Author: Graham Laight
Date: 08:13:41 05/15/01
Go up one level in this thread
On May 15, 2001 at 10:22:26, Stephen A. Boak wrote:
>On May 15, 2001 at 07:56:49, Graham Laight wrote:
>
>>On May 15, 2001 at 06:26:14, Ralf Elvsén wrote:
>>
>>>On May 15, 2001 at 06:03:11, Graham Laight wrote:
>>>
>>>I still say it's quicker and easier to draw a graph of strength of players
>>>plotted against proportion of draws.
>>>
>>>Since I don't have a copy of chessbase, the graph below is based on guesswork
>>>rather than actual study - but here's a quick example of what it would probably
>>>look like:
>>>
>>>Percentage Of Draws
>>>
>>>
>>>100 | *
>>> | *
>>> | *
>>> | *
>>> | *
>>>75 | *
>>> | *
>>> | *
>>> | *
>>> | *
>>>50 | *
>>> | *
>>> | *
>>> | *
>>> | *
>>>25 | *
>>> |*
>>> |
>>> |
>>> |
>>>0 |
>>> ------------------------------------------------------
>>> 1000 1500 2000 2500 3000 3500
>>>
>>> Elo Rating
>>>
>>>
>>
>>Check out this:
>>
>>http://math.bu.edu/people/mg/ratings/Draws.jpg
>>
>>
>>Ralf,
>>
>>Thanks very much for drawing this work to my attention!
>>
>>Since it's done by the chairman of the USCF (home page =
>>http://math.bu.edu/people/mg/ ), I think we can assume that it's a good quality
>>study.
>>
>>The exciting thing (from the point of view of "solving chess" or "playing
>>perfect chess") point of view is that, above 2200 Elo, the proportion of draws
>>shoots up very sharply above 2200 Elo - implying that the limits of chess are
>>being approached quite rapidly now.
>
>Instead, the data may imply:
>A. That the "limits of players" are being approached quite rapidly.
>B. Or that the preference of top players is to draw, rather than to lose or to
>take risks (involving some uncertainty) to try to win.
This implies that the player believes that the risky move is more likely to lose
than to win.
Were this not so, the brave player who played these moves would, in the long
term, get a higher rating than his opponents.
Hence, I can't agree with this
|
|
|
V
>Drawing the conclusion (no pun intended!) that the increasing percentage of
>draws among increasingly high ELO opponents means that chess is likely a forced
>draw is unwarranted.
>
>1. The games relied on are so very, very few in illustrating the possible
>numbers of chess trees and positions that can arise that they can't be deemed to
>have exhaustively sampled chess.
Obviously. We're talking about statistical sampling here.
>2. As the ELO rises for each of a pair of combatants, there are fewer and fewer
>players to draw conclusions from. And, as Bob indicated, there is no proof
>their play is perfect. To the contrary. Even Kasparov, the best player on
>paper, per ELO rating, has made many mistakes in his games.
There's not a chess player in existence (human or computer) who can avoid all
mistakes. If there were, they'd be able to tell us the outcome of a game played
without errors, and we'd know the ultimate result of chess already.
>The reduced set of players from which to draw conclusions does not logically
>increase confidence in the premise that their results tend to show the solution
>to chess (that it is a draw, in the ultimate analysis). It merely indicates
>that many players in the top several hundred or so, often draw when playing each
>other.
The rapidly increasing proportion of draws happens from level 2200 upwards (and
gently up to 2200).
>3. It is sometimes said that great players eschew (avoid) unclear
>positions--ones where they are not sure they still have winning chances, where
>they are not sure they still have a draw in hand.
Again - this implies that the player believes that the risky move is more likely
to lose than to win.
Were this not so, the brave player who played these moves would, in the long
term, get a higher rating than his opponents.
>4. Many fighting draws or 'lesser' draws of strong players are shown by later
>analysis to contain mistakes. The fact that the actual game ended in a draw
>doesn't prove that selecting other moves at other times in the game would also
>have led to a draw and not a win for one of the players.
Again - there's not a chess player in existence (human or computer) who can
avoid all mistakes. If there were, they'd be able to tell us the outcome of a
game played without errors, and we'd know the ultimate result of chess already.
We're talking about "statistical sampling" here.
>5. Draws are sometimes agreed to in unclear positions, where neither player
>wishes to pursue the possibilities of the position by playing on. This is
>further muddied by situations where time pressure on one or both players causes
>them to avoid entering or continuing in unclear positions, since they realize
>they may well not have enough time to work out the problems of the unclear
>position, or may well not have the ability.
The new issue in point 5 is the effect of the clock (the other points are
repetitions of previous points). In many cases, if the player hadn't consumed so
much time, they wouldn't have achieved the winning position anyway.
>6. Even a player with a winning advantage may accept or offer a draw due to a
>shortage of time.
Repetition of point 5 (Stephen's message could have been more concise without so
much repetition :) )
>7. If there is a single (not hundreds, but just one) forced win for a player,
>commencing with the starting position, just because no pair of strong GMs has
>found it, doesn't prove it doesn't exist. It likely is too deep or too
>complicated for the limited human brain. Our hash tables are not what we'd like
>them to be--same for GMs. :) And there may be many forced wins, we don't know,
>from the starting position.
If forced wins exist, then the higher the Elo rating, the more likely that the
player will find them. Hence, one would expect the number of wins to increase as
the skill of the player gets better.
>8. It may be that a forced win lies in one or many of the unclear positions that
>can arise in a game among two strong GMs.
I think this unlikely, because GMs tend to analyse their games afterwards.
>--Steve
>
>>
>>Just to describe the graph (which you can see for yourself by following Ralf's
>>link above) approximately, the draw proportion starts at 15% (presumably because
>>players are unable to obtain a win), drops to 8% at 650 Elo, rises steadily from
>>there to 25% at 2200 Elo, then shoots up rapidly to 48% at 2700 Elo.
>>
>>This would imply that the limit of chess is less than 3700 (because the graph is
>
>9. Chess doesn't have an ELO, players do. An ELO is relative to skill versus
>other players, not relative to the complexity of the game.
That's right. Though the less complex the game, the sooner the ultimate results
are converged on. I doubt it would take long to train most people how to play
perfect tic-tac-toe.
>10. If all your opponents are under 3000 rating, then you will never gain a
>rating of 4000, in practice. If all your opponents are over 4000 rating, and
>you can score at least 50% against them, then naturally you will also have a
>rating of 4000 or more. :)
Here, I can't argue. The SSDF, in their FAQ page say (or did say the last time I
looked) that there might be a flaw in the Elo rating system because, with their
list consisting of huge numbers of games (many more than the equivalent number
of humans would have played), the ratings tend to compress more than one would
expect them to. I'm sure that the chairman of the USCF, who happens to be a
statistical guru, would also admit to the existence of flaws in Elo rating
system (see http://math.bu.edu/people/mg/ ). Also, when computers become better
than the best humans, there's going to be a loss of correlation between human
Elo ratings and computer Elo ratings.
Out of interest, if one only played 2800 opponents, and always won, what would
one's rating be?
-g
>>rising sharply at the end) - so my original guess (2 posts back) of 3500 was not
>>too bad!
>>
>>-g
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