New Ways To Solve Chess

[towforce]

1. Topological Data Analysis

TDA is for problems where the "shape" of data contains critical information that traditional statistical or linear methods might miss. It is particularly effective for high-dimensional, noisy, and incomplete datasets: it identifies global patterns in data that do not follow simple linear trends.

In chess, it has already been used to

* identify skill classification of players without results

* classify styles of play by shape

* measure the stability of a position

* detect engine usage: engines have unique spatial distributions of pieces compared to human play


2. Graph Theory

Chess is a graph where pieces are nodes and their moves are edges. The method that has yielded the most promising results so far is "eigenvector centrality" - the same logic Google used for PageRank, and which has also been used to study which families were most powerful in Italian towns (the quality of the families connected to on the network graph turns out to be more important than the quantity). A piece with high "betweenness centrality" is pivotal because it lies on many shortest paths within the interaction network. Researchers have calculated the "fragility score" of various positions by summing the betweenness centrality values of all pieces currently under attack. A high score indicates a "tipping point" where the game is likely to transform drastically within a few moves. Fragility typically peaks around move 15–16 (ply 32), identifying the most critical moments of the middlegame. In approximately 60% of games, pawns are the key pieces with the highest betweenness centrality because they are central to the board's structure and frequently sacrificed. Knights are the next most common at 20%. Betweenness centrality is superior to simpler metrics like "node degree" (counting attackers/defenders) because it accounts for long-term consequences rather than just the next move.

Also, if we look hard at the flow network of the chess graph, we might be able to create an algorithm to identify a hidden equilibrium point, with the player that controls this "bridge" being the one that will win.


Conclusion: more and more lines of attack against chess are opening up and it's just a matter of time before she crumbles and reveals her innermost secrets to the world. Then all the people who currently say that chess cannot be solved because of its combinatorial complexity will look about the same as WWII encryption machine manufacturers look today.

[syzygy]

This seems to be another sourceless AI-generated post without any real content other than the suggestion that two old terms have an undefined applicability to chess.

[towforce]

This seems to be another sourceless AI-generated post without any real content other than the suggestion that two old terms have an undefined applicability to chess.

I ran my post through a top AI text detector (link), and it said, We are highly confident this text is entirely human. In this case, the detector was entirely correct.

Here's a relevant paper on the application of graph theory to chess: link.

Here's a relevant paper on persistent homology and the shape of evolutionary games - link.

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.

[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.

When you ask AI to find papers potentially relevant to your thesis, do not pose it questions that lead it to want to confirm your belief system.

Also read study the paper and ask yourself "do I truly understand how this is going to solve chess/fulfil my wishes"?
If you don't, then just discard it. Don't assume you are not smart enough but surely the AI must have been right.

[chrisw]

This seems to be another sourceless AI-generated post without any real content other than the suggestion that two old terms have an undefined applicability to chess.

I ran my post through a top AI text detector (link), and it said, We are highly confident this text is entirely human. In this case, the detector was entirely correct.

Bizarre. 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.

AI said:

The "Hybrid" Theory (Most Likely)
Comparing this text to his broader body of work, the most likely scenario is Human-Directed Synthesis:
1. 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."
2. An AI polished the draft: The resulting text retained his specific, unique analogies (the Italian families/PageRank connection) but smoothed out the "rough edges" of a standard forum post.
Conclusion: Did he "write" it?
Conceptually: Yes. The specific combination of TDA, eigenvector centrality, and the "Italian families" analogy is unique to towforce's specific research interests and posting history. You won't find that exact set of connections in a generic AI response unless someone explicitly fed those ideas into it.
Linguistically: 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.
In short: The brain behind the text is towforce; the editor was likely an AI.
————————————————————————————

AI slop, basically.

[towforce]

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. I agree that nobody has attempted to do this - but, per the original post, a number of interesting chess successes have been achieved with TDA.

I have not seen anyone else post about these methods (it might have been done and I missed it of course). I am keeping my eyes open for the method that will solve chess first, and working on my own method (discussed at length in many threads) as and when time permits.

I know some people think it's silly to think that chess will be solved, but it's actually silly to think that it won't be.

[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

[heroku]

Hello I have a script written in a language I call gofchess, that attempts to describe chess tactics it looks like this:

if has_fork_with_checks_and_hanging_for_only_king_evades(bishop, bishop2, king, rook) then
forall king_evades(king, king2) then
if captures(bishop2, rook_bishop3) then
if push_attacks(pawn, pawn2, bishop3) then
if captures(bishop3, pawn2_bishop4) then
if promotes(pawn, pawn2_queen) then
if captures(king3, queen_king4) then


The if keyword(Variables) then structure is fixed and used everywhere, keyword are the second part of the language defined like this:


def triple_fork_with_checks_for_only_king_evades(From, To, King, ForkB, ForkC)
move(From, To)
attack(To, King)
attack(To, ForkB)
attack(To, ForkC)
no_captures(To)
no_blocks_check(To, King)
no_push_blocks_check(To, King)


For example this keyword when defined can be used in the if then form. And the body of the definition uses builtin keywords with specific meanings, where a move(From, To) is a move happening, and attack(To, King) meaning filters To attacks King without moving anything.

The execution is about unification of variables similar to Prolog. Where in the definition Uppercase variable names are used, and if then form uses lower case piece roles, which is run against a chess position and the piece roles are bound to square names.

There is no formal specification or anything, but I hope you get the gist of how it works. I've built several iterations of this working in both Typescript and C++ very efficiently.
I could write a lot of in this language to extract the solution lines of chess puzzles (taken from Lichess DB). But the problem is as the rules get more and more, there are false positive matches, and it grows.

If you are interested in this idea, or have any constructive feedback, I am open to a discussion.

Here's the MIT License form of the engine written in Typescript: https://github.com/eguneys/hopefox/blob ... second.gof

[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.

[petero2]

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.

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