimum rating for
Ghod, but what grandmaster has the time to do it? I sure wouldn't trust
_my_ analysis to pick which games should be upgraded by a half or full
point! ;)
Uterkorner
My friend Brad Tompson has come up with a test procedure to prove whether
chess or any 2 person zero sum game is a win or a draw.
Komputer Korner
Cyber Linguist
This would be interesting indeed! Until I actually see it work on Chess,
though, I confess I find it a bit hard to believe. Look at all the possible
positions in Chess after each ply:
ply (moves made) # possible positions
---------------------------------------------
0 1
1 23
2 529
...and from there, it's headed for the stratosphere. Anyone care to calculate
the possible positions after 3 moves? (you'd have to check for duplicates,
captures, and repeated positions (after 2 White moves, White could be back to
its initial position by having moved a Knight both times, etc.)
I think 20^X where X=number of moves made by both players combined would be a
good (albeit *very* rough) guesstimate of the possible board positions
for the first 20 or so moves. After that, who knows?
Of course, if his test procedure is to simply build a computer fast enough to
solve the game, shame on you. 8-)
Benjamin J. Tilly
> My friend Brad Tompson has come up with a test procedure to prove whether
> chess or any 2 person zero sum game is a win or a draw.
> Komputer Korner
One has been known for a loooong time.
However it takes a while...
Ben Tilly
(PS: If you have access to the computer power to do it within 5 years,
then you should use your computing power in other ways and make a large
fortune!!!!)