Is there any project coming to solve chess?

[jefk]

syzygy you claim that Allis (1) and vd Herik both agree that ultraweak solving requires a proof.

Again, I don't think you're correct here. Both Allis (in his thesis, i looked it up although it is in
postscript) state that it is about 'determining'(the outcome) whether it is a draw or win or loss
from the initial position); they don't talk about a need for a mathematical proof.

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). Imo from the initial position in chess we can determine that the result will
be a draw beyond any reasonable (2) doubt; feel free to disagree. Maybe you will find a 'narrow' line starting with 1.a3 or so.
Well good luck But anyway, i'm out of here again, like i said (for reasons as given earlier).
Happy now ?

(1) who indeed mentioned a certain Paul Colley, only relevant Colley I could find so far only has a
Bachelors degree (and now is head of an information dpt in Berkeley)

(2) whether that's an ultraweak solution in the opinion of prof vd Herik i really don't care, i'm not interested in
nittygritty, math purists nomenclature, arbitrary definitions nor nitpicking ad in finitum. Like i already stated my
main motivation was in pointing out the need for a rule modification in ICCF correspondence chess, not in a
endless discussion with math purists about definitions. The thesis of Allis btw is pleasant reading, you
might be able to learn from that, as you -contrary to Victor Allis- don't have a Phd (whereby as an IP 'lawyer' i would suppose you
would be able to understand what the definition of a definition is. Anyway, i have 'determined' the definition
of an ultraweak solution in game theory is not well established and although it might be subject for further
research depending on further outcomes as subsequently possibly accepted by some (preferably more) academic
professors in game theory, I decide not to use this definition anymore (because it's almost meaningless),
and while vd Herik now is almost with pension, i expect this lousy definition will not survive in game theory anyway. Amen

[syzygy]

syzygy you claim that Allis (1) and vd Herik both agree that ultraweak solving requires a proof.

They define an ultraweak solution as establishing (proving, including computing) the game-theoretic value of the initial position.

So an ultraweak solution is essentially a proof. And this is confirmed by the explanation that it could be a non-constructive proof.

Again, I don't think you're correct here. Both Allis (in his thesis, i looked it up although it is in postscript) state that it is about 'determining'(the outcome) whether it is a draw or win or loss from the initial position); they don't talk about a need for a mathematical proof.

Because they assume the reader is aware what they mean by "establishing the game-theoretic value". This is not the same as convincing yourself based on a large number of games and computer evaluations that the initial position is drawn.

Imo from the initial position in chess we can determine that the result will be a draw beyond any reasonable (2) doubt;

Fine, but this has nothing to do with "solving" the game of chess.

(2) whether that's an ultraweak solution in the opinion of prof vd Herik i really don't care

That is what I have said from the beginning: you are simply not interested in an "ultraweak solution", and that is fine. But there is no need to be upset that there are people who do care. The four-colour theorem is a theorem not because four colours suffice for any map of the earth's countries but because it has been mathematically established that four colours suffice for any possible map that fits on the sphere (or for any planar graph).

[Michel]

However, i claim that if
there is a winning strategy, then a solid Mcts search would increase after time the indication of winning chances. In chess it doesn't.

All you are saying is that there is a lot of evidence that Chess is a draw (I assume everyone agrees with this). But this is very far from a mathematical proof.

[jefk]

syzygy wrote:
"assuming that the reader understands" (?)
? (?????(*&#(*&($@#%^!??) ?!?!??!

Sigh. You may *think* what vd Herik (and at the time Allis were thinking), but this is speculating (or you are psychic maybe ?)
or wishful thinking. Vd Herik now is 76 btw and a professor in informatics/law so i don't think
he is a world authority in game theory anymore. vd Herik stated that the "terminology
was proposed by Allis to *determine* (from the initial position) the outcome of the game.
That's all. No rigorous definition at all. Just some vague talk about 'terminology''

For you apparently the word determine (not establish) implies the need for a rigorous mathematical
proof. Well i continue to disagree, and so will you probably ad infinitum. Lets say agree to disagree.

Sure it would be nice to have a more rigorous proof like for Hex to determine the game is a draw. But again
first. that is wishful thinking. Second like i already wrote, i'm not interested anymore in using this
word 'ultraweak solution' also because it's clear that there is not a clear definition. (whatever
you, vd Herik, the Pope, Terence Tao, or the spirit of the late mr Gauss Hilbert or von Neumann
may like to think). If you want a rigorous proof for a 'ultraweak solving' for a game i
suggest you draft a paper. And refer to Colley, whoever this bloke is and Allis and vd Herik.
And I also suggest send the concept for proof reading to vd Herik before he will join the
spirits of Gauss et al. Here he is:
https://www.universiteitleiden.nl/medew ... erik#tab-1

Post us his reaction, and then maybe i might come back to
this thread (but i suspect it will soon be closed).

PS now seeing also a post by a certain 'Michel' well mr Michel (real names please), first
do some reading of previous postings i suggest, before saying there is no mathematical Proof.
What kind of proof would you like to have ? Ultraweak solution maybe (LOL) or
something else maybe ? You can also suggest (like some others in that time) that Zermelo's
Game Theorem has Not been Rrigorously Mathematically Proven; i don't care. You can go and argue
with syzygy ad infinitum about non-constructive proofs and definitions of ultraweakly solving; again, i
don't care. There also is no mathematical proof that the earth is not Flat, you know.
But it has been determined that the intial position of the game of chess is a draw.
Beyond any reasonable doubt. We even might think (words of syzyg) that
chess has been 'essentially solved' (but not proven ?!?!?&!@**(^$ )
Amen and Goodbye.

[jefk]

and just before i leave, something for the math purists to think about:
I can also argue that a weak solution (like for checkers) is not a rigorous mathematical proof.
It's 'only' number crunching, and Not a Proof (*), just like syzygy admitted his endgame
bases are not proven to be 100 pct solid. Meanwhile you can check for correctness of
the claim Othello has been weakly solved, and that indeed is a useful exercise
(contrary to the repeatedly insisting on rigorous mathematical proofs when we are only
talking about solving a game, strong, weak or ultraweak, or simply determining the outcome
of the game from the initial position, from logical arguments computer science and
proof by contradiction and deduction). A few people here get it, eg Towforce, Uri Blass,
but unfortunately some negative math purists are spoiling the fun. No big deal, I
have better things to do, and may even later attempt a more complete write-up of the
story; not that i would send it to vd Herik for a Phd btw (maybe his successor in Tilburg)

(*) not that Schaeffer would give a shit, i presume and neither do I ofcourse. Amen3 and Goodbye
forever (for this thread at least, and awaiting hopefully a better hosting in the future).

[Uri Blass]

I think that even if some engine is a weak solution for chess then proving it is practically impossible today.

We agree on that. If we could prove it, then we could ultraweakly solve chess, and I do not believe that we can ever do that.

I do not know if stockfish at some 1,000,000,000 nodes per move is a weak solution for chess but even if it is not a weak solution for chess then I believe that we are very close to have a weak solution for chess simply because the draw margin in chess is relatively big,

I do not consider "1 mistake per 1,000,000 games" to be any closer to a weak solution than "1 mistake per 100,000 games". A weak solution cannot make any mistake, ever, no matter the counterplay. Given that the evaluation and search of any engine that plays chess at a few minutes per move will inevitably have holes, I do not believe that we are anywhere close to that. Draw margin has not much to do with that.

The draw margin is clearly important and with bigger draw margin it is easier to have unbeatable engine.

Not if all we need is a position where SF blunders away the draw. You just need a single line where SF misses a crucial variation or severely misjudges the position. SF may be able to hold the vast majority of positions that evaluate to -0.5 or whatever, but this is pretty much meaningless if we are talking about an engine being truly unbeatable.

Imegine a game that I am going to call chessD
when the rules are the same as chess before one side mate the opponent but mate is not the end of the game.

The target of chessD is not only to mate the opponent and after you mate the opponent you are allowed to capture the king of the opponent and do not lose but you need also to capture all the opponent pieces in order to win(otherwise it is a draw).

The draw margin of this game is bigger relative to chess and it is easier to make some unbeatable engine in this case inspite of the fact that the number of legal positions in chessD is higher relative to chess.

I think your game is less drawish since you have abolished stalemate.

No I did not aboished stalemate.
The rules is that you play by normal chess rules as long as there is no mate so stalemate is a draw.
When there is mate you do not consider it as a win but the side that made the mating move cannot lose.

In that case the game continue with the rules that capturing the king is allowed but there are only 2 possible results(win if the side that made the mating move also captured all the opponent pieces or draw if the side that made the mating move did not do it and it may be the opponent captured all of his pieces or draw by repetition or fifty move rule).

For beating stocfish we do not need only a position where SF blunders away the draw but a position that stockfish can get in a practical game and it is not clear if it is possible(I do not claim that it is impossible but even if it is possible then I believe that it is going to be impossible in a few years with some engine).

[Uri Blass]

PS you earlier wrote that in your opinion it's likely that there is a winning linend i would be the ideal person to find such line(s).

I was talking about a winning line against a deterministic engine.
Indeed I am convinced that if someone picks a deterministic engine (e.g. by limiting SF to 1 thread, a fixed number of nodes per move, a fixed size of the TT, etc.) then you will quite easily find a winning line. That winning line will work only against that particular engine.

Brief -superfluous- answer: in the past i tried that, of course, but found out there simply isn't such a line, not in the least because of the relatively high drawing margin in chess with the current rules.

But when you know that the opponent uses a particular fixed opening book, would you not be able to find a line that gains an advantage against that book?

A deterministic engine is basically a very large opening book with one move for each position. Being deterministic is a huge weakness.

I am not convinced about it.
The question is what easily means

Here is a challange
I pick a deterministic engine with fixed number of nodes per move and fixed hash tables (when you need less than X seconds of search to make a move with the relevant fixed number of nodes) and you need to provide a game that you win against the engine.

Denote the time that you need to find the win in seconds Y then it may be interesting to have Y/X for different values of X.

I believe that Y/X>10000 when X=3600
It may be too much work to produce a win when X=3600 and it may be interesting what is Y/X for smaller values.

[towforce]

A few people here get it, eg Towforce, Uri Blass, but unfortunately some negative math purists are spoiling the fun.

With an apology for repeating myself, a quick clarification: my opinion is that "chess is a draw" has been proven to a legal standard of proof ("beyond reasonable doubt"), but I acknowledge that a small number of suspects who were convicted to this standard were later able to prove that they didn't commit the crime.

[chesskobra]

He keeps repeating the phrase 'maths purists' (and now 'negative maths purists') referring to a couple of people here. But I am even challenging his empirical wisdom. All his wisdom is saying that most engine games are drawn or it is difficult to find advantage in any opening or the work on the Chinese database 'indicates that' .... He didn't answer to the comments I made regarding MCTS and its variations. I want to see concrete empirical work, with clearly stated assumptions and other details. He has repeatedly shown inability to engage in an objective scientific conversation.

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.

Also, just bringing up some empirical data on which I would like to see comments from experts. There is an opening set called HERT 500, and it has a subset of 250 lines with lower draw rate. What is interesting about HERT250 is that all these lines have Cerebellum-Score of the end positions between [-0.15;+0.29], where Cerebellum-Score is based on very deep engine analysis. I admit I don't know a lot about the work done by Stafan Pohl and others along these lines, but would like to know. For example, if anybody has intuition that HERT250 is unlikely to contain a winning line for one side, I want to know how you developed that intuition.

[jefk]

while i want to leave this thread, brief commentwhile i want to leave this thread, brief comment
which i'm unfortunately have to make in self defense:

Chess Kobra wrote

"He keeps repeating the phrase 'maths purists' (and now 'negative maths purists') referring to a couple of people here. He has repeatedly shown inability to engage in an objective scientific conversation."

who is 'he' mr Kobra, and who are you to judge my ability to engine in a scientific conversation (i'll report your post
to the moderator(s) with a request to lock this thread. This site nowadays, especially this
thread is full with toxic (and indeed negative) people hiding behind aliases and meanwhile making aggressive remarks
only clearly displaying there lack of understanding in this topic. Some skeptical thinking in science is normal, but insisting
on rigorous mathematical proofs for things which don't require such proofs is ridiculous; like i wrote, there also is
not rigorous proof that checkers has been weakly solved. For a game as Nim there is a rigorous proof, for a game
as chess this might be impossible, this doesn't mean we can't determine that it's a draw (which it is).

you also wrote:
" He didn't answer to the comments I made regarding MCTS and its variations.

well that's a lie, i did reply about MCTS (and Lco) even gave a weblink reference about WDL.

For the rest your posting about HERT, and finding winning lines shows a clear lack of understanding, like also
some others. While i may have a look at this HERT, this won't change anything, and like i said i'm intending
a more comprehensive writeup, but not here. Like i wrote, the GM repertoire opening book
series are much more important, but such facts elude people as yourself

Even then i expect many people won't understand it but that's not my problem.
That's life i guess