Chess will never be solved, here's why

Let's imagine what a solution of chess requires. First it requires a big tablebase (in all seriousness, one that is too big to be infeasible. Let's pretend not and say we have a puny 12-piece tablebase. This requires about 10^24 bytes.  That's about 10000 times bigger than the total storage capacity of all computers on the planet. Ridiculous, but technologically plausible. If you have a few trillion dollars)

Next you need two strategies. The first forces a drawn position in the tablebase with white, the second forces a drawn position in the tablebase with black.

The problem is that it seem rather unlikely you could avoid needing to rely on drawn positions not in the tablebase, if the opponent fails to co-operate in exchanging pieces (eg he blocks the position and shuffles pieces).

But can you somehow get round the need to use a large state space by considering that only opposing moves that produce new positions matter. If the opponent against a drawing strategy moves to a position previously reached he has achieved nothing.

So you don't need the full state for the positions, rather you check whether new positions are already in your strategy.

Thus I think @tygxc is correct to believe that FEN states are adequate for a solution of chess, even if he is woefully wrong on the computing power needed to solve this rigourously, as achieved for checkers.

Any flaws in that reasoning?

@5266
1 e4 e5 2 Ba6? is neither opposition, nor optimal play from both sides.
'Any opposition' means all legal moves that oppose to the game-theoretic value,
otherwise they would write 'all legal moves'.

We can dispense with the rest because it enlarges on the core mistake. 

<<What it amounts to is a poor estimate of a probability in a way that is qualitatively extremely wrong, but pragmatically unlikely to matter.>>

Discussing 1. d4, you seem to see its results as probabilistic.

That's all it takes for me to realise you are unfamiliar with Bayesian probability (the only type of relevance here) where probabilities quantify belief states. Certainty is a probability of 1 or 0, but is only appropriate for propositions that can be deduced from known facts.

So it's simply a fact that quantifying belief about a proposition is probabilistic, only simplifying to boolean logic when the line of inference is deductive from known facts.

We have the same difficulty in quantum mechanics, as I once tried to explain but you failed to grasp it at that time. We accept that probability plays a fundamental part in QM. Is a fundamental entity a particle or a wave? What does wave mean?

Glad to help. A wave function is a mathematical model that obeys a specific law describing how it evolves over time. It is closely related to belief about the state of the system (technically being an integral of complex-weighted eigenfunctions, typically position eigenstates. Momentum eigenstates provide a dual representation).

If we see an entity as existing in a place at a time, we can see probability regarding its position as a waveform. But is that waveform a conceptual idea of our minds or is it intrinsic to the entity when it manifests as a waveform? Could it even be both?

To reiterate, it's a mathematical model that determines everything we believe about the state of a quantum mechanical system and how that belief evolves over time.

We can now leave that indeterminate, because it doesn't apply to 1.d4. The question is "can we be sure that 1. d4 isn't a forced loss for white?" You are suggesting that there's a probability attached to that in such a way that the optimal outcome is represented by a probability.

Yes, remember Bayesian probability uses probabilities to quantify belief states.

But that is a function of the estimated possible error in the machine and algorithms which determine it, or are supposed to. Probability does not exist intrinsically in 1. d4 and its optimum outcome with best play by both sides. It is either one thing or another. A forced win, a forced loss or a draw.

Yes. Like the toss of a coin is a head or a tail. And before it is tossed our belief state might be (half head, half tail).

And that is why your attempt at explaining your belief that we can never be entirely sure fails.

I NEVER said "never". We can be sure once the coin is tossed or the game solved.

It's like agnosticism in religion. Maybe YOU cannot be sure but others believe they can, one way or another. How? The use of reason. Reason used correctly and well. There is no intrinsic probability attached to either matter and so any attempt to use that as an explanatory device is doomed to failure. The probability (or lack of complete certainty) exists in your mind. And that is all.
Bayesian probability is indeed about state of belief in situations involving uncertainty. And it is, as Jaynes said, "the logic of science".

Blind belief is like taking a prior that is certain. It can be done: it's just not optimal. [Note that in terms of quantifying accuracy of beliefs in terms of cross entropy, being certain and turning out to be wrong is infinitely costly. It is much wises to be almost certain, which costs virtually nothing if you are right and costs a finite amount if you are wrong.

@5234

"So relying on the judgement of GMs to eliminate broad categories of games/positions from consideration, thereby making the task easier, isn't actually relying on the judgement of GMs?"
++ The bulk of the work is done by the engines calculating from the humanly prepared starting positions towards the endgame table base or a prior 3-fold  repetition. The GMs initiate the calculation and also terminate it when there is no doubt at all like in the opposite colored bishop ending presented. The GMs use knowledge only, no judgement. 

@5260

"@tygxc does not understand the definition of weak solution"
++ I do understand. I quote peer-reviewed literature on solving games:

You post links to peer-reviewed literature. You misquote (or misinterpret) the content.'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition'
calls for opposition, i.e. an act of opposing, of resisting against the game-theoretic value.

An obvious misinterpretation.'the game-theoretic value of a game, i.e., the outcome when all participants play optimally"
calls for all participants to play optimally't is often beneficial to incorporate knowledge-based methods in game-solving programs'
encourages to incorporate knowledge

Knowledge being distinct from wild guesses with van den Herik's intended meaning.

"1. the initial position is symmetrical, so white cannot be lost"
++ Yes, that is correct. Moreover white has the advantage of 1 tempo.
1 tempo is worth less than 1 pawn, about 0.33 pawn.

By weight or volume?

You can queen a pawn but you cannot queen a tempo.
So black cannot be lost either. So the initial position is a draw.

Struggling to understand that. Can you explain how it works in this simpler position?

"waving hands deals with any possibility of zugzwang"
++ There is no Zugzwang in the initial position.

So you can wave your hands. What a clever boy!

"2. there are a lot more draws between strong players than white wins, so obviously that is the right result."
++ Yes, the stronger the players, the more draws. The longer the time, the more draws.

They rather bizarrely had a chess craze in the public bar of my local once where almost none of the participants had ever played before. Almost all of the games on the first day were drawn on time (closing time); possibly also under the 75 move rule but I don't think anyone was counting.Over the years the draw rate goes up.
It is impossible to explain in a consistent way the results of the ICCF WC: 136 games = 127 draws + 6 white wins + 3 black wins assuming chess being a white or black win.

I see no difficulty. You find it impossible because you're trying to use a flawed method in the explanation.

You've been invited several times to explain the results in a set of SF15 v SF15 KNNvKP games from a position known to be a White win because it's in the tablebases - no response. I post another set of SF15 v SF15 games here, perhaps you could try those.

I haven't indicated whether the starting position is a win or a draw or how many errors I think there are, but you claim to be able to tell that from the results without reference to a tablebase. There are 12 games all drawn by reference to 7 man tablebases (no agreed draws).

I can't get the right results using your method - can you show a worked example please? What should be the result of the starting position and how many errors have been made? (No peeking.)

@5286
"this method relies on admittedly-imperfect human judgement to choose only some positions to be calculated by machines whose evaluation functions have been set by humans with imperfect knowledge."
++ Terminating what an imperfect human player believes to be an obvious draw holds no risk except that of being wrong, just like in every game lost over the board.

Selecting 4 promising lines holds no risk.

Laughable.

"And human history is filled with "facts" that were KNOWN to be true (in virtually every field), only to be upset by later discoveries." ++ Many mathematical proofs had flaws and needed correction. The Four Color Theorem had a flaw at first. No, Kempe's attempt at a proof (1879) had a flaw. Many proofs of the Riemann Hypothesis were found flawed.  No mistaken proof of the Riemann Hypothesis has survived peer review, so the claim that such proofs were taken as fact is delusional.

That is no excuse to refrain from attempting all mathematical proofs. Likewise there might be a mistake is no excuse for not solving chess.

Better analogies are real proofs of the Four Colour Theorem, one of which has been computer verified - the entire proof has been mechanised and the validity of each step checked by the Coq proof assistant. This verification shows that the theorem can be derived from the axioms of graph theory by pure deduction.

Any real solution of chess would be amenable to such computer checking. Your notion of a mock solution would fail at the first hurdle.

++ Terminating an obvious draw holds no risk.

The starting position is an obvious draw.

Oops, I just solved chess.

QED

@tygxc could hardly disagree, but he will feel a bit peeved that you have managed it without a team of GMs and $5 million funding.

ouch... see elroch i would never let him disrespect me like that personally

Chess will be solved when knowledge is accepted. Computer search engines only sees in algorithms, human ( including Susan Polgar) see by both. Computer sees mistake I see sacrifice, checkmate!

One reason for that is because zero is a non-rational number, from the point of view of calculations. ...

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Selecting 4 promising lines holds no risk.

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