Chess is a Draw

[Uri Blass]

To my thinking, "chess is a draw" is in the same category as something like "there are no humans living permanently on the moon". This can't be proven; it is theoretically possible that when we landed on the moon, one or two astronauts secretly remained, drilled deep below the surface, brought enough supplies to last half a century, and have remained hidden there ever since. Hard to disprove this rigorously, but I think almost everyone would agree that the probability of the statement being true is at least 99.9999999%. Similarly we can use statistical arguments using engines to show that chess is a draw with over 99.9999999% probability, we just can't prove it 100%. Some may enjoy the challenge of a 100% proof, but for me I'm willing to accept 99.9999999% as good enough to make all decisions in life. I wouldn't call a claim false just because there might be one chance in a billion or so that it is.

There is no evidence that the claim is false.
What would be false is the claim that it has been deductively established as true. Most of science does not care about such a claim in the first place (and daily life even less).

Most of us just accept certain things as obvious without a formal proof;

Sure, but my point is that you we should not accept that statement X has a formal proof only because X seems to be almost certainly true.

Most of us do not care about whether something has a formal proof. Most statements inherently are incapable of having a formal proof anyway. No law of gravity can be deductively proven. We cannot prove that the laws of nature that are valid today are still valid tomorrow. But we are pretty sure they will be and certainly take life decisions based on this assumption.

But there are areas of knowledge where statements can be deductively decided, and there are people that take an interest in these questions. These are not strange people or "lizard people" as you choose to call them that are unable to cross a street without a formal proof that it is safe. They just have interests that are not shared by everyone.

we are not lizard people, the moon is not made of green cheese, the earth isn't hollow, etc. Things like this can't be totally proven impossible, one can always construct some silly argument as to why they could be true. Similarly chess might be a mate in 385 moves with perfect play

But there is fundamental difference between the statement that the moon is made of cheese and the statement that chess is a mate in 385. The truth of the statement that chess is a mate in 385 moves can, at least in theory, be established purely by deduction and without reference to any observable real-world phenomena. No induction is necessary.

I'm not opposed to the search for a formal proof, I just consider it rather pointless

Chess is not any less pointless, and this is not an attack on anyone who loves to spend time on chess. People have intereststs. Yours are not mine, and that is good. I respect that you have your interests.

Of course it is fine to pursue such interests. I certainly was not referring to people who like to prove things as "lizard people", that was just an example of an absurd belief held by a tiny percentage of people (but in the millions per surveys!) which cannot be disproven. But I suspect that if a proof that chess is a draw ever becomes possible, it would require a massive commitment of resources, which would seem to be not worth the cost just to prove what is already obvious. But if you are a billionaire and want to devote your wealth to such a project, that would be your right.

The related goal that I do find interesting is this: What is the smallest/most acceptable change to chess rules (or start position) that would eliminate draws without obviously favoring either side? Of course any drawless chess would be a forced win for one side, but as long as even the best engines devoting days to it could not make a determination with any confidence, that should be good enough at least for now. Currently my candidate would be "White can only castle short, Black can only castle long, Black wins draws". As far as I can tell, it's too close to tell which side to prefer. Perhaps someone has an even better solution.

I have a different type of candidate.

White is going to win a drawn game if the number of plies in the game is longer than k for some constant k.
The idea is that white try to make the game longer in order to win and black try to make the game as short as possible.

I guess that with the right k you are going to get a result near 50%.

[lkaufman]

To my thinking, "chess is a draw" is in the same category as something like "there are no humans living permanently on the moon". This can't be proven; it is theoretically possible that when we landed on the moon, one or two astronauts secretly remained, drilled deep below the surface, brought enough supplies to last half a century, and have remained hidden there ever since. Hard to disprove this rigorously, but I think almost everyone would agree that the probability of the statement being true is at least 99.9999999%. Similarly we can use statistical arguments using engines to show that chess is a draw with over 99.9999999% probability, we just can't prove it 100%. Some may enjoy the challenge of a 100% proof, but for me I'm willing to accept 99.9999999% as good enough to make all decisions in life. I wouldn't call a claim false just because there might be one chance in a billion or so that it is.

There is no evidence that the claim is false.
What would be false is the claim that it has been deductively established as true. Most of science does not care about such a claim in the first place (and daily life even less).

Most of us just accept certain things as obvious without a formal proof;

Sure, but my point is that you we should not accept that statement X has a formal proof only because X seems to be almost certainly true.

Most of us do not care about whether something has a formal proof. Most statements inherently are incapable of having a formal proof anyway. No law of gravity can be deductively proven. We cannot prove that the laws of nature that are valid today are still valid tomorrow. But we are pretty sure they will be and certainly take life decisions based on this assumption.

But there are areas of knowledge where statements can be deductively decided, and there are people that take an interest in these questions. These are not strange people or "lizard people" as you choose to call them that are unable to cross a street without a formal proof that it is safe. They just have interests that are not shared by everyone.

we are not lizard people, the moon is not made of green cheese, the earth isn't hollow, etc. Things like this can't be totally proven impossible, one can always construct some silly argument as to why they could be true. Similarly chess might be a mate in 385 moves with perfect play

But there is fundamental difference between the statement that the moon is made of cheese and the statement that chess is a mate in 385. The truth of the statement that chess is a mate in 385 moves can, at least in theory, be established purely by deduction and without reference to any observable real-world phenomena. No induction is necessary.

I'm not opposed to the search for a formal proof, I just consider it rather pointless

Chess is not any less pointless, and this is not an attack on anyone who loves to spend time on chess. People have intereststs. Yours are not mine, and that is good. I respect that you have your interests.

Of course it is fine to pursue such interests. I certainly was not referring to people who like to prove things as "lizard people", that was just an example of an absurd belief held by a tiny percentage of people (but in the millions per surveys!) which cannot be disproven. But I suspect that if a proof that chess is a draw ever becomes possible, it would require a massive commitment of resources, which would seem to be not worth the cost just to prove what is already obvious. But if you are a billionaire and want to devote your wealth to such a project, that would be your right.

The related goal that I do find interesting is this: What is the smallest/most acceptable change to chess rules (or start position) that would eliminate draws without obviously favoring either side? Of course any drawless chess would be a forced win for one side, but as long as even the best engines devoting days to it could not make a determination with any confidence, that should be good enough at least for now. Currently my candidate would be "White can only castle short, Black can only castle long, Black wins draws". As far as I can tell, it's too close to tell which side to prefer. Perhaps someone has an even better solution.

I have a different type of candidate.

White is going to win a drawn game if the number of plies in the game is longer than k for some constant k.
The idea is that white try to make the game longer in order to win and black try to make the game as short as possible.

I guess that with the right k you are going to get a result near 50%.

Your proposal would obviously be quite close to balanced with the right choice of K. But it doesn't strike me as a game that many people would want to play. It's just not very chess-like, there is no logic behind the rule except to get rid of draws, and play would be bizarre. I want the game to be as close as possible to normal chess while accomplishing the goal. I think that a better candidate if you want to keep the current opening position and castling rights is to count material and pawn advancement as a tiebreaker by some rule, since these things don't change during a fifty move rule or repetition draw. White can be required to win by K points or he loses (analogous to Komi in Go). This would also be almost fifty-fifty with the right choice of K (depending on the precise rules for counting). At least the players would be trying to win material and/or promote pawns, as they do in normal chess. Whether this is more or less chess-like than the castling proposal is not obvious.

[jefk]

Apparently my posting (about balanced games) was posted twice, i suppose the
second one was slight better (sigh).
Anyway I've also seen some other comments which need a reaction, so I'll make a some brief responses:

- abductive reasoning ? (smatovic)

Looked that up and it’s an interesting concept indeed
https://en.wikipedia.org/wiki/Abductive_reasoning
Maybe that's indeed what i'm trying to some extent

Towforce: two comments first about photonics, and then 2) about (the erroneous concept of) opening advantage for White
1) you mentioned a website where photonics still seems to be some vague concept
Nowadays, however the existence of photonic integrated circuits is well known
https://en.wikipedia.org/wiki/Photonic_ ... ed_circuit
Currently it is seen as promising field in the Netherlands, as you can see here
https://www.utwente.nl/en/mesaplus/news ... plications

2) you mentioned some deficits in handcrafted evaluation (true) and in Nnue;
well Nnue is much better ofcourse (based on millions of games for setting up the neural network)
while preferred openings have changed slightly as result of the new Nnue evaluations,
the basic concepts –and opening theory- have stayed the same to a large extent
(contrary to the game of Go, where the program Katago finds complete new strategies)
Apparently you think it still might be possible to find an advantage from the opening position ,
well forget it, i have another argument besides the engines, namely that for centuries, chess grandmasters
have already tried to buildup some opening advantage from the initial position,
and until recently it was thought White has a slight opening advantage, but not enough
for a win (an idea by Hans Berliner to win with 1.d4 ‘the System’ clearly was refuted).
Nowadays eg from the GM repertoire series (published by 'Quality Chess) it is known
that it simply isn't possible to gain a significant advantage from the opening,
believe it or not; thinking otherwise imo indicates a lack of experience (e.g. in
correspondence chess).
In other words my statement ‘chess is a draw’ is not some belief by me out of the
blue but based on some thirty years of experience with chess opening theory;
as result of such experience I've started to see a clear pattern, that chess is
a balanced game, the winner is determined by mistake(s) by the loser, and
continuously building up an opening advantage right from the beginning isn't possible,
and a forced win from the initial position (for such reasons) simply also is Not possible.
For Black, after 1.g4 there may be a forced mate in eg 223 or less, but then
there are clear indications that this is possible. Again, from the initial position,
a forced win for White doesn’t exist because chess is a balanced game.
If you want to think otherwise, then first show (or better even, prove) why chess is
Not a balanced game. The burden of proof is on you, not on me but
For a start have a look at concepts in game theory
https://en.wikipedia.org/wiki/Solution_concept
Equilibrium situations are a well known phenomena when applied in game theory to some complex situations
as e.g. in economics; but for a relatively simple game as chess we also can establish that it is a balanced game
(as I wrote earlier), in other words in equilibrium; simple as that.

A more constructive discussion indeed is trying to find some simple rule
medications addressing the draw problem, depending on which sort of chess
(correspondence, engine games, etc). Personally I still would like to be rewarded
(in ICCF chess) if I end up with a pawn more in the endgame, but unfortunately no
serious project so far has started to make a study of such rule improvements.

Time for another subject/thread again here, maybe.

[Jouni]

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

[towforce]

With that I fully agree. I don't believe chess will ever be solved, so a project to try to solve it would be pointless. (If someone has a brilliant idea or some unexpected new technology is developed, then I will reconsider; I would be happy to be proven wrong.) And since we can't solve chess, the next best thing is to develop heuristic engines and make them play as well as we can. So that's what we do. But that we don't know the "true" outcome of chess, in the sense of actually solving the game, does (very slightly) bug me. (But if I could choose what open math problem gets solved, chess would not be anywhere near the top of the list.)

Solving chess would have a worthwhile benefit IMO: put an end to the (IMO) nonsense that a game tree outcome can only be proven by crunching out the game tree.

[syzygy]

Towforce's paradox might help, "If it is not a draw, then where is the win?" The deductive approach "just" needs one forced win to prove the others false.

If chess is a win, that would make it a lot "easier" to solve, but it would still be out of reach.
It seems people assume that 1.g4 is losing, but proving it is too difficult. The branching factor of chess is too high, most positions have several playable moves.

Or take the initial position, remove a black rook, and try to solve it as a win for white. I strongly suspect this is not possible with current technology, even though clearly white has a win.

[Chessqueen]

For me Chess is a lost before I make the 1st move whenever I play against a player stronger than me. If you are in doubt you can ask Guenther about it.

[towforce]

For me Chess is a lost before I make the 1st move whenever I play against a player stronger than me. If you are in doubt you can ask Guenther about it.

We're all taught that the quickest win in chess is two moves - but of course if you're black, and white resigns on the first move, you can win without moving at all!

A more serious point: the above quoted text is a VERY serious issue in life: too many men give up without trying in too many situations. In any life situation where there isn't much to lose, give it a go! The gain in experience is more valuable than the 5 minutes of embarrassment, and you'll build your courage.

[CornfedForever]

London Chess Classic 2023 after 4 rounds: 13 wins 7 draws. Long live chess...as it was meant to be played.

[jefk]

copied from an appropriate location (Stoofvlees vs SF) where i responded to ChessKobra

yep (earlier) thought of responding to Towforce, regarding some of his innovative
and original ideas regarding chess evaluation Not long ago a neural net alfazero
style without search already was able to reach GM level (but not 3400 or so like SF);
https://arxiv.org/abs/2402.04494

But no matter how you reason about it (eval) nobody can deny there also must be a search tree in chess,
more prevalent in chess problems, deep tactics, etc, but often also in normal positions.
Cleary indicated by minimax theorem by Von Neumann. see also the well known tree concept
and described eg. by Kotov in his (think like a GM) book eg.
https://www.chess.com/forum/view/genera ... hod?page=2

Symmetry ? well yep, but in addition, and this is more important, it's about the 'degrees of freedom'
(for Black). No matter what White plays from the (historical) 'normal' positions , there always remain
several options for Black to escape situations leading to worse positions. This is different then a situation
as eg. in Four in a row, where gradually the options for the second player become more and more restricted,
and thus the first player indeed can force a win.

Such a high degree of freedom (for Black) is apparent because eg. contrary to checkers, pieces in
chess can move back, there is the 3 pos repetition draw rule etc. And the 50 move (no pawn move)
draw rule, this all leads to a relatively large draw margin in chess. And to an obvious conclusion.
You suggested last year that i should write down my reasoning but i although I made notes during
our discussion(s) i didn't start (yet?) with a coherent and concrete article(*). Maybe because prove the 'draw
conjecture'' rigorously without a -narrowed- 'brute force' calculation (which unless Riemann should be
possible for chess) indeed is not a simple task; contrary to what towforce seems to think imo it will involve
lots of practical examples, concrete reasoning, etc. (and experience helps to get some hunches
about how this works in practical chess, and why White cannot find a forced winning line;
my conviction is more a result of (large and deep) experience than reasoning about symmetry, and
without a deep understanding about some math concepts as 'winning strategies' discussions about
the topic (and skeptical opinions) remain vague and inconcrete. A more suitable game to
explore deductive methods for proving a draw is maybe conventional draughts; it hasn't
been numbercrunched (yet) like checkers, yet most experts now are convinced it's a draw.

So it's complicated indeed, to illustrate with an example: in the position after 1.g4 i cannot
exclude that there's a forced win for Black. So in similar style, when i started my computer
chess opening research more than twenty years ago, i would'nt exclude a possibility that after
e.g 1.e4, d4, or 1.Nf3 (or possibly 1.c4) White might be able to gradually increase it's
positional advantage. And maybe for one or two positions of the chess960 this still could
be possible (unlikelly i admit, but you never know, and i didn't check it). But for the
normal chess position i made it topic of research starting even before the year 2000,
and there's *no* forced win for White as i found in practice(**), already around 2008)
https://superchess.blogspot.com/2008/01 ... rfect.html
https://superchess.blogspot.com/2008/03 ... y-etc.html

(*) but like i wrote, i offer 10 k ($) for the one who finds a forced winning line for White
(**) whereby i went much further than simple stuff as eg. the basic Hert tree (from Pohl)
something you suggested some time ago; this Hert tree is way too small, and thus
has deficicies btw,for example in the Scotch after e4 e5 Nf3 Nc6 d4 exd4
Nxd4 Nf6 Nc3 the move Bb4! (instead of ...d6?!) is the best (drawing) move
but it's not in the Hert500.pgn...

PS as for the Riemann examples i posted, i'm sure that from academic circles there
will be criticism about these 'proofs' or their methods (in particular the FB posting).
The youtube 'proof' (more some sort of inductive reasoning with lateral thinking and thus
probably not a rigorous proof according to some academis) is by a (serious and probably
highly talented) mathematician (and FB contact of me) working in Los Alamos btw.
In other words not a crank (like i know that for the Fermat last theorem there are
many crackpot proofs, also on FB). But despite such academic criticism i think that
such reasoning(s) gradually are making it more likely that the Riemann conjecture
is true, in other words a gradual process like it often is in theoretical physics research.
And although math isn't physics, also in the development of proofs, you often see some
gradual process; the (now accepted) proof by Andrew Wiles for Fermat's last theorem was
a long arduous process, whereby he ofcourse built on earlier works; in other words,
a gradual process, and not a sudden -once in a lifetime- (and required) event by
eg. some lonely genius the kind of Gregori Perelman type or so.

PS2 in addition (to the posting in the Stoofvlees SF thread):
the move 1.g4? indeed breaks symmetery, but symmetry is not enough,
imo there should be enough 'degrees of freedom' always remaining for
the second side to avoid a lost position.
Basic point (again) imo in games like chess (or draughts) is to show it's
the sort of 'balanced game' with outcome draw because there is some
sort equilibrium with perfect play, like Nash equilibrium of whatever.
Symmetry most likely makes this requirement easier, but most likely
isn't sufficient (i can imagine some small symmetrical game with some
rules invented for the purpose where the first player can force a win).
Like i wrote, in first instance oldfashioned draughts (or maybe reversie/othello)
seems an easier game to explore such reasonings than chess with quite some
complicated rules (en passant, endgame rules as stalemate etc).
Regarding reversi/othello, some time ago i looked at a recent strong (nnue?) program
with an opening and endgame base,
https://www.egaroucid.nyanyan.dev/en/
After the opening, it only has to play a few moves (with score 0.0) before hitting the
endgame table, and result draw. Soon we also will get such a situation for draughts, i suspect.
Although this again more looks like the 'number crunching' solution, the additional
reasoning (that you can't find advantage after the minimaxed opening)
is imo already indicating such games are a fundamental draw (more fundamental
proof would be to show that they are 'balanced games' which probably is
easier for draughts than othello i guess (just a hunch); the strongest draughts program
is probably 'Damage' (Dutch author but i couldn't find a download link anymore)
Also strong seems to be Kingsrow
https://edgilbert.org/InternationalDrau ... _links.htm
see also
https://damforum.nl/bb3/viewtopic.php?t=3819