Chess will never be solved, here's why

#2730

"1) as for chess, an optimal strategy and a game-theoretic value for checkers was not known"
++ The game-theoretic value of Checkers was known to be a draw long before that was proven and likewise the game-theoretic value of Chess is known to be a draw before it will be proven. The Riemann hypothesis is known to be true but not yet proven: several people try to prove it, none try to disprove it.

"2) more important to me is that "the vast majority [of openings] can be eliminated due to transpositions and alpha-beta cutoffs." ++ That is what I say about chess all the time.

"they just did not check because the evaluation function at some depth said those positions are almost certanly a loss or a win (like e.g. a -6 or +6 in chess, using the pawn value as a measure of the advantage)"
++ In chess a stable -1 or +1 is enough to win.
"The winning of a pawn among good players of even strength often means the winning of the game." - Capablanca,
"An endgame with an extra pawn is won, the plan is to queen the pawn.
An endgame with an extra knight is won, the plan is to trade the knight for a pawn" - Capablanca
"A pawn is a pawn" - Fischer
1 e4 e5 2 Ba6 is a sure loss for white, without having worked out all possibilities to checkmate.

"That is chess  while other openings almost certainly would lead to a draw, then indeed some approximations would have been made."
++ If 1 e4 and 1 d4 are draws, then 1 a4 is surely no better than a draw either.

"the alpha-beta search (nominal depths 17-23 plies) used in Chinook was not designed to solve checkers, and it occasionally determined a proven win or loss"
++ Stockfish is not designed to solve Chess, but it can be used to weakly solve chess.

"We only needed the bound to prove the root value. At the time of this writing, ongoing computations are working on turning these bounds into proven results (Loss or Draw)"
++ To weakly solve chess we do not need to look at all openings, only those judged relevant.

"machines will be used to solve additional openings"
++ So after chess is weakly solved people can solve 1 a4 as well if they like.

That's not the definition of weakly solved, nor can you assume that a +1 or -1 valuation by an engine represents an actual pawn advantage/disadvantage and then toss out quotes from human chess players that had no more hope of solving chess than you have.

Back to square one, which you have never left except in your imagination.  Did you see that Tromp confirmed 10^44 today?  That guy has some solid numbers, and he makes no illogical leaps.

More often than not, in technical endgames, a single extra pawn isn't enough to win. If you can't leverage the material advantage earlier in the game to build on it, then the game often peters out to a draw.

#2756

"That's not the definition of weakly solved"
++ weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition. - van den Herik
That is the accepted definition of weakly solved, despite some people trying to enforce their personal, erroneous definition here.
'Any opposition' means that white must oppose i.e. resist against the draw.

"nor can you assume that a +1 or -1 valuation by an engine represents an actual pawn advantage/disadvantage"
++ That is what +1 or -1 means: one side is or will be a pawn ahead without compensation

"then toss out quotes from human chess players"
++ "Next to brute-force methods it is often beneficial to incorporate knowledge-based
methods in game-solving programs" - van den Herik.
Solving a game allows to incorporate knowledge of the game and doing so is beneficial.

"Did you see that Tromp confirmed 10^44 today?"
++ I do not doubt that Tromp arrived at 10^44 legal positions. I only say that none of his 538 sampled positions found legal can result from the initial position by a reasonable game with > 50% accuracy and thus that the number of sensible positions is much smaller, e.g. 10^32.

"That guy has some solid numbers, and he makes no illogical leaps."
Tromp concludes from a sample of 538 positions found legal that there are 10^44 legal positions. That is all right, but I receive criticism here for less drastic extrapolations.

#2757
"More often than not, in technical endgames, a single extra pawn isn't enough to win.
If you can't leverage the material advantage earlier in the game to build on it,
then the game often peters out to a draw."
++ Safe heavens are known drawn endgames despite 1 or even 2 extra pawns.
Opposite-colored bishop endings are an example.
Rook endings with pawns on one wing are another example.
However, if one side loses a pawn early,
then the other side can usually win the game by steering around the safe heavens.
That is why gambits are no longer viable in GM or ICCF chess.
One side accepts the pawn, defends, and coasts towards a won endgame.
"It loses by force" - Fischer on the King's Gambit
"I would like to play King's Gambit, but I could not find a way for white to equalise" - Kramnik
If 1 e4 e5 2 f4 is a loss for white, despite the obvious but insufficient compensation,
then 1 e4 b5 or 1 e4 f5 or 1 d4 g5 are sure losses for black. 1 e4 e5 2 Ba6 is a sure loss for white.

I have posted elsewhere a legally reachable position with a +27 advantage for white according to Stockfish that cannot even be won with co-operation. The aim of the game of chess is not to achieve a 6 point advantage according to Stockfish.

In papers it's hard to find statements like "we know that... (thing to prove)" before it is indeed proven; we can find "we know that likely/probably... (thing to prove)", i.e. more or less educated guesses. You use "know" instead of "suppose/hypothesize/postulate", etc. in an attempt to give artificially more strength to your assumptions and deceive people. The rest of your post (link) is a deliberate distorsion of facts.

Check better.

Here's a legal position with 9.19 pawn advantage for black according to 99-ply Stockfish 14.1 analysis. White's drawing strategy is not difficult.

#2762
It is all well known that the evaluation function has its flaws and fails to recognise fortresses and some other known draws. However, an early loss of a pawn means a loss of the game. The side with the extra pawn steers clear of the safe heavens.

"safe havens"

So you freely admit that engines are still flawed and cannot evaluate perfect play, yet your premise is completely reliant upon Stockfish, and you now have hitched your wagon to the idea that a +1 engine evaluation is an absolute win.  Time to resign...

Statistically, the claim that a win of a pawn wins a game is not only unsupportable, it is dubious whether the win of a pawn suffices to make the expectation of the game greater than 75% (which would be the expectation if the probability of a win was the same as the probability of a draw.

Strong evidence for this comes from Stockfish evaluations collated with results and with neural network expections.  My impression is that a 1 pawn advantage gives an expectation of about 0.7. Note that a 1 pawn advantage from Stockfish is what you have if you are 1 pawn up but it evaluates the positional factors to be balanced (positional factors adjust the material balance indicated in the evaluation).

Certainly this needs to be checked empirically in a more systematic way.

#2764
"engines are still flawed and cannot evaluate perfect play"
++ Engine evaluations are flawed especially near the end of the game,
where is does not recognise fortresses or where it does not shed material as it should to win.
That is why the calculation must go on deeply to reach the 7-men endgame table base.

"a +1 engine evaluation is an absolute win."
++ Yes, early enough +1 is a sure win as it allows to steer towards a won endgame.
Late in the endgame +1 or even +5 may not be enough if the safe haven cannot be avoided.
1 e4 b5, 1 e4 f5, 1 d4 g5 are sure wins: pawn down, no compensation.
Most gambits are losing despite the obvious but insufficient compensation.

#2766
"My impression is that a 1 pawn advantage gives an expectation of about 0.7"
Expectation is a notion of imperfect play, linked to probability of error.
A position is either a draw, a win, or a loss.
There are no intermediates.

No, not infinitely variable. That's why we have the 50 move rule.

The idea that "chess computer rated a zillion" can't analyse the Ruy Lopez better than a human is likely best left in the 20th century!

How would such a check tell you anything about perfect play?

If you try a statistical check on the result of KQKNN positions, SF14 with NNUE or human, will tell you they're generally drawn under basic rules, but Nalimov says they're 98% won by the queen.

I think all you get from looking at practical play is information about practical play.

I feel you have entirely missed a crucial fact. Suppose it is the case that a position is evaluated +1 pawns by a super-duper computer (and let's assume one side is actually a pawn up), Then suppose if you play two super-duper computers against each other in this position (or a set of such positions), the score is 70%, most of the results being draws and almost all the rest being wins for the side with the extra pawn.

You claim the mixed results are due to inaccuracy. This is correct from a game theoretic point of view if there are mixed results for a single position. But you also claim the true result is a win. This is not only unjustifiable, it is also likely to be wrong a lot of the time. If the true result was a win, why does the winning side make so many blunders to give away the draw, while the side with a pawn less makes fewer cancelling blunders? 

You can be very confident that a lot of +1.00 positions are draws. The evidence is that it is most of them, but regardless of this the notion that all of them are wins is absurd.

We don't have the 50 move rule any more under basic rules, but even when we did it wasn't compulsory to claim.

We do have a limit on games governed by competition rules since 2017. There is an automatic draw if the ply count reaches 150 or if positions with the same player to move, pieces of the same kind and colour occupying the same squares and the possible moves of all the pieces of both players the same occur five times. 

Evidence?

First, I acknowledge that the actual results of games between imperfect players from positions don't tell you what the tablebase value is. But I conjecture that for a lot of the sort of positions where chess experience is most relevant, they are likely to be some sort of indication. People lose dead lost openings a lot. Top evenly matched players probably draw theoretically drawn positions a lot. Not proof, but seems most likely (like the opening position being a draw is a reasonable conjecture based on white's 54% score in master play (or whatever it is).

Leela has learnt to estimate the expected result in positions reached in games and an informal observation is that a pawn according to Stockfish is somewhere around a 70% expectation.

A random example is not so far from that: