Chess will never be solved, here's why

You don't understand what Schaeffer did. He would tell you where you are going wrong if he had the chance.

It is not accurate to claim that chess is already ultra-weakly solved and that the game-theoretic value of the initial position is a draw. While it is true that the game of chess is generally thought to be a draw when both players play optimally, this has not been proven and it is still possible for one player to achieve a winning advantage through superior play.

Furthermore, it is not possible to fully solve chess in the sense of finding a winning strategy for all legal positions, as there are too many positions to consider. The number of legal positions in chess is estimated to be around 10^44, which is far too large for current computers to analyze and calculate strategies for.

It is also not accurate to claim that weakly solving chess would require calculating 10^17 relevant positions, which present computers could do in about 5 years. This claim does not take into account the complexity and depth of chess positions, and it is likely that significantly more positions would need to be analyzed in order to find a satisfactory strategy.

Finally, while it is true that pruning, the "best first" heuristic, and game knowledge can be useful in the process of solving a game, it is important to recognize that these techniques have limitations and may not be sufficient to fully solve a game like chess. Ultimately, the process of solving a game like chess is a complex and ongoing endeavor that requires a combination of mathematical analysis and understanding of game principles and tactics.

Spot on.  @tygcx seems never to have got far enough in the mathematical sciences to understand what a proof is.

@6945

"Schaeffer's team used Chinook to provide a measure of what the strongest line of play would be" ++ For Chess Stockfish can do the same.

"A win in such an instance is not a characteristic of perfect play by both sides"
++ For Chess 1 e4 e5 2 Ba6? is such a win for black.

"Since a win was achieved so quickly, it means the losing side made a mistake and did not play perfectly." ++ Like 1 e4 e5 Ba6?

"Entire lines of play branching from various positions were eliminated this way, vastly reducing the number of lines that had to be deeply explored." ++ So 1 e4 e5 2 Ba6? can be eliminated.

"Of the 5 x 10^20 possible positions, Schaeffer needed to evaluate only 10^14 to prove that checkers, played perfectly, results in a draw."
++ Likewise of the 10^44 legal Chess positions only 10^17 need to be evaluated to prove that Chess, played perfectly, results in a draw.

Would that be this Stockfish ...

or this one?

@6947

"Would that be this Stockfish"
++ Stockfish is to calculate from the initial position to a 7-men endgame table base draw.

Of course - it will do much better with a few more men to go at. I shouldn't have given it a hard one like king and rook v king.

In fact it will play completely perfectly with more than seven men, because then there's nothing to say otherwise.

Incidentally, when are you going to stop pretending you haven't been invited to apply your "calculations" to this series of games, where the results can be checked against the tablebases? You didn't seem to notice this question last time I asked.

User @cobra91 has kindly done most of the work for you by producing a table of blunders in each of the games, so laziness can no longer be an excuse.

White? (Editor's gone doolally again.)

I see some garbling of the format only in your quote, no problems with colour in either (PC/Chrome).

@Elroch

Talking about the chap with the white pieces.

@tygxc claims the position is a win for Black, in which case isn't it the responses by White that all need to be evaluated to prove that? Some Black moves can be ignored so long as he's found a complete winning half tree in the remainder. E.g. if a forced win is found starting 2...bxa6, Black's 2...Nxa6 doesn't need to be evaluated.

Yes. My carelessness obfuscated the simple point. I think I have a psychological association between white and win.

@6957

"It means moves have been found. NOT a strategy has been determined"
++ A strategy can be a set of moves like Checkers, or a set of rules like Connect Four, or a combination of both, most likely for Chess.
The definitions are carefully worded to include all valid possibilities.

"Finding only one move for each white move, as you insist is correct, assumes that there's no forced win for black."
++ Schaeffer did just the same for Checkers: show how black can draw whatever white does.

"Why is no one, not Chessbase,  or the Stockfish team, or the Komodo team, and the hundreds of other programming teams. or Google or IBM."
++ This is a nonsense argument. It has not yet been done, so it cannot be done.
No human has yet walked on Mars, so it is impossible.

"It is so easy" ++ 5 years, 3 10^9 nodes/s cloud engines, 3 grandmasters is not easy.

"It is only  100,000,000,000,000,000 positions."
++ That is 1000 times more than what Schaeffer did for Checkers.

@6950

"You seem to have forgotten to provide a proof."
++ I have above provided proof that 1 e4 e5 2 Ba6? is a forced checkmate for black.
That is not even necessary. A full bishop up, no compensation of any kind is a win.
When everything else is the same a bishop is enough to win, a pawn is enough to win.

"turning up for a chess game and claiming a draw without moving"
++ Indeed, a tempo up is not enough to win.
So you think a bishop up is not enough to win and a tempo up is enough to win?

"Entire lines of play branching from various positions were eliminated this way, vastly reducing the number of lines that had to be deeply explored." ++ So 1 e4 e5 2 Ba6? can be eliminated.

"It would be necessary to provide a proof with not the slightest uncertainty not a single unevaluated move by black."
++ No, per van den Herik it is beneficial to incorporate game knowledge in solving a game.
Allis even solved Connect Four with just a set of rules.

However let us assume that only a stupid weak solution of Chess were admissible and use of any knowledge were forbidden.
Shannon assumed  a game of 60 moves i.e. 120 plies and 10 choices per ply.
Thus he arrived at his Shannon number of 10^120.
Now we know he was wrong. Tromp proved there are only 10^44 legal positions.
Assuming the 10 choices per ply to be correct, that would lead to only 44 plies i.e. 22 moves for the whole of Chess, all legal positions. That is not plausible 22 moves is too low.
So there are less than 10 non-transposing legal choices per ply.

Let us assume 4 non-transposing legal choices per ply.
10^44 = 4^73. So with 4 non-transposing choices per ply and 73 ply = 37 moves deep we get the whole of Chess. That is more or less plausible. The 37 moves seems a bit too low and thus the 4 is a bit too high. So with about width w = 4 choices per ply and depth d = 37 moves we get the whole of Chess with w^2d = 10^44 legal positions.

If we now attempt to weakly solve Chess, then we need all w legal white moves, then only 1 black response, then all w white moves that do not transpose, then only 1 black response and so on until we reach a 7-men endgame table base position or a prior 3-fold repetition, checkmate, or stalemate. Thus we only need w^d = sqrt (w^2d) = sqrt (10^44) = 10^22 positions.

Thus weakly solving Chess in a stupid way without any game knowledge and talking all legal white moves and 1 black reponse each would take 100,000 years.

That would include such losing stupidities like
1 g4?
1 e4 e5 2 Ba6?
1 e4 e5 2 Nf3 Nc6 3 Nd4?, 3 Nxe5?, 3 Ng5?, 3 Nh4?

It would also include moves that are illogical and do not even try to win,
i.e. do not oppose to the draw, like
1 Nh3
1 e4 e5 2 Nh3
1 e4 e5 2 Nf3 Nc6 3 Ng1

"based on what everyone knows are uncertain evaluations"
++ Everyone knows 1 e4 e5 2 Ba6? is a certain loss for white

"He took approximately the 2/3 power of the number of moves to correctly prove the result."
++ 2/3 power of the number of positions, not moves.
A Checkers board is more crowded than a Chess board: 24 men on 32 squares i.e. 3/4 for Checkers and 32 men on 64 squares i.e. 1/2 for Chess.

When you list piece-up winning positions as having no compensation by definition, then the label is meaningless in the context of solving chess. This is because there's no way of determining (static-ly, from the position itself) which bishop up positions have "no compensation." In other words you have to calculate to find out whether it's winning, and assign the appropriate label afterwards.

Weird naming conventions.

So they name it for how many groups of 3 zeros occur after the initial 3.

Tredecillion is 13 groups of 3 zeros, plus the initial 3, so 10^42, and of course 100 tredecillion makes it 10^44.

https://merriam-webster.com/assets/mw/static/table/collegiate/number.jpg

@6961

"When you list piece-up winning positions as having no compensation by definition, then the label is meaningless in the context of solving chess."
++ No, it is meaningful. We can identify positions where there is no compensation of any kind, like 1 e4 e5 2 Ba6?, or 1 e4 e5 2 Nf3 Nc6 3 Nd4? which are sure losses and do not need any further calculation. It does not even need to be a full piece. A pawn up with no compensation of any kind is a win too, like 1 e4 b5?, 1 e4 f5?, 1 d4 g5?, 1 d4 e5?.

"there's no way of determining static-ly, from the position itself which bishop up positions have no compensation." ++ Not for all, but for many. E.g. I can tell 1235172064527 is no prime, but I cannot tell for any random integer if it is a prime or not.
If no doubt, then dismiss. If any doubt, then calculate. 1 e4 e5 2 Ba6? leaves no doubt.

"you have to calculate to find out whether it's winning"
++ No, I do not have to calculate, I use game knowledge to tell right away that 1 e4 e5 2 Ba6? is a certain loss for white.

In many positions you can do that, yes, but it will take considerably longer than a few years to solve chess if the process involves showing you each indeterminant position.

@6964

"In many positions you can do that, yes"
++ It is a considerable simplification. E.g. just the rule to 'always promote to a either queen, or to a piece already captured' reduces the number of legal positions from 10^44 to 10^38.
Thus weakly solving with only that rule reduces the time from 100,000 years for 10^22 positions to 100 years for 10^19 positions.

Just a few more rules like 'hang no pieces, hang no pawns without compensation of any kind' Reduces the positions to 10^34 thus weakly solving to 10^17 relevant positions and that can be done in 5 years, like Sveshnikov said.
1 e4 e5 2 Ba6?, 1 e4 e5 2 Nf3 Nc6 3 Nd4?, 3 Nxe5?, 3 Ng5?, 3 Nh4? need no calculation.
Also 1 Nh3, 1 Na3, 1 e4 e5 2 Nf3 Nc6 3 Ng1 need no calculation though they may well draw too.
That is just incorporating game knowledge, which per Prof. van den Herik is beneficial.