Some more references for you. Is there something in particular which you'd like to talk about?
1. https://mathshistory.st-andrews.ac.uk/Projects/MacQuarrie/chapter-1/
3. https://firescholars.seu.edu/honors/101/
Where are the pure mathematicians to discuss chess?
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Look up how machines learn chess algorithms
Here is a classic paper
https://www.sciencedirect.com/science/article/pii/S0004370201001527
Dec 7, 2023
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#7
https://tcec-chess.com/#div=sf&game=1&season=25
How can you prove that Stockfish did not play perfect chess in the 25th TCEC tournament, in the superfinal against Lc Zero?
Dec 7, 2023
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#8
It's not Pure Mathematics but I'd also recommend understanding Computational Complexity.
Theoretical Computer Science is very mathematical.
Dec 7, 2023
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#9
demostraciones wrote:
https://tcec-chess.com/#div=sf&game=1&season=25
How can you prove that Stockfish did not play perfect chess in the 25th TCEC tournament, in the superfinal against Lc Zero?
We know none of the Chess engines are perfect by finding better outcomes to those which they arrived at, against the same algorithm. If finding a mistake, fixing it, then the engine continues to a better outcome, you've proven that it's not perfect.
Dec 7, 2023
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#10
It has already been shown that in a perfect game, either the white pieces win, or the white pieces lose, or a tie. but we don't know which one is true. In tournament 25 the TCEC superfinal the results were 27 - 23 = 50 This means stockfish won 27 of the 100 games, lost 23 of the 100 games, and tied 50. taking turns 50 as white pieces and 50 as black pieces First scenario, White always wins, so they should have at least 50 victories, but that was not the case, he obtained 27 victories, of which there were 25 with White, ruled out. second scenario, black always wins, so he should have obtained a minimum of 50 victories with black pieces, but that was not the case, he obtained 2 victories with black pieces, discarded. Third scenario, he should never lose, because if the 2 software played perfectly then he should not lose, only draws, but he lost 23 games. QED, it is proven
Dec 7, 2023
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#11
demostraciones wrote:
It has already been shown that in a perfect game, either the white pieces win, or the white pieces lose, or a tie. but we don't know which one is true. In tournament 25 the TCEC superfinal the results were 27 - 23 = 50 This means stockfish won 27 of the 100 games, lost 23 of the 100 games, and tied 50. taking turns 50 as white pieces and 50 as black pieces First scenario, White always wins, so they should have at least 50 victories, but that was not the case, he obtained 27 victories, of which there were 25 with White, ruled out. second scenario, black always wins, so he should have obtained a minimum of 50 victories with black pieces, but that was not the case, he obtained 2 victories with black pieces, discarded. Third scenario, he should never lose, because if the 2 software played perfectly then he should not lose, only draws, but he lost 23 games. QED, it is proven
I think this can be simplified.
1) Losing a game with the White pieces and losing a game with the Black pieces implies that the player didn't play perfectly in both matches no matter the solution of Chess. Other outcomes reveal nothing unless the opponent is assumed to be perfect or the solution to Chess is assumed.
2) For practical purposes Chess, with perfect play, is assumed, from empirical evidence, to be a draw. Therefore losing with either colour pieces implies that the player played imperfectly.
If Black copies every move White makes should it be a draw?
Dec 7, 2023
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#13
Explore online chess forums, chess clubs, or social media groups to find mathematicians who discuss chess.
putshort wrote:
If Black copies every move White makes should it be a draw?
I've done that strategy before. It always get to a breaking point and I'd say most times I get the advantage.
CraigIreland wrote:
It's not Pure Mathematics but I'd also recommend understanding Computational Complexity.
Theoretical Computer Science is very mathematical.
How do you count floating point operations in a chess game?
Maybe cognitive complexity is more appropriate, should someone ever come up with a quantifiable definition.
Dec 7, 2023
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#16
There is another important fact in the 25th TCEC tournament, they force them to play openings and they take turns openings that are a disaster, however even so, it can be shown that some games were not played perfectly from the opening onwards.
In game 29 Stockfish lost with that opening with black pieces, but in game 30 he failed to win the same position with white pieces, If the position had a disadvantage against black, then why couldn't he win with white pieces? If he didn't have enough of a disadvantage to lose black, then why didn't he draw?
Dec 7, 2023
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#17
CraigIreland escribió:
demostraciones wrote:
It has already been shown that in a perfect game, either the white pieces win, or the white pieces lose, or a tie. but we don't know which one is true. In tournament 25 the TCEC superfinal the results were 27 - 23 = 50 This means stockfish won 27 of the 100 games, lost 23 of the 100 games, and tied 50. taking turns 50 as white pieces and 50 as black pieces First scenario, White always wins, so they should have at least 50 victories, but that was not the case, he obtained 27 victories, of which there were 25 with White, ruled out. second scenario, black always wins, so he should have obtained a minimum of 50 victories with black pieces, but that was not the case, he obtained 2 victories with black pieces, discarded. Third scenario, he should never lose, because if the 2 software played perfectly then he should not lose, only draws, but he lost 23 games. QED, it is proven
I think this can be simplified.
1) Losing a game with the White pieces and losing a game with the Black pieces implies that the player didn't play perfectly in both matches no matter the solution of Chess. Other outcomes reveal nothing unless the opponent is assumed to be perfect or the solution to Chess is assumed.
2) For practical purposes Chess, with perfect play, is assumed, from empirical evidence, to be a draw. Therefore losing with either colour pieces implies that the player played imperfectly.
Yes, it can be simplified, but it could not be said that both games were played imperfectly, at least one was played imperfectly because today we would not be able to know if a perfect game by both is a draw, or perhaps Black has enough disadvantage. losing and winning what I do I couldn't avoid it unless someone proves that a perfect game of both always ends in a draw
Dec 7, 2023
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#18
Game 41 and 42 is even more interesting,
stockfish lost with black pieces, in game 41. but he won with white pieces in game 42. what is the problem? How can you prove that he didn't play perfectly? easy, stockfish lost in game 41 on move 95, and in game 42 he won with 135 moves, Suppose that the black pieces had a sufficient disadvantage to lose, in the number of x moves, We don't know how much x is worth, but stockfish won with 135 moves, suppose x =135 So why did he lose with 95 moves? Now suppose x = 95 So why did he win with 135 moves? Now suppose that x is different from 95, 135, but x < 135, then why did he not manage to win in less than 135, Now suppose that x > 135, but stockfish failed to extend the game to more than 135 moves to lose. it is proven
Dec 7, 2023
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#19
SwimmerBill wrote:
CraigIreland wrote:
It's not Pure Mathematics but I'd also recommend understanding Computational Complexity.
Theoretical Computer Science is very mathematical.
How do you count floating point operations in a chess game?
Maybe cognitive complexity is more appropriate, should someone ever come up with a quantifiable definition.
Chess Engines don't require floating point operations though they do perform arithmetic operations.
The relevant resource for solving Chess as we know it is Time. The complexity class is P.
Without the 50 move rule, it becomes EXP
However the Computational Complexity of solving Chess on a generalised NxN board has been shown to be PSPACE Complete.
Storer: On the Complexity of Chess
A professor at Yale University does some mathematical proofs with chess.
Zermelo and many other mathematicians have talked about chess and game theory