Rating of perfect chess
an18...@anon.penet.fi
Any thoughts on what the rating of theoretically perfect chess would be?
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Martin Karl Unger
: Any thoughts on what the rating of theoretically perfect chess would be?
This question can only be answered when somebody
with the capability to play "theoretically perfect chess"
starts playing.
With the Elo-System not the amount of points is important
but only the difference in the points of two players is important.
Jeff Caruso
>
>: Any thoughts on what the rating of theoretically perfect chess would be?
>
Would it not be the rating of the current top players plus 400 ?
(Maybe a little less, if they achieve the occasional draw against
"Perfecto").
Regards,
-- Jeff C.
******************************************************************
Dr. Jeffrey L. Caruso <j...@triple-i.com>
Information International
Tim Mirabile
>Any thoughts on what the rating of theoretically perfect chess would be?
Well, if perfect chess is good enough to beat any rated human %100 of the time,
then its rating would be infinite.
--
Tim
Colin Hogben
> Well, if perfect chess is good enough to beat any rated human %100 of the time,
> then its rating would be infinite.
If there exists a winning strategy for White (e.g.), then a `perfect'
chess player could only guarantee a win 50% of the time, i.e. when
playing that colour. If (as seems more likely) neither colour can
force a win, the perfect player could only guarantee 0% losses
One interesting thought is that given two `perfect' chess players, one
could still be better than the other. By which I mean: one could
achieve a higher percentage of wins against fallible opponents,
perhaps by selecting lines of play in which there are losing moves not
obvious as such to the imperfect opponent.
There are no winning moves in chess. Only losing ones. All talk of
"black has a slight advantage in this position" is rubbish at a purely
theoretical level - any position is either drawn or a win for one
player. The problem is working out which is which :-(
--
Colin Hogben
===============================================================================
The above article is the personal view of the poster and should not be
considered as an official comment from the JET Joint Undertaking
===============================================================================
Stefan Wehmeier
>> an18...@anon.penet.fi wrote:
>>
>> : Any thoughts on what the rating of theoretically perfect chess
would be?
>>
>> with the capability to play "theoretically perfect chess"
>> starts playing.
>> With the Elo-System not the amount of points is important
>> but only the difference in the points of two players is important.
>>
>>
Another problem is to *define* perfect chess. From the "perfect"
point of view, a position can only be +-,=, or -+ ; there
is no notion of "slight advantage". Maybe the perfect player offers
you a draw after his first move because it's obviously (for him!)
a draw and the game is boring anyway :-)
--
Stefan Wehmeier
ste...@uni-paderborn.de
Joy Sabella
> Well, if perfect chess is good enough to beat any rated human %100 of the
time,
> then its rating would be infinite.
> Tim
Not at all. According to USCF rating system it would be just 400 points
above the highest rater human player. I am pretty sure that there are build
in limits in other rating systems as well.
Otherwise for argument sake you would be able to build an infinite rating
by only playing against let say players rated 1000 points below you.
Konstantin
Lawrence Pepper
>One interesting thought is that given two `perfect' chess players, one
>could still be better than the other. By which I mean: one could
>achieve a higher percentage of wins against fallible opponents,
>perhaps by selecting lines of play in which there are losing moves not
>obvious as such to the imperfect opponent.
>
Duh, what are you talking about? Degrees of perfection? Perfect play
means perfect across the entire move tree, which would include
sub-optimal play. Do you suppose that if there is only one perfect
line of play say 1.e4 e5 2.Qf3 a5 _ _ _ 42 draw. that one could claim
to have a perfect machine just because it knows this one line?
Lawrence P
Jordan Conley
is not perfect game...not even in theory...a perfect player to one
person, is less than perfect to another...that is human nature...
Ed Seedhouse
>> Well, if perfect chess is good enough to beat any rated human %100
of the
>time, then its rating would be infinite.
>Not at all. According to USCF rating system it would be just 400 points
>above the highest rater human player. I am pretty sure that there are build
>in limits in other rating systems as well.
Sorry, but you are wrong on that. You are confusing performance with
rating. A "perfect" player that won *every* game would get a PR 400
points above the average of the opponents in that event. However both
the USCF and CFC ensure that you cannot gain less than 1 point for a
win no matter how weak your opponent is. This is done by limiting the
gap between players for rating purposes.
For example in Canada you get 16 points for the win and lose 4% of the
difference between your ratings (assuming the opponent is lower). But
the maximum difference that may be taken into account is 350 points,
so the maximum loss from that is 14 points, leaving 2 points gained
even if your opponent is 1000 points below you. If you are over 2300
that goes down to 1 point.
So if we give our "perfect" player a rating of 2800 to start with and
let it play 1000 games it will gain at least 1000 rating points in
those games to increase it's rating to 3800.
There is no limit to this and the rating of a perfect player would
increase 1 point for every game played, assuming none of it's
opponents managed to play perfectly themselves and draw the game.
Of course, in practice it would take a long long time for the rating
to go up that high, but in theory it could. There is nothing in the
USCF or CFC rating systems to prevent it, anyway.
>
>Otherwise for argument sake you would be able to build an infinite rating
>by only playing against let say players rated 1000 points below you.
>
>Konstantin
Ed Seedhouse
President, Victoria Chess Club.
CFC Rating: 2100
Benjamin J. Tilly
Lawrence Pepper <pep...@pegasus.ncsl.nist.gov> writes:
Usually perfect play means that it plays lines that are optimal in the
sense that against a perfect opponent, there is no line that is better,
and given any mistake in your opponents response, it will win... You
could theoretically achieve perfect play by consistently playing on
only a small portion of the game tree that is perfect.
Now the issue is (if that we know that it is playing perfectly) that
(assuming the perfect game is a draw) it only wins if its opponent
makes a mistake. Therefore a perfect player could theoretically
"improve" its play by choosing lines which an imperfect opponent is
more likely to make mistakes on. This player could then get a higher
rating because it would win more of its games against the non-perfect
players.
Of course this entire topic is silly because 1) we have no perfect
players and 2) any perfect player would probably beat every existing
player so consistently that it is not funny.
Ben Tilly
Kenneth Sloan
Ed Seedhouse <e...@islandnet.com> wrote:
>...
>... both
>the USCF and CFC ensure that you cannot gain less than 1 point for a
>win no matter how weak your opponent is.
This may be true for the CFC, but it is false for USCF. The USCF system
guarantees at least a 1 point change for an *event* in which you gain
even a fraction of a point - but there is no "1 point for every win"
mechanism. Rating changes are calculated as Real numbers, and rounded
(away from 0.0) at the very end.
>For example in Canada you get 16 points for the win and lose 4% of the
>difference between your ratings (assuming the opponent is lower). But
>the maximum difference that may be taken into account is 350 points,
>so the maximum loss from that is 14 points, leaving 2 points gained
>even if your opponent is 1000 points below you. If you are over 2300
>that goes down to 1 point.
This is the "linear approximation" formula. Does Canada really
use this formula for rating games (as opposed to *approximating* the
ratings change)?
>...
>There is no limit to this and the rating of a perfect player would
>increase 1 point for every game played, assuming none of it's
>opponents managed to play perfectly themselves and draw the game.
Again - in the USCF system, a player who wins every game would
eventually gain exactly one point for every *event*. But, of course,
the effect is the same (only slower): such a player's rating would
increase, without limit.
>
>Of course, in practice it would take a long long time for the rating
>to go up that high, but in theory it could. There is nothing in the
>USCF or CFC rating systems to prevent it, anyway.
Absolutely correct.
--
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/
Tim Mirabile
>In article <3uh392$q...@news.htp.com> Tim Mirabile <t...@mail.htp.com> writes:
>
>> then its rating would be infinite.
>
>chess player could only guarantee a win 50% of the time, i.e. when
>playing that colour. If (as seems more likely) neither colour can
>force a win, the perfect player could only guarantee 0% losses
Even if chess is drawn by force with best play for both sides, perfect
play may well be good enough to beat fallible opponents, including the
human World Champion, all of the time with either color. In that case,
it's rating would be theoretically infinite. Although the provisional
rating formulas would give a finite rating, they are just approximations.
--
Tim
Ian Kennedy
few months using a fresh pool of games played since the last list was
issued, or at least a set of games whose starting point in time moves
forward?
The answer to this question then determines whether a 'perfect' player
keeps getting better with respect to all his non-perfect competitors, or
stays a fixed distance ahead of them.
Ian Kennedy
Ed Seedhouse
>In article <3unau8$o...@sanjuan.amtsgi.bc.ca>,
>Ed Seedhouse <e...@islandnet.com> wrote:
>>...
>>... both
>>the USCF and CFC ensure that you cannot gain less than 1 point for a
>>win no matter how weak your opponent is.
>This may be true for the CFC, but it is false for USCF. The USCF system
>guarantees at least a 1 point change for an *event* in which you gain
>even a fraction of a point - but there is no "1 point for every win"
>mechanism. Rating changes are calculated as Real numbers, and rounded
>(away from 0.0) at the very end.
Thanks for the correction.
>>For example in Canada you get 16 points for the win and lose 4% of the
>>difference between your ratings (assuming the opponent is lower). But
>>the maximum difference that may be taken into account is 350 points,
>>so the maximum loss from that is 14 points, leaving 2 points gained
>>even if your opponent is 1000 points below you. If you are over 2300
>>that goes down to 1 point.
>This is the "linear approximation" formula. Does Canada really
>use this formula for rating games (as opposed to *approximating* the
>ratings change)?
Well according the the article on the subject published in every
August issue of "En Passant", the CFC's chess magazine, anyway.
Computes make this unnecessary, of course, but I don't believe there's
been any change in Canada.
>>There is no limit to this and the rating of a perfect player would
>>increase 1 point for every game played, assuming none of it's
>>opponents managed to play perfectly themselves and draw the game.
>Again - in the USCF system, a player who wins every game would
>eventually gain exactly one point for every *event*. But, of course,
>the effect is the same (only slower): such a player's rating would
>increase, without limit.
>>Of course, in practice it would take a long long time for the rating
>>to go up that high, but in theory it could. There is nothing in the
>>USCF or CFC rating systems to prevent it, anyway.
>Absolutely correct.
In the US, you'd simply have to play more games. :-)
Paul Hsieh
> Any thoughts on what the rating of theoretically perfect chess would be?
Well, if this person/computer/alien were to be an active player, and we
assume that they would win all the time, then the ELO rating system
formulas used by the USCF and CFC indicate that he/she/it would be 400
points higher than the highest rated player that they regularly played.
I.e., Kasparov + 400, or about 3200.
I don't know how the Glicko rating system works, but I assume it would
be about the same.
--
Paul Hsieh
q...@xenon.chromatic.com
What I say and what my company says is not always the same
Kenneth Sloan
Paul Hsieh <q...@xenon.chromatic.com> wrote:
>an18...@anon.penet.fi wrote:
>> Any thoughts on what the rating of theoretically perfect chess would be?
>
>Well, if this person/computer/alien were to be an active player,
Granted
> and we
>assume that they would win all the time,
Why assume this? It seems to me that the answer to the original
question hinges precisely on the question: what would be the score
achieved by "perfect play" against the top 100 players. One possibility
is that "perfect play" will win every game. Another is that "perfect
play" would allow some draws (how many?). Still another is that
"perfect play" would LOSE a game or three (most likely with Black).
> then the ELO rating system
>formulas used by the USCF and CFC indicate that he/she/it would be 400
>points higher than the highest rated player that they regularly played.
>I.e., Kasparov + 400, or about 3200.
Not really. Using, for the moment, the assumptions that "perfect play"
wins every time, and that "perfect play" is active - the ELO rating will
increase without bound (although the increase will excruciatingly slow).
On the other hand, if the humans manage to achieve some small percentage
of draws (or wins) against "perfect play", then the ELO rating will
eventually reach equilibrium (oscillating over a small range). The root
question is: what is that range? The answer to this question depends on
what you think that ratio (the scoring percentage) will be.
Note that we might well expect the top 100 humans to *improve* as they
learn from their defeats. Objectively, their performance with respect
to "perfect play" will improve. But...in my opinion, this will serve to
*lower* the ELO rating of "perfect play" and NOT *raise* the rating of
these players. The reasoning behind this opinion is that these
improvements in play agains "perfect play" will not fully transfer to
improvement in play against other humans - or at the very least will be
imperfectly transferred. Thus, I would expect an initial "stretching"
of the upper end of the scale, followed by a slow retreat as both
"perfect play" and the top 100 fall back towards the peleton.
In an alternate Universe...the top 100 players will learn from "perfect
play", but not be able to turn this knowledge into a higher scoring
percentage against "perfect play". They will still lose the games, but
they will begin to understand *why* they are losing. This may help them
in their play against lower rated humans. In this scenario, the top 100
will improve both their play, and their ratings with respect to the
human pool.
I suppose we'll have to wait for PerfectPlay(tm) to burst upon the scene
to decide the question...
Eric Peterson
>
>Not really. Using, for the moment, the assumptions that "perfect play"
>wins every time, and that "perfect play" is active - the ELO rating will
>increase without bound (although the increase will excruciatingly slow).
A trivial point: Are USCF and FIDE ratings stored as integers or real
numbers? If they are stored as integers, then a rating change of less
than 0.5 won't change a rating. In that case, the "perfect" player can't
get a rating more than about 500 points higher than his closest rival!
So a perfect player beating Kasparov over and over would get a rating of
about 3300 (assuming Kasparov maintained his 2800 rating by playing other
people).
__________________________________________________________________________
Eric Peterson Internet Chess Club: telnet CHESS.LM.COM 5000
USCF Life Master Email for flyer: I...@CHESS.LM.COM
etpe...@netcom.com Web page: http://www.hydra.com/icc/
Ed Seedhouse
>Well, if this person/computer/alien were to be an active player, and we
>assume that they would win all the time, then the ELO rating system
>formulas used by the USCF and CFC indicate that he/she/it would be 400
>points higher than the highest rated player that they regularly played.
>I.e., Kasparov + 400, or about 3200.
Nope. As has been pointed out already the rating would continue to
rise without limit so long as "they" continued active play and won all
games played.
Jack van Rijswijck
: Even if chess is drawn by force with best play for both sides, perfect
: play may well be good enough to beat fallible opponents, including the
: human World Champion, all of the time with either color. In that case,
: it's rating would be theoretically infinite. Although the provisional
: rating formulas would give a finite rating, they are just approximations.
Theoretically, the ELO system gives something like 1/(1+10^d) as
the expected result of a game between players whose ratings differ
by 400*d rating points. If a player wins 100% of the games, then the
rating difference is indeed infinite.
However, the rating difference between a perfect player and Kasparov
is not infinite. If chess is a theoretical draw, then there is a
nonzero chance that Kasparov will actually hold the draw against a
perfect opponent. There even is a chance that a player who plays
random moves holds the draw, just by playing correct moves by pure
coincidence. This chance is of course astronomically small, but
nonzero nontheless. If chess is a theoretical win for white (black),
then the perfect player will always win with white (black) and there
is a nonzero chance that the random player will hold the win, or
at least a draw, with white (black).
If the average game length is l, the number of `considerable' moves per
position is m and the average number of those considerable moves that
are also perfect is p, then the chance of playing a perfect game is
(p/m)^l. This results in a rating difference with a perfect player of:
400 x l x log(m/p) / log(10)
Choose your own favourite values and see what happens.
For a random player, let's say l=100, m=40, p=2. The rating difference
would then be about 52000. For Kasparov, perhaps something like l=50,
m=10, p=2 which means that the rating difference would be about 14000.
Probably more because this assumes that the perfect moves are always
also considerable moves. There may however very well be positions in which
the perfect move looks `obviously losing' to Kasparov. Heck, Kasparov
plays lots of moves that I would never even consider... /-: An imperfect
player can only play a perfect game when no such `trap' positions occur.
Suppose the fraction of games that don't have traps is t, then this
enhances the rating difference by 400 x log(1/t) / log(10) .
So there we have it: the rating of perfect chess would be somewhere in
the 10 000's. (: All this is of course if you use the pure ELO system
with no rounding off, no linear approximations, or whatever. But that's
what the original question was about anyway, I think.
As someone remarked before, there actually are `degrees of perfection'.
Playing in "Lasker style" you don't necessarily want to play the
theoretically best move, but rather the move which maximizes your
chances of winning the game. Some correct moves are more correct
than others. In fact, some INcorrect moves are better than some
correct moves. Suppose for example that the perfect player sees that
it can sacrifice a queen and *almost* checkmate the opponent in 25
moves. Almost, but not quite, because if the opponent plays the one
single correct line for the next 25 moves, the attack will fail and
the perfect player will be a queen down leaving a position which even
a fallible opponent can win against perfect play. On the other hand,
not sacrificing the queen will result in a boring position which even
a fallible opponent will most likely be able to hold to a draw. The
perfect player will have to judge how likely it is that the opponent
finds the refutation of the queen sacrifice. The choice is between a
rather certain draw, or an almost certain win with a small risk of
losing. This way, the perfect player might give away a draw occasionally,
but far more often will it win from a drawn position.
This involves estimating the chance that the opponent will play a
certain move, which is a rather difficult problem... The issue has
already come up though, because it has already happened that chess
computers would suddenly give away a piece against a grandmaster,
to avoid a mate in 6 that the opponent didn't even see. There is
in fact research going on into "opponent modelling" (at least I
think that's what it's called) in AI today.
Jack van Rijswijck
jav...@ib.com
jav...@bausch.nl
Kenneth Sloan
Eric Peterson <etpe...@netcom.com> wrote:
>sl...@willis.cis.uab.edu (Kenneth Sloan) writes:
>>
>>Not really. Using, for the moment, the assumptions that "perfect play"
>>wins every time, and that "perfect play" is active - the ELO rating will
>>increase without bound (although the increase will excruciatingly slow).
>
>A trivial point: Are USCF and FIDE ratings stored as integers or real
>numbers?
Stored as integers.
> If they are stored as integers, then a rating change of less
>than 0.5 won't change a rating.
Wrong. When an event is rated, the rating calculations are done in
floating point. As the very last step, rating changes are rounded away
from zero. Thus, a rating gain of 0.00001 translates into a rating
change of 1.
H Brett Bolen
I wrote a quick program and determined that if a player rated 2800
played a perfect player that won every single game, their ratings
would be
After 115 games: p1 3035 p2 2565
After 1000 games p1 3036 p2 3564
If p2 rating would not change
After 115 games: p1 3275 p2 2800
After 115 games: p1 3276 p2 2800
There does seem to be a upper limit.
sl...@cis.uab.edu states:
>
>... When an event is rated, the rating calculations are done in
>floating point. As the very last step, rating changes are rounded away
>from zero. Thus, a rating gain of 0.00001 translates into a rating
>change of 1.
>
This implies the perfect player would gain 1 pt at every event (
Match, Tourney, Game), Which means that there is no upper limit.
The next question is:
What if a machine could play perfect chess? ( obviously it
could play itself also.)
--
.
construction
sig
Bjørn Ingmar Berg
> The next question is:
>
> What if a machine could play perfect chess? ( obviously it
> could play itself also.)
>
Hi, Brett!
I am unfortunately not as good with chess as I am with computers.
But I guess I have a fair grasp of logic, and I have also looked
into some strategic algorithms in software.
For me the answer to your question seems very simple.
A machine playing perfect chess playing itself, or two such machines
playing eachother, would come to a draw (or is the term stale-mate ?)
every single time.
Perfect strategy vs. perfect strategy is like 1 + (-1) it ends up
zero!
But a game like that could very easy take some million years to
finish :-) (Cracking codes based on prime-numbers takes years
of computer time, and that is EASY in comparision.)
But, assuming we're not living in an 100% deterministic universe,
a perfect chess-player (man or machine) can never exist.
Regards,
Bjorn Ingmar Berg
Colin Hogben
> A machine playing perfect chess playing itself, or two such machines
> playing eachother, would come to a draw (or is the term stale-mate ?)
> every single time.
Agreed.
> But a game like that could very easy take some million years to
> finish :-)
One would hope that these perfect players would be sensible enough to
invoke the 50-move rule.
David Ewart
: Bjørn Ingmar Berg writes:
: > A machine playing perfect chess playing itself, or two such machines
: > playing eachother, would come to a draw (or is the term stale-mate ?)
: > every single time.
: Agreed.
No. Only if the game is not already a forced win for either side from the
start!
Dave.
--
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Ed Seedhouse
>
>A trivial point: Are USCF and FIDE ratings stored as integers or real
>numbers? If they are stored as integers, then a rating change of less
>than 0.5 won't change a rating. In that case, the "perfect" player can't
>get a rating more than about 500 points higher than his closest rival!
>So a perfect player beating Kasparov over and over would get a rating of
>about 3300 (assuming Kasparov maintained his 2800 rating by playing other
>people).
They are stored as integers, but this is beside the point. In Canada
the winner of a game gets at least 2 rating points if under 2300 and
at least 1 rating point if over 2300. In the USA the winner of a
tournament gets at least 1 rating point no matter who he played.
Actually, in my opinion, rather than being stored and displayed as
integers they should be rounded off to the nearest 10 points. A
difference of 10 rating points is insignificant and to display it is
an example of misleading precision.
Christopher Dorr
: Think about this: Perhaps one of the great things of chess is that there
: person, is less than perfect to another...that is human nature...
Uhh, sorry. Since chess is a finite, two-person, zero-sum game, game theory
proves that there are possible games played 'perfectly', i.e. without
mistakes. We don't know whether or notthe 'perfectly' played game would
be a win for white, a draw or a win for black(unlikely, but possible),
but we do know it is possible to play an entire game of chess that leads
to the best possible outcome in all variations, against 'perfect' play.
We can lay out all possible games of chess in an impossibly huge tree,
with one branch coming off at each move. We can follow one branch out
that, via a minimax algorithm, reaches the optimum result regardless of
opponents best play.
Obviously, in practice, there can most likely never be a 'perfect' game,
but in theory it is quite possible.
Chris
Eric Peterson
>
>For me the answer to your question seems very simple.
>playing eachother, would come to a draw (or is the term stale-mate ?)
>every single time.
>zero!
Ah, but you are assuming chess is a theoretical draw with best play
on both sides. It's possible that perfect play leads to a win by
White. We will probably never know for sure (at least not in our
lifetimes).
David Ewart
: "Bjørn Ingmar Berg" <bjorn...@ft.dep.telemax.no> writes:
: >
: >For me the answer to your question seems very simple.
: >A machine playing perfect chess playing itself, or two such machines
: >playing eachother, would come to a draw (or is the term stale-mate ?)
: >every single time.
: >Perfect strategy vs. perfect strategy is like 1 + (-1) it ends up
: >zero!
: Ah, but you are assuming chess is a theoretical draw with best play
: on both sides. It's possible that perfect play leads to a win by
: White. We will probably never know for sure (at least not in our
: lifetimes).
It could be a theoretical win for Black.