Chess will never be solved, here's why

Its a long time since I ever even considered tic tac toe ...
but regarding those two 'not a sure' statements -
I agree. 
And 'sure' anything might never be proven for white nor for black regarding white's 20 opening options because computers and software/programming might never be strong enough.

It also just occurred to me - that if computers eventually did affirm any kind of 'sure' from white's very first move - would humans even be able to understand whatever the computer 'proof' would be ? ...  Maybe.  .  But is it 'sure' ?  That would have to be proven too maybe.  If it could be.

#1434
"We have to establish exactly what "weakly solved" means"
weakly solved = providing an ideal game with proof that all moves are optimal

"We don't know which is this game-theoretic value in chess"
++ We know chess is a draw, it is not yet proven. We also know the Riemann Hypothesis and the Goldbach Conjecture are true but not yet proven.

"The fact that White has an expected score sligthly higher than 0.5 does not prove that Black can only draw, with perfect play."
++ That is right, but does not matter. Drawing is easier than winning. So first try to draw as black and try to win as white. If white cannot win, then it is either a draw or a win for black. Besides the expected score is not the only indicator: white is a tempo up so white has an advantage, but most probably insufficient to win. If chess were a win for black, then white would play to lose a tempo: moving the same piece twice.

"To understand how hazardous this kind of assumption is, think about how many positions we have seen, where one colour is a rook or a queen down: more than 95% of the times, the position is lost for that colour, but we know that there exist positions where a tactical combination, or a particular positional situation, subverts the expected result."
++ That is right and it is the reason why solving chess should not rely on some evaluation function however sophisticated. Solving chess can only rely on calculation from the opening towards the 7-men endgame table base. That is also the way Sveshnikov indicated.

You go on repeating the same statements as if we didn't read them. I said we must establish, and gave Allis' definition of "weakly solved", which is the standard (with some little variations in form, but equivalent) definition used among computer scientists. You gave your own definition, which does not define "ideal" nor "optimal" (which might be not a synonym for "best"). I hope you won't take it as an offense, because it isn't, but are you autistic, by any chance? That would explain some things.

Solving chess is a computational problem, and it falls in the field of mathematics and computer science (which are strictly related). In science "known" means "proven", otherwise we don't know; we just suppose, assume, hypotesize. If you give your own definition of everything, you can "prove" basically anything.

But you cut down entire openings from the search tree because you "know" they are inferior.

That White must lose a tempo to lose the game is still an assumption. Probably it would be an advantage for Black, but someone even says that Black has a compensation for being the second player, because he has more information about the opponent's plan. Besides, you said earlier that you know that the game is a draw, but now you say that most probably the tempo is insufficient to win for White. That's contradictory.

You could not "know" that Black cannot win, if not for the evaluation functions derived from our (and NN) incomplete experience of the game. And if you say I'm right, you cannot exclude to find one of those special cases among the openings you aim to cut down in the process.

You "know" many things that are not known to those who understand them better than you. For example, mathematicians certainly do not know that those two conjectures are true. Even those who believe that they are true would acknowledge uncertainty because it would be foolish to be certain.

There is no shortage in mathematics of things which are believed to be true ending up being proven false. Some of the greatest mathematicians have conjectured things which turned out to be false. An example is Leonard Euler's sum of powers conjecture -  that for all n > 2, there is no solution in natural numbers of the equation:

a_1^n + a_2^n + ... + a_(n-1)^n = b^n

(A strengthened form of "Fermat's Last Theorem" - itself a conjecture for 400 years)

Euler's sum of powers conjecture was proposed in 1769 and until 1966 there were no counterexamples.  (He had proven it for n=3 in 1760 - also the first step towards proving Fermat's Last Theorem).

After being tenable for almost 200 years, in 1966 one counterexample was discovered for n=5. In 1988 counterexamples for n=6 were added. Nothing is known about the truth of the conjecture for n > 5.  

#1469

Allis solved Connect Four which wins for the player going first and his definition relates to that. Part of his solution involved strategy stealing. The definition: 'providing an ideal game with proof that all moves are optimal' is not mine, but more clearly indicates what is to be done.
The 'strategy' in the other definition, what is that for chess? I see no other that strategy = providing an ideal game with proof that all moves are optimal.
"ideal" = without mistakes
"optimal" = no other move provides a better outcome

"I hope you won't take it as an offense, because it isn't, but are you autistic, by any chance?"
++ Of course it is offensive just like those calling me 'crackpot' and other insults because they diasagree and find no valid arguments. Ad hominem arguments are used for lack of valid arguments.

"'In science "known" means "proven""
++ That is not true. Provability is a higher degree of truth. Fermat's Last Theorem and the Four Color Theorem were known to be true before it was proven and so was "Checkers is a draw". Formally these were conjectures or hypothesis.
Also Relativity, Quantum Mechanics, the Big Bang are known to be true: no experiment has ever contradicted these, but not proven.
"No number of experiments can prove me right, one experiment can prove me wrong" - Einstein

"But you cut down entire openings from the search tree because you "know" they are inferior."
++ No it is not like that. White tries to win, black tries to draw. If a candidate ideal game leads to a draw, then only white moves need retracting. If it is proven that 1 d4 Nf6 draws, then it is not necessary to establish if 1 d4 a5 draws as well or not. Likewise we can apply logic. 1...a5 does not contribute to piece development or the center like 1...Nf6. So even without calculating it is evident that if 1 d4 Nf6 fails to draw that 1 d4 a5 is then bound to fail as well. So yes, these two logical principles allow to cut down the effort by a factor of 10. We are allowed to use what we know from centuries of human play and millions of human and engine games and what has been independently rediscovered by AlphaZero with no human input except the rules. The center is more important than the edge. It is good to develop pieces into play. A tempo is worth about 1/3 of a pawn. Being 1 pawn up is enough to win. In my opinion chess is solved once a draw is proven after 1 e4 and after 1 d4. To be extra sure 1 c4 and 1 Nf3 can be calculated as well. 1 a4 or 1 Nh3 are not necessary.

"That White must lose a tempo to lose the game is still an assumption."
++ No, that is not what I wrote.  If chess were a win for black, i.e. white were in Zugzwang, then white should try to lose a tempo in order to try not to lose. If 1 e4 e5 were a win for black, then white would aim for 1 e3 e5 2 e4 not only to avoid losing, but to winning.

"someone even says that Black has a compensation for being the second player, because he has more information about the opponent's plan."
++ That is correct: the information somehow offsets the extra tempo. Even so the information not completely compensates. Black struggles to draw but succeeds.

"you know that the game is a draw, but now you say that most probably the tempo is insufficient to win for White. That's contradictory."
++ I know, but it is not yet proven. That is why I say 'most probably'.

"You could not "know" that Black cannot win, if not for the evaluation functions derived from our (and NN) incomplete experience of the game."
++ No, the calculation towards the table base gives the verdict draw / win / loss. The evaluation function cannot decide that however sophisticated it is. An engine on a desktop can play a decent game even at say 5|0 time control. The engine does that based on its evaluation function, as 5 minutes do not allow to calculate all the way through. However a cloud engine at 10^9 nodes / second (that is 1000 x faster than a desktop) and running for 5 years can calculate all the way from the opening towards the 7-men table base. It does not depend on its evaluation function.

Well over 1000 posts and @tygxc is still oblivious to the fact that just as much has to be proven for white as for black. You don't get a draw for free when you are white!

Difficult to find but this seems to be Allis's definition. It's the one we started with and not so far from tygxc's. It's still meaningless because it requires a stronger solution to provide proof.

Weak: Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. That is, produce at least one complete ideal game (all moves start to end) with proof that each move is optimal for the player making it. 

If Allis didn't understand that, whoever he is, his opinion is worthless. If he understood it, his definition is hypothetical only. If you can refute it, you're cleverer than I am.

Don't forget the thousand or so in each of, I think, two other threads.

A "weak" solution requires the exhibition of practical optimal strategies for _both_ sides plus the reasoning that shows that these strategies are optimal (as achieved for checkers). The only time one of these strategies is trivial is if the other side has a winning strategy.

A valid weak solution proves what the value of the game is and a practical way to achieve this value with either side.

(Check this in any authoritative source which defines the time).

#1474
Allis is the mathematician who solved ''Connect Four''.
I agree with

"Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. That is, produce at least one complete ideal game (all moves start to end) with proof that each move is optimal for the player making it."

In case of chess that would be: 

"Provide an algorithm that secures a draw for black, against any possible moves by the opponent, from the beginning of the game."

What is an algorithm in this context? There are games like Nim with a simple algorithm. Part of the Connect Four proof was also strategy stealing: put a stone on the same column.
It is still unclear what 'algorithm' precisely means in this definition.

That is why I prefer the second wording:

"produce at least one complete ideal game (all moves start to end) with proof that each move is optimal for the player making it."

complete = from initial position to draw/win/loss
ideal = with no mistake i.e. with optimal moves i.e. a tautology, the word 'ideal' could be striken as the 'optimal' already implies that.
optimal = no other move produces a better outcome

There is a massive distinction in time & storage between solving strongly (10^36 positions) and solving weakly (10^17 positions).
The proof that the moves of the 'ideal' game are 'optimal' follows from exhausting the possibilities: from showing that none of the reasonable alternative white moves leads to a win.

Example of what passes for reasoning by @tygx

Checkers was solved with complexity about the square root of the number of legal positions and losing chess was solved with complexity about the fourth root of the number of legal positions, therefore (from this sample of 2) all games can be solved with about the square root of the number of legal positions, including chess.

The number of legal chess positions without promotion is circa 10^37, so since promotion is never "sensible" we can use the square root of this this number.

Therefore Elvis lives.

My words, but honestly representing the "reasoning".

#1478
Well Mr. mathematician, can you come up with a better estimate and provide evidence?
Each pawn move and each capture render huge numbers of positions inaccessible.
Thus the number of positions to visit for a weak solution must be lower than the number of legal and sensible positions.
Checkers like chess is a draw. The rules differ from chess. Square root.
Losing chess unlike chess is a win. The rules are similar to chess. Fourth root.
Hence it is plausible that for chess it is about the square root too.

Promotion is sensible, but it is usually to a piece already captured and usually to a queen.
Multiple excess underpromotions are not sensible.
For each sensible position with 4 queens excluded from 10^37 there are several non sensible positions included in the 10^37, so the 10^37 is an overestimate.

Therefore, a weak solution is not possible, without a semi-strong solution first. Without that, these definitions are totally meaningless.

As I have explained, so address it, please. I don't care about authoritative sources. I have no idea if some "authoritative source" has managed to con the entire academic establishment. If you (or anyone) can't think for yourself and provide good reasoning, then you may as well continue to talk among yourselves, because we're getting absolutely nowhere if you don't understand the procedure necessary to establish a weak solution. That definition is completely empty. It actually consists of incomplete Boolean algebra. Now doesn't it!?

#1480
"Therefore, a weak solution is not possible, without a semi-strong solution first."
Checkers has been weakly solved without any other solution first.
Losing chess has been weakly solved without any other solution first.

Allis' is a general definition.

And who says that? Oh yes Wikipedia.

But don't you see that this definition is redundant? If both players don't make mistakes, how could they make moves with a better outcome? Better stick to the first part of the definition on Wikipedia.

Autistic minds work in a different way. It does not mean an autistic person is wrong or inferior. I said that, because it seems that all posters here have difficulties communicating with you. One asks: "what do you mean by that?" and you repeat the exact same thing with the same words. You have done this so many times and that's unusual. You give your own definitions and opinions (or just another person's) as if they were absolute, totally neglecting what others here and specialists think about those definitions and opinions. And this behavior is restricted only to this "5 years to solve chess" topic, for apparently no reason; you do not behave like this in other threads with different topics. You said that you will hold to your position until others will prove you wrong, but none has understood what kind of proof you would accept.

Since you did not answer the question, I will act as if the answer was yes, but only to try to find another way to talk to you, if possible.

What is this, fuzzy logic? Formal logic uses only two discrete value of truth: true and false.

Maybe they thought them true, but as @Elroch said, the vast majority of scientists refrain to say they know they are true, do you agree?

In fact, they are not proven, that's why we still call them "theories". We use them because they provide the best predictions and are not yet contradicted (indeed, quantum entanglement seems to contradict relativity). Do phycisist know they are true? Idk, never heard them say that. If scientists know that a theory is true, how could they abandon it, if falsified (as it happened to Galilean relativity an classical mechanics)?

Right! Some theories can be proven, other not. If we solve chess in 5 years, then it is proven it is feasible; and we could discover a solid POC that it is feasible in 5 years, because it is mostly a mathematical problem; but our knowledge of the universe is incomplete, so tomorrow we could discover a new phenomenon, which contradicts relativity for example, as electromagnetism led physicists to abandon Galilean relativity.

No need to say that. They simply play the best moves, right?

Why? Isn't it an ideal game?

You earlier agreed with me that to solve chess that would not be enough, right?

You cited A0. It doesn't consider the game won in this case, it depends on positions. It's a good advantage, though (expected score about 0.75 according to evaluation functions of strong engines).

I respect your opinion even if we disagree.

If chess is a win for Black, with optimal moves, it's a win for Black. Period. Agree?

Right, statistically, but we have to calculate to prove it is always the case, correct (you say that!)?

Ok.

Ok, understood, you know that Black cannot win by all the experience we have gathered through the centuries.

Check in the notes who gave that formulation and stick to the first part.

What is the point of this? Are you going to be any more successful than the rest? Try to understand the necessity that no "weak" solution is possible without a semi-strong one first. If the people you are quoting don't understand that, they are as confused as everyone here seems to be.

For some reason, I thought it was you rather than tygxc who answered:
<<"Therefore, a weak solution is not possible, without a semi-strong solution first."
Checkers has been weakly solved without any other solution first.
Losing chess has been weakly solved without any other solution first.>>

Hence, I answered <<Just like others are frustrated with tygxc failing to understand, I see no difference at all between him and the rest. All are equally blind and incapable of doing anything more than making quotations and sticking steadfastly to them, without knowing what they mean. Occasionally, Elroch shows flashes of sanity but then, so does playerafar.>>

All you are doing is blocking up the thread with an extremely repetitive answer to all tygxc's assertions, as though you're going to acheive something with that. It's true I had hoped for better from you. There is no point to that. Your guess re your debating partner is correct.

There's a difference between draughts and chess. The former is extemely simple in comparison. A bit like solving naughts and crosses! i.e. "checkers has been weakly solved, therefore chess". Or "I can jump over a three foot hedge; therefore I can jump onto the moon."