Is there any project coming to solve chess?

[syzygy]

Anyway, this thesis was from 1994, much has happened since then but most people were busy with 'weakly' solving games (like checkers, or now the Othello attempt) and not discussing possible methods to determine a priori
the outcome of a game (like i did for chess).

"Solving" a game, such as in the subject line of this thread and in the Othello paper, is and has always been about establishing with certainty, i.e. mathematical certainty, the game-theoretic outcome. Typically this involves a brute-foirce computation, but for some games an argument can be found that avoids the need for computation.

If you believe Van den Herik does not agree, then good for you.

To put it differently: there are people who are interested in establishing the game-theoretic outcome of a game with mathematical certainty. Which term should they use for this, according to you?

[jefk]

Final relatively short comment, also again required unfortunately, so posting it here and then leaving, not because
some sharks are smelling blood and will happily continue to post insinuating garbage doubting my view(s)
but simply because this thread imo should be closed (and there is another thread,
'chess is a draw', with obviously a much better subject title

syzygy as i already predicted you are repeating yourself and emphasizing the importance of 'mathematical(*) 'certainty'.
Then you state that weakly solving a game (like checkers) means establishing the outcome with mathematical certainty,
well I have Not suggested otherwise. But You, your self, suggest that 'establishing' something is different (less) than a rigorous mathematical proof. Also, i have no
problem with that, but then i also see no need for rigorous proofs for checkers, draughts, chess, etc.

Only remaining dispute we have (and which has not been discussed elegantly in the thread) is that i claim that
by now we can determine with certainty the outcome from the initial position (draw) without even the need for
a more complete ('weak') solution like for checkers. There are many arguments for this which all combined
make the (draw) 'conjecture' or whatever you like to call it even more certain, and this certainty is growing
nowadays ever year. In other words, for math purists we at least are (Bayesian?) estimating the outcome
of the game (although MCts is more than 'estimating' because it's not worse than minimax, at least
when programmed properly and with sufficient calculation time and we know the result; draw. see also
my comment in the thread 'chess is a draw' about the definition of an ultraweak solution (with which you
will -continue to- disagree (**) , but then repeating myself, i suggest you contact prof vd herik) that's all. Amen (I have better things to do)

NB for the game of Nim an elegant mathematical proof was found, fine, for chess this might be almost impossible (unless
some AGi with graph theory on a supercomputer comes with some complex logical arguments for such a proof
but even then i expect combined with emperical findigs.

(*) which is why i used the term math purists or theoretical mathematicians; but there's also a field of meta-mathematics
you know, yet imo it goes to far imo to delve into such a topic here, related to computer chess).
(**) wishful thinking (about that definition, before vd Herik would comment) imo can be regarded as a cognitive bias

[syzygy]

https://www.cs.utexas.edu/~marijn/publi ... _games.pdf

In this paper we will focus predominantly on solved games - those games for which this game-theoretic value is known - and on the solving procedures used to obtain these values.

(...)

The game-theoretic value of most games can easily be predicted without actually solving it: either the player with the initiative can force a victory, or the opponent has enough possibilities to force a draw. For example, on the highest level of competition, games of checkers and chess frequently result in a draw. Even though both games have not been solved yet, it is very likely that their game-theoretic value is a draw.

What a surprise, an academic paper about solving games which distinguishes between "solving" a game, i.e. establishing its game-theoretic value, and merely predicting what is very likely the game-theoretic value of the game.

[syzygy]

other relatively short comment, also again required unfortunately, so posting it here and then leaving, not because some sharks are smelling blood and will happily continue to post insinuating garbage doubting my view(s) but simply because this thread imo should be closed (and there is another thread, 'chess is a draw', with obviously a much better subject title

This thread is about whether chess can be solved. The other thread is about speculating about the game-theoretic of chess. Different questions.

syzygy as i already predicted you are repeating yourself and emphasizing the importance of 'mathematical(*) 'certainty'.

I am not emphasising the importance. My point is only that establishing its game-theoretic outcome with mathematical certainty is a valid concept which does not interest you but does interest many others, in particular academics. The academic term for this concept is "solving" the game.

If you wish to hijack the term "solving" a game, then what other term do you propose academics use from now on?

Only remaining dispute we have (and which has not been discussed elegantly in the thread) is that i claim that
by now we can determine with certainty the outcome from the initial position (draw) without even the need for
a more complete ('weak') solution like for checkers. There are many arguments for this which all combined
make the conjecture or whatever you like to call it even more certain, and this certainty is growing
nowadays ever year. In other words, for math purists we at least are (Bayesian?) estimating the outcome
of the came (although MCts is more than 'estimating') and we know the result; draw. see also my comment in the
thread 'chess is a draw' about the definition of an ultraweak solution (with which you will disagree (**) , but then repeating
myself, i suggest you contact prof vd herik) that's all. Amen

I have already explained a few times that for you the Riemann Hypothesis has apparently been solved/proved because we know that the first trillion zeroes are on the critical line, so what more evidence could we wish for?

[towforce]

Regarding 'beyond reasonable doubt' argument, I have a simple question. How do you put probabilities on the two possibilities - (I) a narrow winning path for one side and (II) a draw with perfect play? Let us consider two subtrees of the game tree T. One (possibly empty) subtree T1 consisting of forced win for one side, and another subtree T2 consisting of forced draw (where by forced draw I mean either a forced draw with perfect play or forced draw when the side that has winning strategy makes mistake and allows a draw with perfect play from that point). Now obviously any empirically derived probabilities would depend on relative sizes of T, T1, T2. Now 'beyond reasonable doubt' I would only believe that T is huge, T2 is quite small and T1 possibly extremely small. But if anybody has more intuition than that, I would like to know. I personally believe that even the drawn engine games are unlikely to fall within T2, and that T1 and T2 are both so small compared to T that simulations are unlikely to shed light on their sizes. I would, for example, like to know an estimate for the probability that a high level engine game belongs to T2 conditional on the event that it is drawn, and an estimate for the probability that a high level engine game belongs to T1 conditional on the event that it is won by one side. IMO, such estimates are required for the 'beyond reasonable doubt' argument, and are difficult to make. So it is unlikely that even a court would accept the argument, leave alone a negative maths purist.

I am mystified as to why you allow subtree T2 to contain errors. Why not just make T2 the subtree in which both sides can obtain a draw without errors?

I can say that subtree T1 (forced win) is empty "beyond reasonable doubt" (but not mathematically proven) for the following reasons:

1. the people who made today's chess rules were nowhere near the standard of today's top chess players

2. top chess players have been studying openings for hundreds of years, with thousands of books about opening having been written

3. today, chess computers have looked at openings in way more depth than these humans ever have

4. no way has been found to win a piece or a pawn from the opening (it's probably even fair to say that no way has been found to come out of the opening with a significant advantage that could possibly lead to a win)

5. Given point (1), I'm satisfied that chess is proven to be a draw to the legal standard of proof. If there is a win for white (or even a way to get a good advantage in the opening), it really, really should have been found by now

For me, this evidence is far stronger than the evidence on which most murderers are convicted in court. But as I said, a small number of convicted murderers were later able to prove that they didn't commit the crime.

Here's another example of "good evidence, but not outright proof": people are 10x more likely to have a camera with them today than they were before phones had cameras, so the number of photos presented as ghosts or UFOs should be about 10x higher. It isn't. Therefore ghosts/UFOs aren't real.

[syzygy]

Regarding 'beyond reasonable doubt' argument, I have a simple question. How do you put probabilities on the two possibilities - (I) a narrow winning path for one side and (II) a draw with perfect play? Let us consider two subtrees of the game tree T. One (possibly empty) subtree T1 consisting of forced win for one side, and another subtree T2 consisting of forced draw (where by forced draw I mean either a forced draw with perfect play or forced draw when the side that has winning strategy makes mistake and allows a draw with perfect play from that point). Now obviously any empirically derived probabilities would depend on relative sizes of T, T1, T2. Now 'beyond reasonable doubt' I would only believe that T is huge, T2 is quite small and T1 possibly extremely small. But if anybody has more intuition than that, I would like to know. I personally believe that even the drawn engine games are unlikely to fall within T2, and that T1 and T2 are both so small compared to T that simulations are unlikely to shed light on their sizes.

If the initial position of chess is a draw, then I am fairly sure that many engine-engine games, in particular the most boring ones, have only perfect moves, i.e. moves which preserve the game-theoretic outcome.

If the initial position of chess is a win for white, then 1.e4 f6 2.d4 g5 3.Qh5# may well be a perfect game.

I would, for example, like to know an estimate for the probability that a high level engine game belongs to T2 conditional on the event that it is drawn, and an estimate for the probability that a high level engine game belongs to T1 conditional on the event that it is won by one side. IMO, such estimates are required for the 'beyond reasonable doubt' argument, and are difficult to make. So it is unlikely that even a court would accept the argument, leave alone a negative maths purist.

I would not be shocked if a court decided that chess is a draw beyond reasonable doubt based on expert declarations, e.g. from Carlsen. Courts are not the best place for deciding mathematical truths.

If I had to bet money on chess being a win for white, draw, or win for black, all three giving equal payouts, then my money would be on chess being a draw. This bet seems very safe. (Still, I might lose the bet.)

[jefk]

syzyg '(I have to see if i can put you on ignore mode, or something like that).
No i don't hijack the definition of 'solving' a game, but my interpretation may sometimes be slightly
different than yours; and you are not such a big authority in academic game theory (like vd Herik or
Uiterwijk or some others. And because i'm not mathematician that apprently for you means
my opinions if deviating from yours must be incorrect; this is not sound reasoning.

Example it must be clear that a weak solution of a game is less than a (rigorous mathematical
proof, otherwise there would not be a definition of s 'strong solution' of game (more brute
force, and establishing with more certainty, ie more like a rigorous proof. And i agree we are far
from 'strongly solving' chess with brute force but for correspondence chess that's also irrelevant.
It's also irrelevant for academic game theory, i would suggest (because weakly solving
would be interesting enough, again, like done for checkers, and maybe Othello.
But this may lead again to some possible ad inifintum discussions , so again, i'm out
of here. Happy discussing with chesskobra (who probably is not a mathematician btw,
he sounds more like a programmer to me (and a medium/low ability chess player).
My 2 cnts

[Uri Blass]

Regarding 'beyond reasonable doubt' argument, I have a simple question. How do you put probabilities on the two possibilities - (I) a narrow winning path for one side and (II) a draw with perfect play? Let us consider two subtrees of the game tree T. One (possibly empty) subtree T1 consisting of forced win for one side, and another subtree T2 consisting of forced draw (where by forced draw I mean either a forced draw with perfect play or forced draw when the side that has winning strategy makes mistake and allows a draw with perfect play from that point). Now obviously any empirically derived probabilities would depend on relative sizes of T, T1, T2. Now 'beyond reasonable doubt' I would only believe that T is huge, T2 is quite small and T1 possibly extremely small. But if anybody has more intuition than that, I would like to know. I personally believe that even the drawn engine games are unlikely to fall within T2, and that T1 and T2 are both so small compared to T that simulations are unlikely to shed light on their sizes.

If the initial position of chess is a draw, then I am fairly sure that many engine-engine games, in particular the most boring ones, have only perfect moves, i.e. moves which preserve the game-theoretic outcome.

If the initial position of chess is a win for white, then 1.e4 f6 2.d4 g5 3.Qh5# may well be a perfect game.

I would, for example, like to know an estimate for the probability that a high level engine game belongs to T2 conditional on the event that it is drawn, and an estimate for the probability that a high level engine game belongs to T1 conditional on the event that it is won by one side. IMO, such estimates are required for the 'beyond reasonable doubt' argument, and are difficult to make. So it is unlikely that even a court would accept the argument, leave alone a negative maths purist.

I would not be shocked if a court decided that chess is a draw beyond reasonable doubt based on expert declarations, e.g. from Carlsen. Courts are not the best place for deciding mathematical truths.

If I had to bet money on chess being a win for white, draw, or win for black, all three giving equal payouts, then my money would be on chess being a draw. This bet seems very safe. (Still, I might lose the bet.)

The question is how do you define a perfect game.

Even if white is winning then from my point of view the number of moves is also important and losing in 50 moves is clearly better than losing in 3 moves so the fact that there is no forced mate in 3 from the opening position means that 1.e4 f6 2.d4 g5 3.Qh5# is not a perfect game.

I understand that you do not care about the number of moves but I care because practically usually if the number of moves is bigger there is a bigger probability that the opponent is going to blunder.

[syzygy]

Example it must be clear that a weak solution of a game is less than a (rigorous mathematical
proof, otherwise there would not be a definition of s 'strong solution' of game (more brute
force, and establishing with more certainty, ie more like a rigorous proof.

Did you not read the definitions of "weak" and "strong" solution at all?

Weak: strategy achieving the game-theoretic outcome from the initial position.
Strong: from any position.

[syzygy]

If the initial position of chess is a draw, then I am fairly sure that many engine-engine games, in particular the most boring ones, have only perfect moves, i.e. moves which preserve the game-theoretic outcome.

If the initial position of chess is a win for white, then 1.e4 f6 2.d4 g5 3.Qh5# may well be a perfect game.

The question is how do you define a perfect game.

In the context of "solving" chess, there is no requirement of a shortest (or longest) solution. A win is a win, a draw is a draw, a loss is a loss.