Chess will never be solved, here's why

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tygxc

#2918
""towards a full solution""
++ That is not what Sveshnikov wrote. He wrote:
"I will trace all variations from the opening towards tablebases and 'close' chess."

tygxc

#2919

"What??"
++ It is a deep insight. It may be surprising at first, but it shows how well he understood chess.

"As a mathematician I point out that it is necessary to deal with all 20 opening moves for white, with over 400 opening variations after 3 ply and so on."
++ I disagree.
"weakly solved means that for the initial position a strategy has been determined to achieve the game- theoretic value against any opposition" - Prof. em. J. van den Herik.
'Any opposition' does not mean 'any move': the move must oppose, i.e. resist against, achieving the game-theoretic value.

playerafar

Mistake here:
from this post:  https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?page=146#comment-68810283
"Also, as an aside, it often turns out that people disagreeing with me are wrong to do so, because I have a good general knowledge and the intelligence to use it well."
Again - from the same person.  happy.png
Has anybody in this forum ever fallen for this kind of assertion?

playerafar
Elroch wrote:

Seems your problem is lack of understanding of what a proof is.

This term does not have a place in science or any empirical subject. A proof never involves inductive reasoning. Never.

The word "proof" not have a place in the application of statistics, except in the trivial sense that an example of something proves the existence of an example with its properties.  For example you can never prove that all humans are less than 2.X meters tall by examining a random sample of N humans. No clever statistical argument will exclude the possibility of a counter example you have not seen.

Proof does have a place in the theoretical foundation of statistics, but here it only involves deductive reasoning about abstract concepts, starting with axioms.

"Seems your problem is lack of understanding of what a proof is."
That was addressed to @tygxc I believe.
Who can always counter with the phrase: 'weakly' solving.
By invoking the word 'weakly' - he can and does and will continue to circumvent issues of 'proof'. 
Then - the issue might become semantics of the phrase 'weakly solving'.
The definition of which isn't Ordained anywhere.
"Weakly solving" could be anything that anyone or his grandmother wants it to be.

And we had:

Elroch
 
8 hrs ago
 
 
 -1 

There is no excuse for you ignoring the posts where people corrected your entirely unreliable assumptions. It's dishonest.

There is some validity in what Elroch is saying there.  
But there's this next too:

"As for 'weakly solved' - that could mean almost anything."
Then there was this reply from @tygxc :

++ No, Prof. Em. van den Herik has defined it precisely:
"weakly solved means that for the initial position a strategy has been determined
to achieve the game-theoretic value against any opposition"

Whatever den Herik's credentials are does not make him Ordainer of what a definition of something is to be for anybody else.
It does not make him Creator of dictionaries not that dictionaries should be regarded as bibles in any case.  
Nor does a mini-religion need to be made out of the subject of 'solving' chess.

But looking at ty's post a little more ...
ty is claiming 'has defined it precisely' ...  suggesting that it is for him @tygxc to decide what is 'precisely' and also that 'weakly solving' would have a Unique definition.  Which doesn't follow.  
If the forum title had been 'chess will never be Weakly solved' - then people could disagree right away and even claim chess was 'solved' 100 years ago with no computers necessary.
Coming up on 3000 posts - is the discussion to revolve around semantics of the word 'weakly'?
But other things have come out though - like the two positions that computer engines are erroneously assigning as wins.
That most players would find to be draws.  And quickly find to be.
Which is a crippling blow to computers 'solving' chess happy.png
(and the reply could almost be predicted 'such positions would not come up in 'normal reasonable' chess' with attempted linkages with 'weakly' and ven den Herik ' ...


haiaku
tygxc wrote:

[ . . . ] So weakly solving chess benefits from incorporating the accumulated knowledge of Capablanca, Fischer, Sveshnikov and others: Steinitz, Lasker, Lucena, Philidor, Kling, Troitzky, AlphaZero.

I have never denied that; the problem is how and how much you rely on that "knowledge" to solve chess.

As for ICCF WC games I have demonstrated that 99% of ICCF WC draws are ideal games with optimal moves, i.e. perfect play.

As I said, you are the only one who thinks you have demonstrated such a thing.

Prof. Em. van den Herik has defined it precisely:
"weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition"

The problem is the meaning you give to that "any opposition". I provided a paper that explains clearly what authors think is the meaning of that definition. I asked you to provide a paper where van den Herik's definition is interpreted in your way.

So everybody who disagrees with your view has neither sense nor understanding?
It is rather the opposite: those who do not understand the numbers or processes that would need to be involved believe it is not possible and then present their belief as knowledge.

You have used the very same argument you criticize, even in the very same post now.

"you can never prove that all humans are less than X meters tall by examining a random sample of N humans."
++ We disagree. We can prove that of 8 billion humans none is taller than 3 m by measuring only 1 million of them.

If you lived in Europe before 1790 you would have concluded that black swans did not exist. You even contradict yourself:

tygxc wrote:

"No number of experiments can prove me right, one can prove me wrong" - Einstein

As for your theory as a whole, science is based on agreement: if someone says s/he is scientific, while everybody else thinks the opposite, s/he can be a misunderstood genius, a fool, or someone who tries to deceive people to gain some kind of advantage (or even just for the hell of it). We can try to fight disinformation as we can, but it is not even our responsibility to prove you wrong; that's an argument used by pseudoscientists. The burden of proof is on the claimant and what you call proofs are not proofs for our standards, nor you can prove they are for scientists' standards outside this thread, because you said you have not published anything on the subject. There cannot be with you any real discussion about a theory to provide a proven solution for chess, if there is not even agreement on the criteria to prove something.

playerafar

"There cannot be with you any real discussion about a theory to provide a proven solution for chess, if there is not even agreement on the criteria to prove something."
I agree with @Haiaku on that - and I"m thinking that @tygxc doesn't intend to change his mind about any of this ...  happy.png
but on the other hand the posts of @tygxc have been catalysts for other things.
Various things coming out about subjects related to 'solving'. 

haiaku
Optimissed wrote:

This assumes that the discussion is regarding deductive proof, which is normally taken to be the meaning of "proof" within mathematics and the pure sciences.

Within applied sciences and engineering, maybe a different perspective is possible.

We don't know all the laws of physics, nor the exact structure of the universe, so theories about it are just more or less accurate models. They are in fact approximations and scientists have understood that long ago. You know that QM and GR do not explain everything and likely they will be superseded, as others theories before.

But solving chess is another thing. We know all the laws (the rules) of the game and its structure (64 squares, 32 pieces...), and the number of positions and possible games is finite; thus an exact solution must exist. When a game is announced weakly solved (in the game-theoretic meaning), nobody really expects that some day that solution will be falsified. The only way to be sure of that is to test a strategy (which provides a move every turn) against all the possible opponent's replies, or to provide a general theorem (even by mathematical but only mathematical induction) that encompasses all the possible situations a player can face along the path, no exception. The latter seems impossible, considering the game complexity, so a solution has to rely on computations to provide the first type of proof. Heuristics provide strategies to be tested in an ordered fashion (so e.g. if a strategy wins from a position, no need to search for something better), but if they cut off lines according to a non exact evaluation (that is, not a tablebase hit or a 3-fold repetition), the strategy is not 100% reliable. The greater the number of non-exact cutoffs, the greater the risk the "solution" will be falsified later.

DiogenesDue
Optimissed wrote:

But solving chess is another thing. We know all the laws (the rules) of the game and its structure (64 squares, 32 pieces...), and the number of positions and possible games is finite; thus an exact solution must exist.>>

No, I don't think it exists and any proof it exists is also an inductive proof.

What does "no, I don't think it exists" even mean?  That you do not believe a solution can exist?  That you disagree that a full 32-man tablebase would be a valid solution if it were ever achieved?

The point is valid.  Every discrete piece of knowledge needed to solve chess and a valid method for solving it already exist, the solution is just not achievable until some pretty large breakthroughs that will likely not occur in our lifetimes are made.  What you are saying is like saying that is is impossible to count the grains of sand on a beach...but it *is* quite obviously possible, just entirely infeasible at present.

MARattigan
btickler wrote:

...

That you disagree that a full 32-man tablebase would be a valid solution if it were ever achieved?

...

I would say that the method of constructing the tablebases is already a solution. The tablebases don't actually need to be constructed. We have in fact always had a solution of chess.

That's why I inserted the word "timely" in my definition of a solution. 

For example the checkers solution needs about two minutes to return a move, so it wouldn't be much use in a ten minute blitz game (if they have such things in draughts). 

Asking someone to go through the 32 man tablebase construction process similarly wouldn't be much use in a ten minute blitz game of chess.

A solution is only a solution if it's timely for the purpose for which it's required.

haiaku
Optimissed wrote:

I also disagree with the idea that <<an exact solution must exist>>.

It's Zermelo's theorem in game theory. So if the game value is a win, a win can be forced, otherwise both players can force a draw.

playerafar
btickler wrote:
Optimissed wrote:

But solving chess is another thing. We know all the laws (the rules) of the game and its structure (64 squares, 32 pieces...), and the number of positions and possible games is finite; thus an exact solution must exist.>>

No, I don't think it exists and any proof it exists is also an inductive proof.

What does "no, I don't think it exists" even mean?  That you do not believe a solution can exist?  That you disagree that a full 32-man tablebase would be a valid solution if it were ever achieved?

The point is valid.  Every discrete piece of knowledge needed to solve chess and a valid method for solving it already exist, the solution is just not achievable until some pretty large breakthroughs that will likely not occur in our lifetimes are made.  What you are saying is like saying that is is impossible to count the grains of sand on a beach...but it *is* quite obviously possible, just entirely infeasible at present.

Of course its valid.  
The logic of the point is valid. 
The number of possible chess positions is finite - therefore a solution exists.
Where whoever might go wrong on that - is to believe that since a solution hasn't been found - 'it doesn't exist' ...  that is illogical.
A solution can exist - before it is found.
Claiming its not so is similiar to the error claiming a tree falling in the forest 'doesn't make sound' unless someone is around to hear it.
Of Course the falling tree makes sound Anyway !   happy.png

"Mathematics"  doesn't care if something hasn't been found yet.
The ratio pi is the same too - whether there's people around or not.
That ratio doesn't need people around - to be the ratio of the circumference of a circle to its diameter.

Regarding those who don't understand - they're ignoring the significance of the 'finite' part. 
Not grasping the nature of that fact.
But that's their choice. 
There are no 'Thought Police'   happy.pnghappy.png

Can anybody do somebody else's thinking for them?
The short answer is no -
but to understand the nature of 'finite' there ...
consider hypothically if there were 'infinite' chess positions - then in that imaginary case it could be argued that chess could never be solved because there would always be more positions to solve.
By itself would that be enough to prove the converse?
Not quite.
But the point about finite - (this is a hint - since there's no 'Vulcan mind meld') ...  is that eventually - given enough time - positions to solve would be 'run out of'.   
Can semantics of words like 'inductive' substitute for mathematical reasoning and logic ?
People who try to use semantics alone to reason - might run into errors of illogic.
Often it occurs that people who excel in subjects like English and History - do poorly in math. 
English and history would be considered 'humanities' I believe.
Does it matter?  Chess is a subject of leisure I'd say - not of necessity.

playerafar

Invalid claims do get attention though.
That part works.  happy.png
And illogic is more entertaining than logic.
Hollywood exploits that all the time !

tygxc

#2925

'"Towards" tablebases literally means towards a full solution.'
++ I interpret is as starting from the opening and working towards i.e. in the direction of the 7-men endgame table base, as opposed to strongly solving chess by generating 32-men table bases starting from the 7-men endgame table base and working towards i.e. in the direction of the opening.

'I'm trying to be generous to Sveshnikov but I must admit "and 'close' chess" sounds very much like your interpretation.' ++ Yes, I think so too.

"In that case it was clearly an empty claim, which he would never have been capable of carrying out: and so you've chosen to believe a completely empty claim."
++ I do not think it is an empty claim and certainly not clearly. I believe he could have carried it out given the modern computers and the good assistants. 

"I wonder why you imagine he could have done it."
++ I admit when reading it first I found it hard to believe, but after thinking more and checking some facts & figures I believe he was spot on.

"Bobby Fischer made various claims, which tended towards subjectivity, such as the "best by test" garbage."
++ Most of Fischer's claims turned out right too. Apparently the participants of the Yekaterinburg Candidates' also believed his "1 e4 best by test": 1 e4 was both played more and with better results than 1 d4, 1 c4, and 1 Nf3 combined. Also 'the King's Gambit loses by force' was vindicated by AlphaZero and Kramnik.

"As well as holding various political opinions, which were rather off the rails."
++ Political and religious beliefs do not disqualify opinions on other subjects. A good example was Nobel prize winner Schockley. Alekhine and Karjakin are other examples.

"Sveshnikov's claim is not a chess-related claim at all."
++ It is a chess-related claim, it is about chess analysis, that was his job.

"It's a computing-related one."
++ No, it is not computing-related. His 'good assistants' should be grandmasters or even better ICCF grandmasters, skilled in chess analysis with engines. They must use the engines, not create them. The good assistants must understand chess so as to prepare the 26-men tabiya for calculation and so as to halt calculations when a known drawn endgame of >7 men is reached, like the 2 ICCF WC example games I posted.

"He is/was not a particular expert in computing"
++ He was an expert in chess analysis. He was so before engines existed, and he still was so after engines emerged. We won the world senior chess championship. He wrote the ultimate books on the Sveshnikov Variation, the Kasashnikov Variation, the French Advance Variation, and the Alapin Variation.

"otherwise he would not have made the false claim"
++ This is a circular reasoning. You think his claim is false. Because you think so you consider the claim false is true. Because of that you conclude Sveshnikov was no expert. I turn this the other way. Sveshnikov was an expert at chess analysis with and without engines. Therefore his claim is true. Therefore you are wrong dismissing his claim. Therefore you are no expert at chess analysis.

"You see, you have managed to persuade me that he probably did make the false claim. I had assumed he didn't."
++ Now comes the second part: managing to persuade you that his claim is not false and thus you were right assuming he did not make a false claim.

Elroch

I have great respect for Sveshnikov as a chess player and researcher. I have no fewer than three full length books on the Sicilian variation he breathed new life into. As for the ageing Sveshnikov as computational game theory researcher, well, he just doesn't cut it. He has no publications and no background of the sort of formal discipline needed. He is 100% focussed on the competitive game and practical chess to the extent that he seems even to be unable to realise that more rigour is required in game theory.

My understanding of the character of his viewpoint is that he reckons that past experience of chess, consisting of large numbers of games not a single one of which is KNOWN to be optimal is sufficient to ignore the move 1. a4 as inferior.  This is ok for practical chess but entirely inadequate for game theory. There is no room for compromise. To prove chess is a draw it is NECESSARY to PROVE black can draw against 1. a4, not just assume this without anything close to an adequate argument.

[Note: sadly Sveshnikov died in August 2021 from complications of Covid-19. He will be long remembered and respected as a chess player and writer].

tygxc

#2930
'the problem is how and how much you rely on that "knowledge" to solve chess.'
++ IMHO the knowledge cannot be incorporated into an evaluation function: we know from Stockfish vs. LC0 that thin nodes i.e. deep calculation with a lean evaluation function beats thick nodes i.e. shallow calculation with an elaborate evaluation function. 
IMHO knowledge should be incorporated by the 'good assistants' to prune the search tree. They should prepare the relevant 26-men tabiya for calculation. They should prune known inferior possibilities like 1 a4 or 1 e4 e5 2 Ba6 and handle transpositions. They should also stop the calculation when an known drawn endgame of > 8 men is reached, like with opposite colored bishops or rook endings 4-4 or 4-3 on one wing.

"you are the only one who thinks you have demonstrated such a thing."
++ OK, let me be the only one. Let all others then come up with another way to explain the available data.

"If you lived in Europe before 1790 you would have concluded that black swans did not exist." ++ It is impossible to prove non-existence of unicorns, Martians, the Loch Ness monster etc. However statistics is extensively used in many sciences and in industry to draw conclusions about a larger set by sampling a subset. That is also what Tromp did to arrive at his 10^44 legal chess positions.

As for your theory as a whole, science is based on agreement: if someone says s/he is scientific, while everybody else thinks the opposite, s/he can be a misunderstood genius, a fool, or someone who tries to deceive people to gain some kind of advantage (or even just for the hell of it).
++ The everybody else (or rather the other 5) may also be unscientific, fools, or people who try to deceive people to gain some kind of advantage (or even just for the hell of it) or people unable or unwilling to accept certain facts & figures. E.g. while that would lead to a conclusion they dislike. 'I do not want chess to be solved.' -> 'Chess cannot be solved.' -> 'Whoever says differently must be unscientific / a fool / a deceptive person / a liar / an autist.' -> 'Whatever he says must be obviously / clearly / blatantly wrong / a lie / ridiculous...'

"it is not even our responsibility to prove you wrong"
++ It is not my responsibility to prove anything either. I try to the best of my abilities. People can claim without proof. "Chess is a draw", "1 e4 best by test", "King's Gambit loses by force" are Fischer's claims without proof which I believe to be true.

"The burden of proof is on the claimant"
++ The claimant GM Sveshnikov is dead. I kind of load his burden on my shoulders.

"what you call proofs are not proofs for our standards, nor you can prove they are for scientists' standards outside this thread" ++ Assessing the feasibility does not require any proof in the purist sense: plausibility is enough.

"you have not published anything on the subject" ++ No, I have not and I do not intend to. I have never worked in the field of game theory and do not intend to.

"There cannot be with you any real discussion about a theory to provide a proven solution for chess, if there is not even agreement on the criteria to prove something."
++ In this thread there is no agreement on anything: not on definitions, not on the meaning of words in a dictionary, not on facts, not on figures, not on the Laws of Chess. This is a public forum free for all, it requires no scientific degree or chess rating.

playerafar

@MARattigan
Your post #2949 is apparently a response to my post #2945
a few before.
This one:  https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?cid=68837185&page=148#comment-68837185
A main point about that post of mine was about the relevance of 'strong' to weak.  Strong mathematics.  Exact mathematics.
I brought up the relevance of 13 to the 64th power much earlier in the forum.
That and factorials for ways to have 32 squares empty got a good reception.
The relevance of 'strongly solving' is not just as part of the whole process.
Its also relevant for the purpose of contrast.
To understand what is being done with 'weak solving' by comparing with thorough solving.  Obvious relevance.  'Meaningfulness'.
Also called 'the big picture'.  'View from the balcony'.  

Elroch
tygxc wrote:

 They should prune known inferior possibilities like 1 a4

This is an error. You confuse knowing something and believing it because of woefully incomplete and imprecise evidence.

Like a poor chess player making the same error time and time again, you will surely continue to make this error. The above is of course not a chess error: it is an error about reasoning in game theory.

There isn't even a lot of evidence on the move 1. a4. This is itself because of belief, not because of knowledge. People believe it to be pragmatically inferior (quite a different thing to game theoretic inferiority. Most likely, 1. a4 is an optimal move leading to a draw (IMHO)).

Don't get me wrong, it is a good bet that 1. a4 is not better than 1. d4 (say). It would be fair to ascribe a low probability to it being better. But it is no more genuine knowedge than you can have knowledge that a very good horse will win a race.

playerafar

Yes - but there is reason to believe that @tygxc will not concede that error nor any other error he's making.
But its a paradox because he keeps it civil.

Elroch

Not really a paradox. Just often not so in such circumstances!

MARattigan
playerafar wrote:

...

Now:
"That is also what Tromp did to arrive at his 10^44 legal chess positions."
'arrive'. 
Sure?  Should anybody care what 'Tromp did' if it doesn't begin with straight Math ?

It does.
Regarding 'weakly' solving - that process can still begin with straight mathematics.
First upper bound:  13∧64.
Explanation:  Every square on the chessboard can have up to 13 states -
there are 64 squares ... so the first upper bound is 13 multiplied by itself and raised to the 64th power.
Which is approximately 2 x 10∧71  
A  71 digit number. (72 digit number.)
(I'm looking on google now to see if there's a way to type 'superscripts' in Windows 11 and also algebraic x)

That gives the number of diagrams in which the types of piece defined in art.2.2 of the FIDE laws occupy unique squares and no square is occupied by more than one piece and there is no requirement that the diagram can occur in a legal position.

I mean by "legal position" a situation that is not an illegal position as defined in the FIDE laws by 

Art. 3.10.3 A position is illegal when it cannot have been reached by any series of legal moves.

That is distinct from what would usually be meant by "legal position" in the absence of art. 3.1.3, viz. a situation that can legitimately occur during a game. This, for example is a diagram that could, and often does legitimately occur in a game


but not in a legal position if "legal position" is taken to mean the opposite of what FIDE defines as an "illegal position", because the starting position has no pieces that do not occupy squares and a legal move never results in a piece that was occupying a square finishing in a position on the board where it doesn't occupy a square.

Tromp's number takes into account that both players can have the move, whether an en passant capture can be made, whether castling rights exist and whether the diagram and the other attributes mentioned could simultaneously occur in a legal position in a game played under basic rules. That would determine what further play can legitimately occur under basic rules. In particular it would determine the game tree under basic rules if each node in the tree represents one of Tromp's "positions". (Strictly speaking, what pieces have been touched by the player having the move, whether a draw has been agreed and whether anybody has resigned are also necessary as well as further information about arbiters and clocks and whether both players have turned up.)

So does Tromp have a different idea of the meaning of "position" from you?

For a game played under competition rules the attributes mentioned above are not sufficient to determine what further play can occur, and therefore don't determine the game tree under competition rules (@tygxc's search space with his last definition of the game he wants to solve).

Would you have the same idea of "position" under basic rules and competition rules?

What, in short, do you mean by "position".

...