Is there any project coming to solve chess?

[Uri Blass]

In chess, it is far more likely that white has a very ingenious winning strategy that is completely overlooked by humans and engines than that chess allows for some very ingenious "short" mathematical argument that proves it to be a draw.

This is certainly true, but I’d go much further.
We don’t even know the theoretical game result.
All the draws make people overlook how narrow the path to equality has become at the same time
Does anyone know a clear way to equality for black after 1. E4 c5 2. Nf3 d6? I don’t.
So what is left to break? The Petroff, the Marshall, the Berlin, maybe some Kan or Sveshnikov Sicilian – these look difficult to win against right now . But this is not that many lines.
Uri Blass is the only one here who dared to make an absolute claim like: you can’t beat Stockfish at 1h/move on some computer – my intuition tells me that I’d make a good bet on Stockfish thinking for 100 hours , or in other words: chess is far away from being solved IMHO.

If you claim that stockfish at 100 hours per move can beat stockfish at 1 hour per move with no opening book then I see no evidence of this type of result even at faster time control.

I remember that a big majority of the games between stockfish and itself at 10M nodes per move against 1000M nodes per move ended in a draw.

People can try it today(stockfish with many cores is not determinstic so you can expect different games)

[Uri Blass]

People as Uri Blass (a correspondence chess player), Larry Kaufman Dann Corbit, and e.g. Magnus Carlsen all agree chess is a draw.

For the Nth time: all experts agreeing that chess is almost certainly a draw has absolutely nothing to do with a proof or the feasability of a proof.

One more example by Peter Berger:
“Sf can be beaten no matter how much time you give it”
Again, this imo is nonsense, who is going to beat SF then in such situation, you yourself maybe ? Or Magnus Carlsen, or the world champ correspondence chess ? Forget it. Or SF itself with even longer time controls ??

You are the perfect person to find a win against a deterministic engine. Just keep analyzing openings and SF's deterministic replies until you find a weakness. I have no doubt that any deterministic version of SF has at least one weakness that lets the opponent force a winning position from the initial position.

Under normal circumstances SF is not deterministic, but the point remains that it will have such a weakness. The problem with a non-deterministic engines is that it is not possible to find such a weakness in the way you can find any weakness of a deterministic engine if you just have enough patience.

Stockfish with one core is deterministic and I would like to see if somebody can produce a win against it at 1,000,000,000 nodes per move that is clearly less than one hour per move.

Maybe it is possible but I am not sure if it is possible and I believe that only using stockfish at 100,000,000,000 nodes per move is not enough.

[Uri Blass]

I think we already have a weak solution to chess (run SF for 30 minutes per move on a decent ThreadRipper + provide a very simple opening book so it doesn't go into complicated stuff with black).
I don't think the discussion about rigorous mathematical proof is very interesting - it's clear we don't have it and won't have it for foreseeable future.
The question if current SF on set hardware can ever be beaten from a starting position is an interesting on though.

As to the term "weakly solved in practice" I am not sure why some people find it so offensive. I think it's a very useful term and the meaning is clear as well: "the game is weakly solved in practice if we have a solution that is as good as the real one in practice" or in other words: "If we use that solution instead of an oracle spitting out real weak solution no one is going to notice the difference".

Chess is not weakly solved. Chess is weakly solved in practice. It wasn't 20 years ago. Many other games still are not. That means the term has meaning and describes a reality which a traditional mathematical term wouldn't be able to.

I would like to see some opening trap that stockfish can fall into it with black when stockfish with no book can choose the opening with black.

[Uri Blass]

A few numbers about Othello
The number of games is approximately 6,5 10⁵⁴ (and not 10⁵⁸ as written many places from a gross but false approximation given by Victor Allis). The number of position is less than 2⁴ * 3⁶⁰ = 6,7 10²⁹ and can be reduce to about 10²⁸ when taking into account symmetries. This is also a large upper limit as it does not take into account that all discs should be connected and that some disc patterns are unreachable (for example XOXOXOXO on an edge). My guess is than the number of position is more likely around 10²⁴.
On my computer (a ryzen 9 5950x with 16 cores running at 4.2 Ghz) the speed of Edax integrated benchmark is 708 million nodes/s.
The work done by Hiroki Takizawa is remarkable by the computation power used having Edax searched 1,5 10¹⁸ positions on a super computer.

Back to chess
According to Wikipedia, the number of games is about 10¹²³ and the number of position 8 10⁴⁵.
The speed of Stockfish on my computer is 46254607 nodes/s (46 millions nodes/s) using its integrated benchmark.
Note also that for solving purpose, Edax disables any pruning losing information (mainly probcut) in its last stage, the full board is stored in the hashtable, and its access is locked. All this should be done in Stockfish which would surely impaired its performance.Actually, what is needed is not a stockfish like engine, but a fast mate finder.

So basically the effort is several order of magnitude harder for chess than for Othello. I guess the computational effort should be a at least a billion time harder than for Othello. I do not think we are going to see a solution any time soon.

For solving chess you not only need a mate finder but a draw finder.
There are many positions when it is possible to prove that white can force a draw by repetition or black can force a draw by repetition but stockfish does not tell me if it is the case.

We need a candidate drawing strategy to prove.
candidate drawing strategy may be simply play the moves that best engine is going to suggest(stockfish of today may be too weak but hopefuly in the future(maybe in 2040) some engine will be able always to play non losing moves even at 0.1 seconds per move with one core when the moves it is going to play will be only a function of the position when you ignore the 50 move rule.

Now you can try all the possible ways to beat the best engine and save every position that you can get in the games so you never play the same position twice
Hopefully the number of possible positions that you get is only something like 10^18 so you need 0.1 second per move multiplied by 10^18 that is 10^17 seconds.

This is too much time but you can use smp with 10^9 cores to get it with 10^8 seconds that are some years.

When you never play the same position twice the number of games that you have is less than 10^18 and you can see that every deviation from lines that you played already lead to a position that you played in a different game so you can continue to this game to get the move of the drawing strategy.

Maybe I am too optimistic believing that 10^18 classes of position are enough(I say classes of positions because I think for example it is stupid to have 2 identical positions except symmetry as 2 different positions) but my guess is that something like this will be possible in the future even if not in the next 10 years.

[Chessqueen]

In chess, it is far more likely that white has a very ingenious winning strategy that is completely overlooked by humans and engines than that chess allows for some very ingenious "short" mathematical argument that proves it to be a draw.

This is certainly true, but I’d go much further.
We don’t even know the theoretical game result.
All the draws make people overlook how narrow the path to equality has become at the same time
Does anyone know a clear way to equality for black after 1. E4 c5 2. Nf3 d6? I don’t.
So what is left to break? The Petroff, the Marshall, the Berlin, maybe some Kan or Sveshnikov Sicilian – these look difficult to win against right now . But this is not that many lines.
Uri Blass is the only one here who dared to make an absolute claim like: you can’t beat Stockfish at 1h/move on some computer – my intuition tells me that I’d make a good bet on Stockfish thinking for 100 hours , or in other words: chess is far away from being solved IMHO.

If you claim that stockfish at 100 hours per move can beat stockfish at 1 hour per move with no opening book then I see no evidence of this type of result even at faster time control.

I believe that Stockfish with a 4 moves opening book will have the same percentage of Stockfish with 8, 12 or 16 m0ves Opening, it is very simlpe to come out with that conclusion given enough time per move or even 15 seconds per moves after 1000 games you will not notice a big advantage with a bigger opening book

[chesskobra]

It is not a problem for me if you define 'weak solution in practice'. It could be useful to some people (even though it is not of interest to me). But if someone says chess has already been weakly solved in practice, I would like to know what definition they used, how they did it, and so on. And I still don't have that information. So I am not looking for new proposals for such a definition.

I think I would have a lot of questions about whatever definition of 'weak solution in practice' one suggests. Kasparov, Carlsen etc. can have their beliefs. I agree with syyzygy that what Carlsen thinks is irrelevant from game theoretic perspective. I only feel extreme surprise that they have no doubts while I have many doubts. If raising these doubts offends people, then they have some problems to solve. I am also quite sure that people like John Nunn, Jonathan Spielman, Karsten Müller, Noam Elkies would have similar doubts as I have.

I would also speculate, like syzygy, that there may be a very narrow path for one side to win. Moreover, I know that we can construct games where there is a very narrow path to win for one side, but if you don't know that path then no matter how big computational experiments you run, you would likely be very off from the game theoretic value. This is why statistical evidence and centipawns is pseudo-science from game theoretic perspective. (Centipawns may still be useful in practice.)

Personally for me chess is uninteresting from game theoretic perspective. It has weird rules. I suspect that Go will be solved before chess is solved, because Go is much more likely to have some underlying mathematical structure. For me, solving Go is somewhat like solving a difficult conjecture in graph theory or topology, a conjecture that has some structure. I can't imagine that kind of structure in chess. A game is mathematically interesting if it has simple rules but is difficult to solve. So people should really go after Hex (which is known to be ultra-weakly solved - first player wins with perfect play) or Go. Here is a challenge for people interested in 'weak solutions in practice': by doing computational experiments alone, confirm that 'weak solution of Hex in practice' matches with the theoretically known solution.

[syzygy]

Stockfish with one core is deterministic and I would like to see if somebody can produce a win against it at 1,000,000,000 nodes per move that is clearly less than one hour per move.

It is just a matter of finding a single position that can be reached from the initial position and where Stockfish's search and evalution mess up.

It can be highly difficult to find such a position in a reasonable time, but given enough time you can systematically probe how deterministic SF responds to your moves. If you don't give SF a book, known opening theory will probably already allow you to get SF into a position where it has to play carefully.

Maybe it is possible but I am not sure if it is possible and I believe that only using stockfish at 100,000,000,000 nodes per move is not enough.

This statement suggests that you do not appreciate what it would mean for a deterministic SF to draw against ANY play.

FInding a win against a determinisitc SF is not a matter of "if SF uses N nodes per move, then it can be beaten by SF using 1000*N nodes per move". It is about finding a single line where SF happens to screw up. You are allowed to investigate a trillion lines to find a single one that the particular version of deterministic SF you picked cannot handle.

[syzygy]

I think we already have a weak solution to chess (run SF for 30 minutes per move on a decent ThreadRipper + provide a very simple opening book so it doesn't go into complicated stuff with black).

Not a weak solution according to the definition.

I don't think the discussion about rigorous mathematical proof is very interesting - it's clear we don't have it and won't have it for foreseeable future.

The question that started this thread was about "solving" chess. You may not find the question interesting, but it is the question that was posed (because of the recent announcement of Othello having been weakly solved).

I agree with you that the answer is that we haven't solved chess and will not solve it any time soon.

The question if current SF on set hardware can ever be beaten from a starting position is an interesting on though.

So this asks how likely it is that SF provides a weak solution.

My answer to this question I have already given: for me it is inconceivable that SF or any other existing engine can draw against ANY play. It may be that a sufficiently indeterministic version SF will be able to draw a billion or trillion games before it screws up, but SF's search and evaluation have holes and I find it not realistic to believe that these holes couild never cost SF a game.

As to the term "weakly solved in practice" I am not sure why some people find it so offensive. I think it's a very useful term and the meaning is clear as well: "the game is weakly solved in practice if we have a solution that is as good as the real one in practice" or in other words: "If we use that solution instead of an oracle spitting out real weak solution no one is going to notice the difference".

"as good as the real one in practice", "no one is going to notice the difference", what does that even mean?
Are you saying "it is OK if the 'weak solution in practice' loses a game every now and then because nobody is perfect and people should stop complaining so much"?

As to the term "weakly solved in practice" I am not sure why some people find it so offensive. I think it's a very useful term and the meaning is clear as well:

Becaiuse it does not have a clear meaning at all and in the next breath many of these people then conclude that therefore a weak solution is either already there or just around the corner.

The best way to let discussions derail is to make up your own terminology and definitions (and change them halfway a paragraph if you need that to avoid conceding a point).

[syzygy]

I think I would have a lot of questions about whatever definition of 'weak solution in practice' one suggests. Kasparov, Carlsen etc. can have their beliefs. I agree with syyzygy that what Carlsen thinks is irrelevant from game theoretic perspective. I only feel extreme surprise that they have no doubts while I have many doubts.

I suppose for them being 99.9% confident that chess is a draw means "no doubt". Not dissimilar to how I have no doubt that chess will never be solved by mankind. It does not mean that I can prove it or that I believe it can be proved.

I would also speculate, like syzygy, that there may be a very narrow path for one side to win. Moreover, I know that we can construct games where there is a very narrow path to win for one side, but if you don't know that path then no matter how big computational experiments you run, you would likely be very off from the game theoretic value. This is why statistical evidence and centipawns is pseudo-science from game theoretic perspective. (Centipawns may still be useful in practice.)

To be clear: my speculation is not that such a narrow path exists. The point is that we cannot know that it does not exist without either (1) verifying computationally that it does not exist, or (2) find an ingenious argument that shows that it cannot exist (or some combination of (1) and (2)).

Option (2) is extremely, extremely unlikely for the reasons you state: chess does not have a nice mathematical structure that could potentially allow for such an argument to exist. There are some special cases of endgame positions that can be reasoned about, and there may be some fortresses which can be fully analysed, but that is about it. The existence of a narrow winning path from the initial path, however unlikely, is vastly more likely than option (2).

Option (1), a computational verification, is in principle trivial. A 16-bit computer with a few hundred kilobytes of RAM can be programmed to do it if time is not an issue (I first wanted to say that an 8-bit computer with 64KB should suffice, but if the program needs to search a few thousand plies deep, it might run out of memory). But time evidently is an issue.

Personally for me chess is uninteresting from game theoretic perspective. It has weird rules. I suspect that Go will be solved before chess is solved, because Go is much more likely to have some underlying mathematical structure. For me, solving Go is somewhat like solving a difficult conjecture in graph theory or topology, a conjecture that has some structure. I can't imagine that kind of structure in chess.

If I thought a solution might be computationally feasible, then I would be interested in the computational problem for the reason that we are talking about chess and not some random made-up problem.

[Uri Blass]

Stockfish with one core is deterministic and I would like to see if somebody can produce a win against it at 1,000,000,000 nodes per move that is clearly less than one hour per move.

It is just a matter of finding a single position that can be reached from the initial position and where Stockfish's search and evalution mess up.

It can be highly difficult to find such a position in a reasonable time, but given enough time you can systematically probe how deterministic SF responds to your moves. If you don't give SF a book, known opening theory will probably already allow you to get SF into a position where it has to play carefully.

Maybe it is possible but I am not sure if it is possible and I believe that only using stockfish at 100,000,000,000 nodes per move is not enough.

This statement suggests that you do not appreciate what it would mean for a deterministic SF to draw against ANY play.

FInding a win against a determinisitc SF is not a matter of "if SF uses N nodes per move, then it can be beaten by SF using 1000*N nodes per move". It is about finding a single line where SF happens to screw up. You are allowed to investigate a trillion lines to find a single one that the particular version of deterministic SF you picked cannot handle.

I clearly understand that you need only to find a single line that you can beat stockfish at 1,000,000,000 nodes per move.
I understood that finding a single line is good enough.
I did not claim that it is impossible to find a single line but only that probably stockfish with more nodes is not going to be enough.
I believe that it is not going to be easy to find it and even if it is possible in a few years we are going to get some engine that make it impossible.

I would like to have anti-X engine that the target of it is to beat deterministic engine X as fast as possible in chess by investigating many lines but unfortunately I know no engine that does it and people are not going to investigate manually a lot of lines to find a single one to beat X.

The interesting question for solving chess is not how many position you have but how many positions you can get that you cannot calculate the result of them very fast when one side is using a perfect good strategy.

It may be interesting to have the reply for this question for other games that we already weakly solved or for smaller versions of chess that we can solve(I can think about 8 files but less than 8 ranks when with 4 ranks it is mate in 1 and it is interesting if we can solve 5 ranks or 6 ranks with the same rules today)

There are many uninteresting chess positions because of one of the following reasons:
1)You will never get them in a chess game against specific deterministic unbeatable engine that you will use in the furute to weakly solve the game.
2)Result of the position is already known by some simple calculation(for example I can be sure that some KPPPPPPP vs K that it is a win for the side with many pawns with no calculation).