New Ways To Solve Chess

[syzygy]

Neither method is anywhere near solving chess - but they would be if they had received the effort and competition that selective search and AI training has.

Neither paper has anything to do with solving chess. The second paper has nothing to do with chess at all. The first is just an attempt to define a measure of "fragility" of a chess position, apparently by somehow counting the number of ways in which pieces attack and defend each other. The paper does not do anything with this measure other than presenting some statistics collected from some games. This paper gets just as close to "solving chess" as the primitive evaluation of chess positions proposed by Turing.

The two methods presented both have more potential to solve chess in polynomial time than current methods.

Absolutely not. (And this is not criticism of the papers because the papers don't claim anything like that.)

Look, I know how to read a paper. I understand what I am reading. You apparently do not. This is not a discussion worth having.

And "in polynomial time" is totally meaningless when talking about solving 8x8 chess.

If you mean solving generalized NxN chess in time polynomial in N, then it has already been shown that this would imply P=NP, which is (1) unlikely to be true, (2) certainly not approachable with any "method" discussed in those two papers.

It's even worse than that, since generalized chess is EXPTIME complete, so not even P=NP would help. It has already been attempted to explain to him what implications this has, but the attempt was apparently not very successful.

viewtopic.php?p=961574#p961574
viewtopic.php?p=962478#p962478

Yes, I guess verifying a solution is about as bad as finding one (a non-deterministic machine basically gives you optimal move ordering).

I had this discussion with him before as well:
viewtopic.php?p=859438#p859438
After that I usually manage to ignore his posts.

[syzygy]

Neither method is anywhere near solving chess - but they would be if they had received the effort and competition that selective search and AI training has.

Neither paper has anything to do with solving chess. The second paper has nothing to do with chess at all. The first is just an attempt to define a measure of "fragility" of a chess position, apparently by somehow counting the number of ways in which pieces attack and defend each other. The paper does not do anything with this measure other than presenting some statistics collected from some games. This paper gets just as close to "solving chess" as the primitive evaluation of chess positions proposed by Turing.

The two methods presented both have more potential to solve chess in polynomial time than current methods.

Absolutely not. (And this is not criticism of the papers because the papers don't claim anything like that.)

Look, I know how to read a paper. I understand what I am reading. You apparently do not. This is not a discussion worth having.

And "in polynomial time" is totally meaningless when talking about solving 8x8 chess.

If you mean solving generalized NxN chess in time polynomial in N, then it has already been shown that this would imply P=NP, which is (1) unlikely to be true, (2) certainly not approachable with any "method" discussed in those two papers.

Both methods go to fundamentally new ways of getting big picture information about chess, and either method would, if had been studied and competed like selective search, have got us closer to a final solution than other methods (unless you want to make the case that chess is now solved because it's no longer possible to win a game in correspondence time intervals). If there's a criticism to be made here, it's that the title should have been "Potential New Ways To Solve Chess".

You just keep repeating an empty statement, I suppose because you are unable to go into an actual argument (perhaps you do not even recognize an argument, it's a foreign concept to you?).

As I have already explained to you, the first paper just calculates a value for a position based on the number of pieces that attack and defend each other. This is what hand-crafted evaluation functions have been doing since forever. Please explain how such a concept could possibly help "solve" chess.

The second paper is not about chess at all. It is about "evolutionary games", which chess is not. Please explain how the second paper could possibly help "solve" chess.

Your P=NP argument is false.

Let's go back first to your "in polynomial time". What do you mean by it? Do you have any actual idea of what it means in this context? Please explain,

And please do not bother us with more irrelevant LLM slop.

[towforce]

It's even worse than that, since generalized chess is EXPTIME complete, so not even P=NP would help. It has already been attempted to explain to him what implications this has, but the attempt was apparently not very successful.

viewtopic.php?p=961574#p961574
viewtopic.php?p=962478#p962478

Thank you for those references - it will save anyone from having to go through the proofs again.

As you can see, I have read the papers, and I have stated in a straightforward way what is proven and what isn't. I'll restate that here:

What IS Proven

As the size of a chessboard increases, the time it takes to play the game increases exponentially (it takes a lot more moves to do something that you can do when the opponent is trying to stop you).

Why do you talk ambiguously? Let me quote the abstract of the paper (that you had cited in the past).

A. S. Fraenkel and D. Lichtenstein. Computing a perfect strategy for nxn chess requires time exponential in n. J. Combinatorial Theory, Series A 31, 199-214 (1981).

Abstract: It is proved that a natural generalization of chess to an n x n board is complete in exponential time. This implies that there exist chess positions on an n x n chessboard for which the problem of determining who can win from that position requires an amount of time which is at least exponential in sqrt(n).

The "implication" (their choice of word) is implicitly based on the idea that the only way to determine who can win is to play out all possible games from the current position. This is based on the fact that all the paper actually proves is that the game becomes longer at an exponential rate as the board size increases - and hence from most positions it will take more moves to get to a position in which the outcome is clear to a strong human player. There are, however, many positions in which a GM will know which side is going to win without having to generate such a proof, and hence there will be many more positions (very likely all of them) where it is possible to know as well.

What IS NOT Proven

There is no proof (nor even any hint of evidence) in the referenced papers that it is not possible to construct an algorithm that solves chess in a reasonable time on a cheap computer.

Not responding to this since you are not stating your claim precisely. First let us know if you are talking about 8x8 chess or nxn chess. Then also clarify what is reasonable time and cheap computer.

8x8 chess (because otherwise you could go to any size of board). An example of a cheap computer is the The Acer Chromebook Plus Spin 714.

[towforce]

In short: The brain behind the text is towforce; the editor was likely an AI.

You've invested a lot of time and bandwidth to come to a very silly conclusion. I don't write posts and then ask a chatbot to rewrite them. When I use a chatbot:

1. I tag then text that's written by a chatbot

2. It's done to provide a concise and accurate summary of valuable information in a video

Your comprehension skills are not good.
The allegation is that: "Towforce provided the specific prompts/ideas: "Write about Topological Data Analysis and Graph Theory (betweenness centrality) applied to chess, mentioning the Google PageRank and Italian families analogy."

You didn't write any text, you gave an AI a leading prompt and the AI wrote the text. Then you present it as if you wrote it. But that falls flat because it uses words and language structures way above your pay grade and understanding. Why you behave like this is fathomable. Attention seeking.

I've proved that to be incorrect: the top AI text detector (which I linked) stated that my text (the OP) is 99% certainly written by a human.

The AI text detector is correct. You are wrong.

Pfff. A selected AI proves NOTHING. Do you know what a PROOF is, actually? Disingenuous, as ever. To repeat, I asked the AI: "I ran your post through an AI and asked it to compare towforce other talkchess posts and comment on whether the towforce entity wrote it himself."

Not asked if AI wrote it, asked if YOU wrote it by comparing to your other talkchess posts. The AI wasn't asked if an AI wrote it, no leading question was posed.

The AI responded: Likely assisted. The prose is too "perfect" compared to his other 2,000+ posts on the forum. It lacks the "human noise" (slight repetitions, informal phrasing) present in his live discussions.

Then the AI added: Comparing this text to his broader body of work, the most likely scenario is Human-Directed Synthesis:.Towforce provided the specific prompts/ideas: "Write about Topological Data Analysis and Graph Theory (betweenness centrality) applied to chess, mentioning the Google PageRank and Italian families analogy."


So, who wrote it? Obviously not you, the terminology and style is way above your pay grade as ani fule kno. Yet the post has your name on it, no attribution to anyone else, and now your claim that "a human" wrote it. Which human? Which human can you freely plagiarise without attribution? Which human is going to write such discombobulated nonsense anyway? An prompted AI, very likely. An expert with some knowledge/experience, highly unlikely? Please do tell.

Everything in the above post has already been asked and answered.

[towforce]

I had this discussion with him before as well:
viewtopic.php?p=859438#p859438

From that post: "The whole point of referring to this paper and such results in general is that it shows that in general there is no quick way to solve games like chess."

That statement is plain wrong. It shows that there's no quick way to solve it by reduction - and that is the absolute limit of what it shows.

[chesskobra]

Thank you for those references - it will save anyone from having to go through the proofs again.

As you can see, I have read the papers, and I have stated in a straightforward way what is proven and what isn't. I'll restate that here:

What IS Proven

As the size of a chessboard increases, the time it takes to play the game increases exponentially (it takes a lot more moves to do something that you can do when the opponent is trying to stop you).

Why do you talk ambiguously? Let me quote the abstract of the paper (that you had cited in the past).

A. S. Fraenkel and D. Lichtenstein. Computing a perfect strategy for nxn chess requires time exponential in n. J. Combinatorial Theory, Series A 31, 199-214 (1981).

Abstract: It is proved that a natural generalization of chess to an n x n board is complete in exponential time. This implies that there exist chess positions on an n x n chessboard for which the problem of determining who can win from that position requires an amount of time which is at least exponential in sqrt(n).

The "implication" (their choice of word) is implicitly based on the idea that the only way to determine who can win is to play out all possible games from the current position. This is based on the fact that all the paper actually proves is that the game becomes longer at an exponential rate as the board size increases - and hence from most positions it will take more moves to get to a position in which the outcome is clear to a strong human player. There are, however, many positions in which a GM will know which side is going to win without having to generate such a proof, and hence there will be many more positions (very likely all of them) where it is possible to know as well.

The word 'implication' does not mean what you imagine and there is no implicit assumption that you claim. You have zero idea about what that paper has proved or not proved. You can't even see that GMs knowing the outcome of some positions is irrelevant to the result. You think authors spend months and years figuring out that game becomes or can become longer and longer as the board size increases? Yeah, not easy to prove that. Do you think "exponential complete" means it takes exponential time to complete the game? That is the only phrase in the abstract that would explain your understanding.

[towforce]

As I have already explained to you, the first paper just calculates a value for a position based on the number of pieces that attack and defend each other. This is what hand-crafted evaluation functions have been doing since forever. Please explain how such a concept could possibly help "solve" chess.

Maybe it won't - but betweenness centrality, as explained, is very different from an attack table, and yields more valuable information - so:

1. Maybe looking at it more closely will yield more breakthroughs

2. It shows that there are aspects of the mathematics of chess to be uncovered

The second paper is not about chess at all. It is about "evolutionary games", which chess is not. Please explain how the second paper could possibly help "solve" chess.

This is all explained in the original post: persistent homology provides a way to uncover shape in noisy data of many dimensions - which is a good basic description of chess.

Your P=NP argument is false.
Let's go back first to your "in polynomial time". What do you mean by it? Do you have any actual idea of what it means in this context? Please explain,

The same as everybody else who uses the expression.

And please do not bother us with more irrelevant LLM slop.

There has been no chatbot text from me in this thread.

[towforce]

The word 'implication' does not mean what you imagine and there is no implicit assumption that you claim. You have zero idea about what that paper has proved or not proved. You can't even see that GMs knowing the outcome of some positions is irrelevant to the result. You think authors spend months and years figuring out that game becomes or can become longer and longer as the board size increases? Yeah, not easy to prove that. Do you think "exponential complete" means it takes exponential time to complete the game? That is the only phrase in the abstract that would explain your understanding.

Please refer to the previous threads linked earlier in this thread. I'll summarise:

1. The chess paper claims an implication that there are positions in chess in which it will take exponential time in relation to the size of the board to determine which side will win

2. The word "imply" means "seems to" - it does not claim a proof

3. That bad chess paper relies 100% on a good paper

4. The good paper limits the exponential-in-board-size claim to showing that it's exponential to board side in proving by reduction only (using the exact words "by reduction")

5. The good paper makes ABSOLUTELY NO OTHER CLAIMS WHATSOEVER

Therefore, the bad paper's "implication" claim is overreach.

[syzygy]

The "implication" (their choice of word) is implicitly based on the idea that the only way to determine who can win is to play out all possible games from the current position. This is based on the fact that all the paper actually proves is that the game becomes longer at an exponential rate as the board size increases - and hence from most positions it will take more moves to get to a position in which the outcome is clear to a strong human player.

So you do not understand the meaning of the word "implication"!!

The proof presented in the paper is nothing like what you are suggesting.
The paper reduces a problem known to be in EXPTIME to the generalized NxN chess problem.
This shows that if an "efficient" algorithm existed for NxN chess, the known EXPTIME problem could be solved efficiently.

[chesskobra]

The word 'implication' does not mean what you imagine and there is no implicit assumption that you claim. You have zero idea about what that paper has proved or not proved. You can't even see that GMs knowing the outcome of some positions is irrelevant to the result. You think authors spend months and years figuring out that game becomes or can become longer and longer as the board size increases? Yeah, not easy to prove that. Do you think "exponential complete" means it takes exponential time to complete the game? That is the only phrase in the abstract that would explain your understanding.

Please refer to the previous threads linked earlier in this thread. I'll summarise:

1. The chess paper claims an implication that there are positions in chess in which it will take exponential time in relation to the size of the board to determine which side will win

2. The word "imply" means "seems to" - it does not claim a proof

Why don't you write to the editors of J. Combinatorial Theory, Ser. A and ask them to retract the paper since the paper is making claims without proving?

3. That bad chess paper relies 100% on a good paper

4. The good paper limits the exponential-in-board-size claim to showing that it's exponential to board side in proving by reduction only (using the exact words "by reduction")

Do you know what 'reduction' means in the context of complexity proofs?