Is there any project coming to solve chess?

[syzygy]

question to syzygy: do you accept that Othello has been ultraweakly solved ?

It might be, but I have not read the paper (which I believe is only a preprint).

The best evidence would be a publicly available file with the minimum proof tree and source code of a program that verifies the tree. Then anyone could check the correctness of the claim for themself.

What I do know is that the author or authors of the paper claim an actual mathematical (and computational) proof. They accept the well-established meaning of "ultraweakly solved" (which you do not).

[syzygy]

I hope these references can be useful to all of you.

I'm afraid not, because the dispute here is about what it means to "know".

Jefk "knows" that the Riemann Hypothesis is true because it has been numerically verified that the first trillion zeroes are on the critical line.
In a mathematical sense, however, the truth of the Riemann Hypothesis is not yet known.

[syzygy]

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.

I think you are right that the numerical evidence for chess being a draw is still inconclusive.

As for SF, I am convinced that it can be beaten no matter how much time you give it.
If you make SF deterministic (single-threaded and a fixed number of nodes per move), it is just a matter of trying enough variations of counterplay until you find one that beats SF. You can then beat SF each and every time (since it is deterministic).

[abulmo2]

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.

[jefk]

As result of some recent postings I'm going to leave this discussion, as it has become a unprofessional and simplistic yes/no debate.
But before I leave still some necessary reactions:
- syzygy , I do NOT deny/contradict the definition of ‘ultraweak solving’,
The Riemann hypothesis which you gave as example is different btw, and such
additional reasoning still doesn’t exist or isn't sufficiently rigorous, anyway you are misrepresenting my thoughts and claims.

Ronald de Man aka syzygy you are a mathematician and well respected for your Egtb work, but don't seem to have the experience (nor knowledge) in chess opening theory which i have built up over more than some thirty years. People as Uri Blass (a correspondence chess player), Larry Kaufman Dann Corbit, and e.g. Magnus Carlsen all agree chess is a draw.

First an in-between reaction tp Peter Berger: contrary to what you
are suggesting most (solid) in chess variations are a draw because
of the big drawing margin in chess (and because of the definition
of solid), after e.g. 1.e4 c5 2.Nf3 d6 you probably want to play Bb5 (after d4 it's also draw), well then after 3...Nbd7 and so on it's a draw
And most well established defensive lines in chess imo are solid.
Have a look eg. at the Chinese databse. some 15yrs ago I
already claimed chess is a draw, and now the Chinese database
is corroborating my earlier claims. Only problem left is finding a rigorous ‘proof’; well this imo won’t be difficult.
That some persons don't understand this, i.e. don’t want to
believe it no matter what is their problem, not mine. There
may be kiddies of 5 yr old rating 900 who may claim that 1.h4
is the best move because it will attack the Black king,
and thus say that maybe 1.h4 could win; nonsense. There also are people
who may claim you cannot prove the earth is a globe (and not flat)
and thus is may well be flat. And I’m not going to argue with them.
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 ??
Again, forget it, such situations will converge to more and more drawish positions, and there will be no gain of such exercises and no winning result for White, no matter how long you calculate. Similar in Tictactoe an increase in calculation time will yield no better results.

mr Berger you seem to have been an opening book author, but it seems
your experience is not up to date anymore; I also can't find you e.g. in the ICCF player list, so you probably don’t have experience in computer assisted correspondence chess. Then why making such claims, that there may be a win for White ? It’s nonsense.The burden of proof is on you, not me, and like Peter Osterlund also suggested, it's up to you to show us
a winning line for White which nobody can refute. good luck (lol)

Then RdM syzygy again, you wrote
“In chess, it is far more likely that white has a very ingenious winning strategy that is completely overlooked by humans and engines”
Well as you already understood, I strongly disagree with this, by now it's clear there is no such 'ingenious winning' strategy. Example, against 1.g4 there may be a winning strategy for Black, but then this is indicated by the initial back-solved score for g4 which is -150 or so.
But from the initial there is *zero* advantage for White, also (especially) confirmed by MCTS search (yes i'm repeating myself here, and nobody seems to
understand the importance of this, i.e. the MCTS search).
Concluding I claim that with some additional reasoning, which I won't
post here(*), it soon (within a few years) can be claimed that chess is ‘ultraweakly’ solved.
Subsequently (e.g. after i've written a paper) in academic circles (and not here) people can try to find holes, i.e. showing my claim isn't rigorous enough. When Andrew Wiles published his first proof about Fermat's Theorem, a few scholars found a flaw. But Wiles wasn’t discouraged, within about a year repaired that flaw, and now his proof for Fermat's Theorem has been widely accepted. (meanwhile people (as syzygy or PB?) may still be trying to find a counter example with some supercomputers, well i wish them good luck. And later, when the official result is announced, still some (amateurs) want to to disagree. Up to them, I also predict that within about ten years we will have such intelligent AGI that it will also be better in this field than most mathematicians and game theorists, and it will agree with my claims. So i bet one bottle of wine with you Ronald de Man (or other volunteer naysayers) that this will happen, and since you are so convinced of yourself, suggest you in exchange will reward me with fifty thousand dollars when i'm right (if i'm still alive). Yes even then a few people will continue disagree (flat-earthers) the kiddy with 1.h4, etc. Well i don't care. For the rest i'm not going to -endlessly- repeat myself anymore in this annoying forum,
Goodbye
jef

[swami]

If an engine never loses a game, Chess is going to be boring (rather than solved - there'll always be an argument that some drawn games could have been avoided)

In future, we would be wading through hundred thousands of drawn games to see if a possibility of win is missed out by the strongest super computer available.

[Peter Berger]

I have never been an expert on chess openings, this computerchess wiki page is very nice but not too true.
There was a certain point in time when I understood that the then computerchess opening books were done in a wrong way. And I spent like six weeks doing a book in a different way, full-time. I deserve credit for these six weeks as I really worked hard. I had a book that was kind of complete in the end, but without any move that hadn’t been checked by an engine which was kind of an original idea.
Computerchess was crazy opening-wise back then. There were some experts who duelled each other at WCCCs, but their work really got out of hand. I remember Fritz-Shredder, Ramat-Gan 2004, as I witnessed it personally. You could have used any engine, wouldn’t have mattered, the book authors were having their way.
My find was genuine, but I remember it now because someone else had worked in a similar way, Marc Lacrosse – we talked a little, then we sent each other simply EVERYTHING we had instantly – you may well call this open-source.
For a little time I think Marc and me just had the best books around. But as our idea wasn’t exactly rocket science, others caught up soon. I saw the Rybka book in Turino – and I realized, that this was a level of professionalism ahead.
Sorry for not really replying to your post – why being so aggressive?

[syzygy]

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.

I suppose you consider the claims in the paper to be believable?
https://arxiv.org/pdf/2310.19387.pdf

Apparently there are 2,958,551 positions reachable after 5 moves (10 plies), i.e. with 50 empty squares, but white and black each have drawing strategies that guarantee that only 2587 of those positions occur (i,e. white can force such a position to occur whatever black plays, and black can force such a position to occur whatever white plays). I guess one should indeed expect something in the order of the square root of the number of positions (size of minimal tree should be about 2*sqrt(total_positions).)

As far as I understand, Takizawa identifies those 2587 positions by evaluating each of the 2,958,551 positions using your engine and classifying each as one of "likely drawn", "perhaps win for white", "perhaps win for black", and then doing a 10-ply search from the initial position to find a minimal tree that gives white a strategy to reach a likely draw and a minimal tree that gives black a strategy to reach a likely draw. The leaf positions of those trees correspond to the 2587 positions. Now all that is left is to prove that each of those 2587 positions is indeed a draw.

He then repeats the exercise for each of those positions but now searches 7 moves (14 plies) ahead to positions with 36 empty squares. The relevant positions with 36 empty squares are then proven by an exhaustive (alpha-beta) search. (I have no idea if a 36-ply full-width search is feasible in Othello, but I guess it is?)

It would be nice if Takizawa had stored the proof trees to a depth which can be verified in, say, about 100ms of searching (or some other amount of time that keeps the size of the trees within reasonable proportions).

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.

The Wikipedia numbers might not mean too much. Losing/suicide chess should have about the same number of positions (actually it has more), but it has been solved (white wins). This is because losing chess has a very small branching factor.

Chess has a much larger branching factor with many moves that do not "obviously" lose (and even for moves that do "obvioulsy" lose it is very difficult to actually prove that they lose). Also, chess has repetitions which is very annoying for proving a draw (no practical limit on the length of a game, infinite headaches caused by GHI problems, etc.). In Othello each move makes progress towards the end of the game simply because of the rules of the game.

One advantage of chess is that endgame tablebases make sense, but they quickly become too large.

What seems to have been of decisive help for Othello's proof is that your engine could reliably predict the outcome of enough positions with 50 empty squares that it was possible to find those 2587 positions. Apparently all these predictions turned out to be correct.

Congratulations on your contribution to the soltuion!

[syzygy]

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.

[OneTrickPony]

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.