Theoretical chess rating question...

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Cyber Linguist

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Apr 17, 1996, 3:00:00 AM4/17/96
to
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...

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
----------------------------------------------------------------------------
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>+

Paul Rubin

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Apr 17, 1996, 3:00:00 AM4/17/96
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In article <4l1krg$k...@maui.cc.odu.edu>,

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

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Apr 18, 1996, 3:00:00 AM4/18/96
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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.
>
>

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

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Apr 18, 1996, 3:00:00 AM4/18/96
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p...@netcom.com (Paul Rubin) wrote:
>
> In article <4l1krg$k...@maui.cc.odu.edu>,
> 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.
>

How this ? 1000 Elo is the base. How to be worse then the worst ?

Chris Whittington


Kenneth Sloan

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Apr 18, 1996, 3:00:00 AM4/18/96
to
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/

Ed Seedhouse

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Apr 19, 1996, 3:00:00 AM4/19/96
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Chris Whittington <chr...@cpsoft.demon.co.uk> wrote:

>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

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Apr 19, 1996, 3:00:00 AM4/19/96
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In article <8298621...@cpsoft.demon.co.uk>,
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.
>>
>>
>
>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 ?

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

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Apr 19, 1996, 3:00:00 AM4/19/96
to
Chris Whittington (chr...@cpsoft.demon.co.uk) wrote:
: ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
: > What would be the estimated ELO ratings of:
: > [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

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Apr 20, 1996, 3:00:00 AM4/20/96
to
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!

Peace,
Fritz

Cyber Linguist

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Apr 20, 1996, 3:00:00 AM4/20/96
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In article <317893...@frontiernet.net> Kevin Clinefelter <kcln...@frontiernet.net> writes:

>Paul Rubin wrote:
>>
>> In article <8298621...@cpsoft.demon.co.uk>,
>> 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"
>> >>
>> >> * "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

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Apr 20, 1996, 3:00:00 AM4/20/96
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In article <phrDq3...@netcom.com>, Paul Rubin <p...@netcom.com> wrote:
>
>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

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Apr 20, 1996, 3:00:00 AM4/20/96
to

No, not any God -- just his little brother *Ghod* almighty. 8-) You know,
not-quite-a-god wannabe, but plays totally perfect chess...

Javhar

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Apr 20, 1996, 3:00:00 AM4/20/96
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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

Paul Rubin

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Apr 21, 1996, 3:00:00 AM4/21/96
to
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?

Chris Whittington

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Apr 21, 1996, 3:00:00 AM4/21/96
to
p...@netcom.com (Paul Rubin) wrote:
>
> In article <8298621...@cpsoft.demon.co.uk>,
> 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.
> >>
> >>
> >
> >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 ?
>
> 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.

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

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Apr 21, 1996, 3:00:00 AM4/21/96
to
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.

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

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Apr 21, 1996, 3:00:00 AM4/21/96
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sl...@cis.uab.edu (Kenneth Sloan) wrote:
>
> 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/

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

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Apr 21, 1996, 3:00:00 AM4/21/96
to
In article <phrDq6...@netcom.com>, Paul Rubin <p...@netcom.com> wrote:
-->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

unread,
Apr 22, 1996, 3:00:00 AM4/22/96
to
Paul Rubin (p...@netcom.com) wrote:
: 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

unread,
Apr 22, 1996, 3:00:00 AM4/22/96
to
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.
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

unread,
Apr 22, 1996, 3:00:00 AM4/22/96
to
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. 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

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Apr 22, 1996, 3:00:00 AM4/22/96
to
In article <317b7997...@news.cc.utexas.edu>,

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

unread,
Apr 22, 1996, 3:00:00 AM4/22/96
to
jav...@ib.com (Javhar) wrote:
>
> 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

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
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

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

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
In article <8301993...@cpsoft.demon.co.uk> Chris Whittington <chr...@cpsoft.demon.co.uk> writes:
>
>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

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
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. 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.

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

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
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.

Javhar

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
Chris Whittington (chr...@cpsoft.demon.co.uk) wrote:
: 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

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
Shouldn't the cross-posting be cut back? Check follow-ups...

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

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Apr 23, 1996, 3:00:00 AM4/23/96
to

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

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
Check follow-ups.

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

unread,
Apr 23, 1996, 3:00:00 AM4/23/96
to
In article <4lhs2e$n...@news.accessone.com> rt...@accessone.com (Dan Thies) writes:
>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

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Apr 24, 1996, 3:00:00 AM4/24/96
to
In article <4lisf8$8...@maui.cc.odu.edu> ca...@tigerlily.cs.odu.edu (Cyber Linguist) writes:
>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

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Apr 24, 1996, 3:00:00 AM4/24/96
to
ca...@tigerlily.cs.odu.edu (Cyber Linguist) wrote:
>

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

unread,
Apr 24, 1996, 3:00:00 AM4/24/96
to
Ed Seedhouse (e...@islandnet.com) wrote:
: 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

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Apr 24, 1996, 3:00:00 AM4/24/96
to
Cyber Linguist (ca...@tigerlily.cs.odu.edu) wrote:

: >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

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Apr 24, 1996, 3:00:00 AM4/24/96
to
Dan Thies (rt...@accessone.com) wrote:
: 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

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Apr 24, 1996, 3:00:00 AM4/24/96
to
jav...@ib.com (Javhar) wrote:
>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

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Apr 24, 1996, 3:00:00 AM4/24/96
to
In article <4llgf9$g...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
>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

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Apr 24, 1996, 3:00:00 AM4/24/96
to
Kenneth Sloan wrote:
>
> 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

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Apr 25, 1996, 3:00:00 AM4/25/96
to
In article <DqC0x...@boss.cs.ohiou.edu> bar...@ouvaxa.cats.ohiou.edu writes:
>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

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Apr 25, 1996, 3:00:00 AM4/25/96
to
jav...@ib.com (Javhar) wrote:
>
> Chris Whittington (chr...@cpsoft.demon.co.uk) wrote:

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

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Apr 25, 1996, 3:00:00 AM4/25/96
to
: 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.)

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

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Apr 26, 1996, 3:00:00 AM4/26/96
to

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

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Apr 27, 1996, 3:00:00 AM4/27/96
to

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

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Apr 27, 1996, 3:00:00 AM4/27/96
to

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

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Apr 27, 1996, 3:00:00 AM4/27/96
to

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

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Apr 27, 1996, 3:00:00 AM4/27/96
to

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

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Apr 28, 1996, 3:00:00 AM4/28/96
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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

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Apr 28, 1996, 3:00:00 AM4/28/96
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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

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Apr 28, 1996, 3:00:00 AM4/28/96
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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

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Apr 28, 1996, 3:00:00 AM4/28/96
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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

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Apr 28, 1996, 3:00:00 AM4/28/96
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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

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Apr 28, 1996, 3:00:00 AM4/28/96
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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

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Apr 28, 1996, 3:00:00 AM4/28/96
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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

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Apr 29, 1996, 3:00:00 AM4/29/96
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In article <4llgf9$g...@da.bausch.nl>, Javhar <jav...@ib.com> wrote:
>Ed Seedhouse (e...@islandnet.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

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

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Apr 29, 1996, 3:00:00 AM4/29/96
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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
> >co