Is Chess Something We Can Solve?

that requires invariants, which have not been discovered yet for chess positions, and currently it doesnt look like they will ever discover them. invariant manipulation is the "game knowledge" that occurs in other game solution proofs that aren't complete game trees.

an invariant is a property of a system that remains provably constant (or extremely predictable) after certain functions are applied to it. (technically the term is only really supposed to be for the constants but the application is the same for 'extremely predictable' that it essentially functions as an invariant would, and in fact one could call the prediction function itself an invariant)

im going to simplify/give a specific case for what an invariant would have to look like for chess. it would be a simple evaluation function of a position (could be anything from counting the number of black squares covered to the number of pieces on the board to the number of pawns stuck) that remains constant or easily predicted, and each move played (the function) would change that evaluation in such a predictable way (most often keep it a constant) that you would show that you could trace through all relevant positions to the desired end evaluation, and how you could force your moves to follow that evaluation path.

While generally I wouldnt even think to mention this, tygxc is so uneducated and stupid that I have to add on the note that each aspect of this must be rigorously proven from the ground up. "convention knowledge and intuition dictate that this position is winning" doesnt count as an invariant.

But think, what invariant could chess even use? you cant use some sort of piece count (sacrifices for mates are all too common), you cant just count how 'in danger' the king is in, , every position has so many interactions its near impossible to begin to check to see if they could be used as an invariant in a simplification proof, and the amount of work required to check each interaction, and each function on those interactions is quite possibly the same amount of work (or more) as the game tree itself, especially considering how abstract invariants are.

tygxc has fallaciously claimed that engine evaluations, player intuition, and conventional knowledge count as the "game knowledge" used in other proofs that dont contain full trees, but this is objectively false, they are using the type of invariants described above.

Here is an example game that is solved with invariants.

a random number "n" is chosen. two players take turns subtracting positive palindromic numbers from "n" until one player reaches 0, of which then that player wins. (you cant go negative, and palindromic numbers are numbers that are the same backwards and forwards, so 11, 929, 89398, single digit numbers, etc).

given 'n', show which player (the player going first or second) has a strategy to guarantee a victory.

this is a relatively simple problem once u figure it out, so ill leave it to yall to answer it. (tbh im particularly interested if optimissed could solve it, ill give him a generous 50-50).

And check it is perfect. Complexity around 10^30.

It's like someone asserted a proof of Fermat's last theorem based on the existence of a group of people all of whom had independently made poor attempts to solve it.

There is a reason why @tygxc is psychologically incapable of answering the question of exactly how many ICCF draws were needed to solve chess (in his mind). Was it just one draw? Seems absurd. Two? Three? Forty seven? All equally absurd, including 111 and 112. Being precise about the way knowledge evolves throws light on reasoning that is simply wrong.

Games are empirical evidence and as such can only be used to modify strength of uncertain belief. If everyone learnt about Bayesian reasoning - the precise formalism for all reasoning with empirical data - it would be better.

@194

"if you let the engine play itself"
++ This shows ignorance of ICCF play. ICCF is not an engine playing itself.
It is 2 ICCF (grand)masters each with engines and data bases playing one another.

In the ICCF preliminaries, semifinals, candidates there are decisive games. That is how the finalists qualified. Even in the finals there were decisive games in previous years, now none.

The Russian players use worse hardware because of sanctions, but 4 of the 17 finalists are Russian. Thus the player has more influence than his engines.

@tygxc "logic": if the first 112 people you meet when in a new country are white, there are no black people in the country. [Honest analogy].

But he also says:

1. the fact that all the 112 games are drawn proves the result and that the play is perfect 
   AND
2. there are likely to be decisive games in future competitions.

[I observe that this would be a valid proof that the play is imperfect]

ive literally been trying to verify this and your claims are literally the only results. plus sanctions would literally not change their hardware, and the servers used would be international.

ive had my arguments against tygxc verified by literal mathematicians so at this point it is purely a psychological issue on his end.

@197

"the fact that all the 112 games are drawn proves the result and that the play is perfect"
++ Yes. The most plausible error distribution is 112-0-0-0-0.
It could be that the error distribution were e.g. 110-0-2-0-0,
but even in that case the redundancy of the solution renders it fail safe.
It is absurd that the error distribution were e.g. 60-0-52-0-0. There are arguments why some errors could come in pairs, but not all errors. It is absurd that there would be 60 games with 0 error and 52 with 2 errors and 0 with 1 or 3 errors.

Even if we have only 1 game with 0 error, that is an ultra weak solution of Chess.

It is absurd that the error distribution would be 0-112-0-0-0.
The 17 independent entities would have to collude to ensure 1 error and no more.
You could argue 1 a4 wins for white, but that defies all logic.

"there are likely to be decisive games in future competitions"
++ Yes, because of human errors, human illness, power breakdowns, floods, earthquakes, wars, wildfires, computer crashes, power blackouts...

tygxc, why arent you addressing the fact that ive had my arguments against you literally personally verified by mathematicians?

this is literally the easiest thing imaginable for you to verify if you had evidence for this tygxc, where is it?

this is literally a side question on a provably irrelevant tangent. and you still cant properly answer it?

@201

"This criticism would have been valid 10-15 years ago, but not today."
++ Take this October 28, 2022 interview with the reigning ICCF World Champion Jon Edwards:
'the key is planning, which computers do not do well'
'computer engines did not understand the main ideas and suggested in most middlegame positions that all candidate moves were equivalent'
'Too many tournaments, even strong tournaments, are decided by human error when making a move. I thankfully managed to avoid clerical errors throughout the entire process.'
'it’s not just about the hardware, but also about one’s ability to make the most of the hardware'
'a sequence that no computer would consider or find'

your quotes, taken out of context, STILL literally contradict your argument lmfao.

"Is it possible to play top-level, international correspondence chess without a powerful computer?

Not today! To me that’s like asking if you can play effectively in the National Football League without a helmet. I have two servers, each capable of calculating more than 90 million positions a second."

and the 'a sequence that no computer would consider or find'

the reason why the sequence isnt considered is falsely implied by tygxc to be because the human was better at finding that type of sequences. this is false. if you read the interview you'll find that the sequence had literally the same ending as the normal computer ending, and in addition, the sequence was found by a computer using a varied parameter of search. hes saying 'no computer would find' in the context of a computer seeking optimal play/efficiency rather than just trying to extend the game.

"It should be noted that the lack of decent equipment is being felt quite notably in Russia, where embargoes have limited access to new hardware and the latest chess tools. As a consequence, the Russian team finished near the bottom of the standings in the last Correspondence Chess Olympiad"

quite contrary to tygxc's claims, huh, but at least he wasnt outright lying this time.

So now, you're not a mathematician?

what's the answer opti?

But don't post the answer just yet. @Optimissed might like to work on it (and so would I).

I suppose following these "invariants" it might be possible to show you cannot force a bare king with sufficient mating material on your side?

This wouldn't prove that chess is a draw; but it would prove that chess is either a draw or a middlegame checkmate, which I think is an achievement. Especially since I think most people who think chess is a win for white imagine them winning in an endgame scenario.