Chess is a Draw

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Chessqueen
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Full name: Jorge Picado

Re: Chess is a Draw

Post by Chessqueen »

Jouni wrote: Mon Dec 04, 2023 1:39 pm My current feeling: chess is 100% sure draw. And there is 10% chance it will be solved in our lifetime.
As long as the Opening is balanced or with less than 0.50 of an advantage the top 4 chess engines will most likely draw their games. That is the reason why TCEC is chosing openings that give one of the side an edge of more than 0.85. For instance lets take this game and at the end of White opening moves Stockfish is already with a huge advantage, therefore, it will win easy, but if you take the same game and limit the opening to only 4 moves the advantage is reduced to less than 0.50 and in the 2nd game both engines will draw their game 98% of the time.
NOTE: Here in the 2nd game same opening but limited to only 4 moves where the advantage is reduced to less than 0.50 both top engine drew their game.
[pgn][Event "TCEC Season 26 - Division P"]
[Site "https://tcec-chess.com"]
[Date "2024.05.03"]
[Round "34.1"]
[White "Stockfish-windows-x86-64-avx2"]
[Black "Berserk-13-avx2"]
[Result "1/2-1/2"]
[BlackElo "3610"]
[ECO "D15"]
[Opening "Slav"]
[Time "23:45:10"]
[Variation "Chameleon, 5.c5"]
[WhiteElo "3645"]
[TimeControl "3600+5"]
[Termination "unterminated"]
[PlyCount "73"]
[WhiteType "program"]
[BlackType "program"]

1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. Nf3 a6 5. c5 {(c4-c5 b7-b6 c5xb6 Nb8-d7
a2-a3 Qd8xb6 Nc3-a4 Qb6-c7 g2-g3 e7-e6 Bc1-f4 Bf8-d6 e2-e3 e6-e5 d4xe5
Nd7xe5 Bf4xe5 Bd6xe5 Bf1-g2 Ra8-b8 Nf3xe5 Qc7xe5 O-O O-O Ra1-c1 h7-h5 h2-h4
Bc8-g4 Qd1-d4 Qe5xd4 e3xd4 a6-a5 f2-f3 Bg4-d7 Rf1-f2 Nf6-e8 Rc1-c5 Ne8-d6
Rc5xa5 Rf8-e8 Bg2-f1 Re8-e1 Kg1-h2 Bd7-e8 Na4-c5 Nd6-f5) +0.27/40 131} b6
{(b7-b6 c5xb6 Nb8-d7 Qd1-c2 Qd8xb6 Bc1-f4 e7-e6 a2-a3 Bc8-b7 Nc3-a4 Qb6-a7
e2-e3 Bf8-e7 Bf1-e2 a6-a5 O-O O-O Rf1-c1 Rf8-c8 b2-b4 Bb7-a6 Be2xa6 Qa7xa6
Na4-c5 Qa6-b6 Ra1-b1 a5xb4 a3xb4 Qb6-b5 h2-h3 h7-h6 Bf4-g3 Ra8-a3 Kg1-h1
Rc8-a8 Nc5xd7 Nf6xd7 Qc2xc6 Qb5xc6 Rc1xc6 Ra3-a1 Rb1xa1 Ra8xa1+ Kh1-h2
Be7xb4 Rc6-c8+) -0.31/42 187} 6. cxb6 Nbd7 7. e3 Qxb6 8. Na4 Qc7
9. Bd3 e6 10. O-O a5 11. Qe2 Bd6 12. Bd2 Ne4 13. Rfc1 Nxd2 14. Qxd2
Bb7 15. Rc2 O-O 16. g3 Rfd8 17. Rac1 Qb8 18. Bf1 Qa7 19. Qd3 h6 20. h4 Rac8
21. a3 Rc7 22. Qe2 Ra8 23. Qd1 Rac8 24. Rc3 Ba6 25. Bxa6 Qxa6 26. Kg2 Qb5
27. Qb3 g6 28. Ne1 Qxb3 29. Rxb3 c5 30. dxc5 Nxc5 31. Nxc5 Rxc5 32. Rxc5
Rxc5 33. Kf1 a4 34. Rb4 Rc4 35. Rb6 Bc7 36. Ra6 Kg7 37. Nd3 Bd8 38. Ke1 Bc7
39. Kd2 g5 40. hxg5 hxg5 41. Nb4 Be5 42. Nd3 Bf6 43. f3 Kh6 44. g4 Kg6 45.
Ra7 Kg7 46. Ra6 Kg6 47. Ra7 Bh8 48. Rb7 Bg7 49. Rb8 Bf6 50. Rg8+ Kh6 51.
Rb8 Kh7 52. Rb7 Kg7 53. Ra7 Kg8 54. Ra6 Kf8 55. Ra5 Kg7 56. Ra7 Kg6 57. Ra8
Bg7 58. Ra5 Kh7 59. Ra7 Kg6 60. Ra5 Kh6 61. Ra7 f5 62. gxf5 exf5 63. Ra6+
Kh5 64. Ra5 Kg6 65. Rxd5 Rh4 66. Rd6+ Kh5 67. Rd7 Kh6 68. Ra7 Rh2+ 69. Ke1
Bxb2 70. Nxb2 Rxb2 71. Rxa4 Ra2 72. Kf1 Kg6 73. Ra6+ Kh5 74. Ra5 Kg6 75.
Ra6+ Kh5 76. Ra5 Kh4 77. Rxf5 Rxa3 78. Ke2 Ra2+ 79. Kd3 Kg3 80. e4 g4 81.
fxg4 Ra3+ 82. Kc4 Kxg4 83. Rf1 Kg5 84. Kd5 Ra5+ 85. Ke6 Ra6+ 86. Kd5 Ra5+
87. Kd6 Ra6+ 88. Ke5 Ra5+ 89. Kd6 Ra6+ 90. Kc5 Ra4 91. e5 Ra5+ 92. Kb6 Rxe5
93. Rb1 Re8 94. Kc7 Kf5 95. Rc1 Kf6 96. Rc2 Re6 97. Kd7 Re3 98. Kd6 Kf7 99.
Ra2 Kg8 100. Kd5 Re1 101. Ra8+ Kf7 102. Ra7+ Ke8 103. Kd4 Rd1+ 104. Ke3
Re1+ 105. Kf2 Rb1 106. Ra8+ Kf7 107. Ra6 Rb2+ 108. Kf3 Rb8 109. Ra7+ Ke8
110. Ra2 Kf7 111. Kg2 Rh8 112. Rf2+ Ke6 113. Re2+ Kd5 114. Rd2+ Ke6 115.
Re2+ Kd5 116. Rd2+ Ke4 117. Rd1 Ke5 118. Re1+ Kd6 119. Rd1+ Ke6 120. Ra1
Kf7 121. Ra7+ Ke6 122. Ra1 Kd6 123. Rd1+ Kc7 124. Re1 Rh7 125. Re6 Rg7+
126. Kf2 Rf7+ 127. Kg1 Rf8 128. Re7+ Kb8 129. Re2 Rg8+ 130. Kf1 Rc8 131.
Rb2+ Ka8 132. Ra2+ Kb7 133. Rb2+ Ka8 134. Rb1 Rd8 135. Ra1+ Kb8 136. Rb1+
Ka8 137. Ra1 {User Adjudication} 1/2-1/2[/pgn]
Last edited by Chessqueen on Fri May 03, 2024 2:20 pm, edited 5 times in total.
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Chessqueen
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Re: Chess is a Draw

Post by Chessqueen »

My current feeling: chess is 100% sure draw. And there is 10% chance it will be solved in our lifetime.
[/quote]

As long as the Opening is balanced or with less than 0.50 of an advantage the top 4 chess engines will most likely draw their games. That is the reason why TCEC is chosing openings that give one of the side an edge of more than 0.85. For instance lets take this game and at he end of White opening moves it is Stockfish is already with a huge advantage, therefore, it will win easy, but if you take the same game and limit the opening to only 4 moves the advantage is reduced to less than 0.50 and in the 2nd game both engines will draw their game 98% of the time.
NOTE: in this game TCEC made sure that after 9 moves White had a clear advntage of more than 0.05, therefore, Stockfish did NOT had any problem of keeping that advantage to the very end :roll:
[pgn][Event "TCEC Season 26 - Division P"]
[Site "https://tcec-chess.com"]
[Date "2024.05.03"]
[Round "34.1"]
[White "Stockfish-windows-x86-64-avx2"]
[Black "Berserk-13-avx2"]
[Result "1-0"]
[BlackElo "3610"]
[ECO "D15"]
[Opening "Slav"]
[Time "23:45:10"]
[Variation "Chameleon, 5.c5"]
[WhiteElo "3645"]
[TimeControl "3600+5"]
[Termination "normal"]
[PlyCount "207"]
[WhiteType "program"]
[BlackType "program"]

1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. Nf3 a6 5. c5 Bg4 6. Ne5 Be6 7. Qb3 Ra7 8.
e3 g6 9. Bd2 Bg7 10. f3 O-O 11. O-O-O Nfd7 12. Nxd7 Bxd7 13. Na4 e5 14.
dxe5 Bxe5 15. g4 Bg7 16. h3 Re8 17. Bd3 a5 18. Rhe1 Na6 19. Bc3 Be6 20. a3
Nc7 21. Bxg7 Kxg7 22. f4 d4 23. Bc4 Qf6 24. Rxd4 Qh4 25. Rh1 Bxc4 26. Qxc4
Rxe3 27. Nb6 Ne6 28. Rdd1 Rf3 29. Rhf1 Qxh3 30. Qe2 Re3 31. Qd2 Rf3 32.
Rxf3 Qxf3 33. f5 gxf5 34. gxf5 Qxf5 35. Rg1+ Kh8 36. Qg2 Qxc5+ 37. Kb1 Qf5+
38. Ka2 Ng5 39. Qxg5 Qxg5 40. Rxg5 h6 41. Rg2 Kh7 42. Nc8 Ra8 43. Nd6 b5
44. Nxf7 Re8 45. Rc2 Kg6 46. Nd6 Re7 47. Rg2+ Kf6 48. Rh2 a4 49. Rxh6+ Ke5
50. Nc8 Rc7 51. Nb6 Kd4 52. Rh5 Re7 53. Nc8 Rc7 54. Nd6 Rd7 55. Ne8 Rb7 56.
Nf6 Rg7 57. Rh7 Rg6 58. Nd7 Kd5 59. Nb8 Kd6 60. Na6 Kd5 61. Rh1 Kd4 62.
Rd1+ Kc4 63. Rc1+ Kd4 64. Nc5 Rd6 65. Nb7 Rf6 66. Re1 Rg6 67. Rd1+ Ke5 68.
Nc5 Rg8 69. Na6 Ke6 70. Nb4 Rc8 71. Rh1 Kd7 72. Rh6 c5 73. Nd5 Rf8 74. Rg6
Rf5 75. Nc3 b4 76. axb4 cxb4 77. Nxa4 Rf8 78. Kb3 Rf4 79. Ra6 Kc7 80. Rb6
Rh4 81. Rxb4 Rh3+ 82. Nc3 Rh2 83. Rc4+ Kd6 84. Ka3 Kd7 85. Rc5 Rh4 86. b4
Rg4 87. b5 Ke6 88. b6 Rg8 89. Kb4 Rb8 90. Kb5 Kf6 91. Ne4+ Kg7 92. Rc6 Kh7
93. Nc5 Rd8 94. b7 Rd1 95. Kc4 Rb1 96. Nb3 Rb2 97. Kc3 Re2 98. b8=Q Re3+
99. Kc4 Re7 100. Nd4 Rd7 101. Qe8 Rxd4+ 102. Kxd4 Kg7 103. Rg6+ Kh7 104.
Qg8# 1-0[/pgn]
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jefk
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Full name: Jef Kaan

Re: Chess is a Draw

Post by jefk »

yep, 5...Bg4?! probably isn't good.

Using suboptimal book lines is the way -to get differences- when (top) engines are equally strong.
In much broader/bigger tournaments with various engine strengths, it still may not be necessary,
because then the winner is decided by how often it beats the weaker engines.

Example from international (computer) draughts, which isn't dead (yet?)
like i thought, but still recently had this tourn:
https://results.fmjd.org/tournaments/20 ... ngs&9.html
as was discussed on
https://damforum.nl/bb3/viewtopic.php?f ... 8&start=30

Scan is made by Fabien Letouzey (!) a familiar name in computer chess (Fruit)
https://hjetten.home.xs4all.nl/scan/scan.html

PS regarding the drawish nature of draughts, because setting up Scan seems
to be a hassle, i'm currently testing on a boring & rainy Friday Kingsrow (free)
vs Dragondraughts (free, but then limited search edition) with two games. Even
with search of Dd free limited, the first game i'm playing now looks very drawish
(about 1min search/move). In second game going to use full Dd strength
https://mdgsoft.home.xs4all.nl/draughts/register.html
Another third strong draughts program might be Mobydam
https://hjetten.home.xs4all.nl/mobydam/mobydam.html

PS2 for towforce regarding 'balanced games': intnl draughts is symmetric but
symmetry is quickly broken during the opening moves (not many degrees of
freedom because of the take piece obligation in draughts/checkers).
Nevertheless, when hitting the endgame(s) the degrees of freedom drastically
increase because the promoted draughts piece can move many directions
(and backwards).
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towforce
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Location: Birmingham UK

Re: Chess is a Draw

Post by towforce »

jefk wrote: Fri May 03, 2024 2:25 pmPS2 for towforce regarding 'balanced games': intnl draughts is symmetric but
symmetry is quickly broken during the opening moves (not many degrees of freedom because of the take piece obligation in draughts/checkers).

There are symmetries apart from rotations and reflections of the whole board - but I'm going to leave that until a simple way to explain this comes to me (I clearly haven't managed that yet because nobody has understood my point about symmetries the way I intended - and this is my fault for being unable to articulate what I have in mind).

You've stimulated me to think about the big picture of how chess works, and this is an "initial thought", and thus may have no value, but...

When you move a piece in chess, how strongly is the new position related to the previous position? Do you now have:

1. a completely different position?

2. a position with strong mathematical similarities to the previous position?

If the answer is (2), then maybe some sort of closed form expression that doesn't grow exponentially with the number of moves from the current position might be viable. I'm not too optimistic right now, though, because even if it's more (2) than (1), it still might not be possible to construct a closed form expression (e.g. the three-body problem in mechanics, in which the relationship between the 3 bodies is really good, but a closed-form expression cannot be constructed to calculate the future positions).
The simple reveals itself after the complex has been exhausted.
Uri Blass
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Re: Chess is a Draw

Post by Uri Blass »

proving that chess is a draw does not mean that you find a draw strategy.

I can show it by having a different game that it is easy to prove that it is a draw without having a strategy to draw.
I call is chessplus.

The rules of chessplus are the same as chess except the fact that the sides play 2 chess games(one with white and one with black).

If the result is 1-1 then it is a draw. otherwise there is a winner.
It is obvious that chessplus is a draw with perfect play but it does not give us a draw strategy so maybe we can also prove that chess is a draw without having a draw strategy.
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towforce
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Re: Chess is a Draw

Post by towforce »

The evidence that chess is drawn is overwhelming: if there was a way to get a winning advantage from the opening, it would have been found by now (especially given how much computer horsepower has been thrown at the problem).

However, until it is proven, there's always the nagging possibility that we've all missed something. I don't think we have, but...

* some people used to think that searching deeply enough would get us to ultimate chess. Given how much progress was made (and how quickly) with this strategy, it was very believable. But... it hasn't happened... yet...

* despite being able to train large NNs, they (without search) haven't got us to unbeatable chess

So there are still some important things we don't know about chess. But what? We know there's critical knowledge we don't have, but, maddeningly, we don't know what it is!

The above is all true, but yes - chess is a drawn game. :)

Another question: if we had the extra knowledge to protect ourselves from falling into a losing position, would we then need the lighter knowledge? I remember when authors were removing knowledge from the eval because the newer, faster computers took the search deep enough to make that knowledge completely redundant, so investing time on it was a complete waste. One would expect the same to apply to knowledge: when you have sophisticated knowledge, the deep secrets of the game, the simple things you learned when you started to play are no longer of any use.
The simple reveals itself after the complex has been exhausted.
fsanders
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Re: Chess is a Draw

Post by fsanders »

So chess is a draw. By now it is not 99.999 pct certain that chess with
current rules is a draw, it's 100 pct certain. Whether you like it or not.
So can you give us a scientific explanation of your thesis, or is it just a guess based on your gut instinct?
jefk
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Full name: Jef Kaan

Re: Chess is a Draw

Post by jefk »

fsanders (real name plsz !?!?): a scientific proof of my thesis ? Well First of all it's not a Thesis.

Second, it is well known in math that 1/2+1/4+1/8 + 1/16 etc ergo 0.99999... etc is converging to and
identical to 1.000.. and so on. Similar 99.999.. etc in the limit is the same as and identical to 100.0... pct.
How I can prove the second statement ? Well that's not so difficult, multiply the first line with ten,
and then you might be able to figure out the rest yourself :-)

In your posting July 2023 you wrote that the world champion correspondence chess could
beat Stockfish. can you give a scientific proof of such (an incorrect) statement ?
Incorrect, because with sufficient calculation time and good book for Stockfish
the program is unbeatable. Simply because, yep, some may already guess it:
Chess is Draw (not only with perfect play, but actually with sufficient strong play).

In an earlier posting mr towforce stated that with changing neural nets and so on, he still can't
exclude there might be a win for White. Not so. Black can always escape a forced loss, because
there are sufficient degrees of freedom (and a high branching factor) for such a purpose, also
considering the relatively high drawing margin in chess as result of some endgame rules.

In earlier postings (with references to Zermelo's game theorem and the application of Mcts in large
opening books such as the Chinese database) i sufficiently explained my reasoning. It may be insufficient
understanding of Zermelo's theorem (winnning strategy) why some people still seem to doubt such
reasoning. But whether such (imo solid) reasoning is a 'proof' or not according to some math fundamentalists,
in academic ivory towers, or not, i really don't care. So i won't get an Abel prize in math ? Well again i don't
care, really. You don't consider my reasoning a 'scientific proof' of my 'thesis'? Well, guess what, I do Not
care (to phrase it in polite terms otherwise i would say i do not give a sh.). Should i 'prove' to you that
the earth is not flat ? Well a certain G. Bruno tried and as reward he was burned at the stake.
As mr syzygy rightly so pointed out, we cannot prove that gravity exist; well actually some in
superstring theory tried, but the seem to have failed miserably; maybe because there already
exists another theory, namely General Relativity which explains gravity as a result of curved
spacetime. For chess (the heliocentric model and gravity) the proof is in the pudding.
In science (well except fundamental math, maybe) the falsification principle by Popper is well
accepted. So like i wrote, i offer 10k $ for anyone who can falsify that chess is a draw, by showing
us a force win from the starting position, eg. after 1.d4 (like years ago H.Berliner claimed)
Good luck.
Vice versa, if those guys who after having spent ten or more millions on supercomputers
and energy after ten years find with selective number crunching that it's a similar
draw as in checkers (or tictactoe) i suggest they reward me 100k $ as recognition for my
finding (from opening theory research) already in 2008 that chess is draw.

As long as no one can find such a force win (which is impossible of course), it must accepted chess
is a draw with perfect play. Something already known since (at least by) Steinitz btw. There later
have been some (incorrect) narratives in chess strategy like e.g Karpovian methods of squeezing
the other side like a cobra) and ultimately winning the game, yet from extensive computer chess
experience and correspondence chess i know that such situations always were the result of suboptimal
play of the loser (often already starting with suboptimal play during the opening phase).

The game of Othello also is a draw btw. (and international draughts as well). Just as some zillions
of other balanced two player games, because there is a fundamental equilibrium which can't be
broken through unless one side makes a fundamental mistake. This is well known in game theory
and i don't have to prove that to you; you simply can look it up.

PS if 'leaders' (dictators) of countries like Ruzzia (and China) would recognize that in
modern or hybrid warfare also such equilibria -often- exist, we would have less
bloodshed, slaughter and money waste into bloody war toys and also less threats
regarding a democratic country as Taiwan etc. If the Usa in the past would have recognized
they cannot always win with their self perceived image of 'good guys' they would have changed
their policy in Vietnam, Afghanistan, etc. Similar with Israel/Palestine btw, like it or not,
no side can 'win'. Although this is more a topic for the chess thinkers forum if it still exists.
lkaufman
Posts: 5981
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Location: Maryland USA

Re: Chess is a Draw

Post by lkaufman »

jefk wrote: Sun May 05, 2024 6:36 am fsanders (real name plsz !?!?): a scientific proof of my thesis ? Well First of all it's not a Thesis.

Second, it is well known in math that 1/2+1/4+1/8 + 1/16 etc ergo 0.99999... etc is converging to and
identical to 1.000.. and so on. Similar 99.999.. etc in the limit is the same as and identical to 100.0... pct.
How I can prove the second statement ? Well that's not so difficult, multiply the first line with ten,
and then you might be able to figure out the rest yourself :-)

In your posting July 2023 you wrote that the world champion correspondence chess could
beat Stockfish. can you give a scientific proof of such (an incorrect) statement ?
Incorrect, because with sufficient calculation time and good book for Stockfish
the program is unbeatable. Simply because, yep, some may already guess it:
Chess is Draw (not only with perfect play, but actually with sufficient strong play).

In an earlier posting mr towforce stated that with changing neural nets and so on, he still can't
exclude there might be a win for White. Not so. Black can always escape a forced loss, because
there are sufficient degrees of freedom (and a high branching factor) for such a purpose, also
considering the relatively high drawing margin in chess as result of some endgame rules.

In earlier postings (with references to Zermelo's game theorem and the application of Mcts in large
opening books such as the Chinese database) i sufficiently explained my reasoning. It may be insufficient
understanding of Zermelo's theorem (winnning strategy) why some people still seem to doubt such
reasoning. But whether such (imo solid) reasoning is a 'proof' or not according to some math fundamentalists,
in academic ivory towers, or not, i really don't care. So i won't get an Abel prize in math ? Well again i don't
care, really. You don't consider my reasoning a 'scientific proof' of my 'thesis'? Well, guess what, I do Not
care (to phrase it in polite terms otherwise i would say i do not give a sh.). Should i 'prove' to you that
the earth is not flat ? Well a certain G. Bruno tried and as reward he was burned at the stake.
As mr syzygy rightly so pointed out, we cannot prove that gravity exist; well actually some in
superstring theory tried, but the seem to have failed miserably; maybe because there already
exists another theory, namely General Relativity which explains gravity as a result of curved
spacetime. For chess (the heliocentric model and gravity) the proof is in the pudding.
In science (well except fundamental math, maybe) the falsification principle by Popper is well
accepted. So like i wrote, i offer 10k $ for anyone who can falsify that chess is a draw, by showing
us a force win from the starting position, eg. after 1.d4 (like years ago H.Berliner claimed)
Good luck.
Vice versa, if those guys who after having spent ten or more millions on supercomputers
and energy after ten years find with selective number crunching that it's a similar
draw as in checkers (or tictactoe) i suggest they reward me 100k $ as recognition for my
finding (from opening theory research) already in 2008 that chess is draw.

As long as no one can find such a force win (which is impossible of course), it must accepted chess
is a draw with perfect play. Something already known since (at least by) Steinitz btw. There later
have been some (incorrect) narratives in chess strategy like e.g Karpovian methods of squeezing
the other side like a cobra) and ultimately winning the game, yet from extensive computer chess
experience and correspondence chess i know that such situations always were the result of suboptimal
play of the loser (often already starting with suboptimal play during the opening phase).

The game of Othello also is a draw btw. (and international draughts as well). Just as some zillions
of other balanced two player games, because there is a fundamental equilibrium which can't be
broken through unless one side makes a fundamental mistake. This is well known in game theory
and i don't have to prove that to you; you simply can look it up.

PS if 'leaders' (dictators) of countries like Ruzzia (and China) would recognize that in
modern or hybrid warfare also such equilibria -often- exist, we would have less
bloodshed, slaughter and money waste into bloody war toys and also less threats
regarding a democratic country as Taiwan etc. If the Usa in the past would have recognized
they cannot always win with their self perceived image of 'good guys' they would have changed
their policy in Vietnam, Afghanistan, etc. Similar with Israel/Palestine btw, like it or not,
no side can 'win'. Although this is more a topic for the chess thinkers forum if it still exists.
Although I fully agree that chess is drawn with correct play, with at least 99.9999999% probability, I don't think this can be deduced by any general reasoning. You mention that Othello is now a proven draw; yes it is, but as far as I know this is just a surprising coincidence; it would not be surprising if the optimal result were a score like 33 to 31 for example. In the case of chess, if we change a few rules, for example forbid repetitions, call stalemate a win and bare king a loss (as the rules were long ago), then I wouldn't be so sure that chess is a draw, White might very well have a forced win. Probably it would take another rule change or two to make that true, but with enough changes it would be won for White. As it is, the evidence is so overwhelming that chess is a draw that it doesn't seem like a good use of time and resources to prove so, but some people enjoy proving things that are "known" to be true but unproven.
Komodo rules!
jefk
Posts: 682
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Location: the Netherlands
Full name: Jef Kaan

Re: Chess is a Draw

Post by jefk »

mr LK wrote: "evidence is so overwhelming that chess is a draw"

yep, in a current Iccf tourn at master level where i participate all games are
becoming a draw (2/3 finished and all draws0, and thats with participants rating 'only'
between 2300 and 2400 (but with comp use allowed). And not even all book moves were
boring/solid, i encountered some interesting opening moves in a few games, in one game
clearly a suboptimal line by Black in the French but then even with an advantage of 0.3 I now
can't convert it to a win (in a bishop/pawn endgame. In the current ICCF word championship
the late world champ GM Dronov passed away but for the rest all games are draws.
And yes for correspondence chess it -still- would be interesting to see how
some rules could be modified to reduce the draw problem (other option would
be similar methods as used in TCEC, e.g unbalanced openings or some lousy
openings with both sides to play the same opening (the latter not present
in the current tournament system.

Whereas a general deduction is unlikely, one of the most convincing evidence
imo is coming from the chinese database (confirming what i found earlier);
rules of chess are complicated but nevertheless graph theory may later
give some deeper insights in the game if some academic researchers would
continue to work on that (i recall some work done years ago). There probably
are other games or systems more interesting for the application of graph theory.
https://www.perplexity.ai/search/how-ha ... dBrvVUyQ#0

and this is what chatgpt4 has to say :

### Integrating Network Theory with Deductive Arguments to Explore Chess as a Draw
Using network theory along with deductive reasoning can create a robust framework to analyze whether chess might theoretically end in a draw. Here’s how these two methodologies can be conjoined:
#### 1. **Premises Based on Network Theory**
- **Nodes and Edges**: Considering each chess position as a node and each legal move as an edge, the game of chess can be visualized as a vast network or graph.
- **Finite Network**: Despite the complexity, the chess network is finite, as there are a limited number of possible positions and moves.
- **Recurrent Positions**: Some positions recur, indicating cycles in the network.
#### 2. **Deductive Reasoning from Network Analysis**
- **Starting Assumption**: If chess is a perfect information game with finite possibilities, then theoretically, an optimal play defined path should exist (as per Zermelo's Theorem).
- **Cyclic Paths Analysis**: Deductively, if you can prove that all starting positions either lead to cycles that include previously acknowledged drawn positions or directly result in such positions, then the game can be deduced to be a draw.
#### 3. **Exploring Connectivity for Drawn Networks**
- **Drawn Configuration Identification**: Begin with known drawn positions and states (e.g., insufficient material, perpetual checks). These are like "terminal nodes" in terms of game theory which do not lead to wins.
- **Backward Induction**: Start from these terminal drawn positions and explore backward through the game’s network to see if all paths inevitably lead to one of these positions.
#### 4. **Game Reductions and Simplification**
- **Reductive Deductions**: By applying reductive strategies (simplifying the game to known drawn positions and their reachability), one maps out paths from typical game starting points to these end-states.
- **Choke Points in Network**: Identify critical nodes (positions) that frequently transition to or sustain drawn games. Overwhelming connectivity to drawn nodes could underpin a deductive proof.
#### 5. **Further Deductive Inferences**
- **If there exists at least one non-drawn ascent path**: The entire premise can be challenged. Hence, one needs to deductively prove that every path has its end in a draw under optimal play.
- **Complete game survey**: Deductively, one might argue that given a comprehensive enough analysis or simulation, all play variations can be reduced to outcomes that predominantly link to draw nodes under optimal strategies.
#### 6. **Practical and Theoretical Limits**
- **Ideal Assumptions**: This approach assumes optimal play, which is more theoretical and not often practical.
- **Computational Constraints**: Even with strong deductive arguments and network mapping, the real-world computation and validation of these deductive pathways over the vast chess network pose significant challenges.
### Conclusion
Proving chess is a draw using network theory combined with deductive reasoning presents an intellectually stimulating but formidable challenge. Theoretically, if every game path can be linked to a cycle involving network nodes representing known draw positions, and no new winning strategies emerge from the analysis, the game could be deductively argued as drawn under optimal play. This, however, remains an overarching theoretical exercise, constrained by practical computational capabilities and the infinitude of real-game variables and strategies.

My comment: some interesting insights here in the above, whereby i do not agree with the 'infinitured of
real-game variables and strategies' After all chess is a finite game and draw eg. by 3 pos repetition is a draw,
in fact chatgpt4 in the conclusion seems to contradict itself regarding it stated earlier.
Whether this method would be easier then selective (alfa/beta type) number crunching in checkers
(or Othello) style of course remains a question.

PS as for mr Sanders (?) maybe i overreacted a little, he just asked for a scientific 'explanation' not a proof
(in fact i tried to make a last edit, but this then was refused, a time out, ah well no big deal).
There is a Lewis F Sanders btw, Fide rated 1840 or so. As for explanation(s) that chess is draw, 'scientific' or
not 'fsanders' may not have seen all earlier discussions, there was a thread 'is there a project to solve chess'
with a lot of yes/no arguments about what a real proof should be, and then this thread with also some
arguments from my experience. We have scientific explanations that the earth isn't flat, general relativity
to explain gravity And yep, we there also is a Chinese database showing that in chess White can
not find a fundamental opening advantage from the opening stage, which maybe isn't a
'scientific' explanation but nevertheless imo a significant empirical finding. If i fly in one direction
from London and then after many hours endup in London again, having viewed some curved horizons,
it still maybe doesn't qualify as a 'scientific' explanation that the earth isn't flat (unless many scientists
would do it and write a paper, i suppose). In a similar way inspecting the Chinese database means almost
by deductive reasoning that White can not find a forced win (with other engines e.g Torch
or whatever the tree again would be slightly different but with new analysis the drawish nature
(and thus imo the draw result) would again be confirmed. And for those not believing this there's
my 10 k$ challenge; if i would be rich i would offer a million, no big deal.
So good luck again, and now instead of number crunching you can also try to use network
theory to prove in chess there is a forced win for White (thus having solved the game).
tip: don't try 1.g4 for such a purpose