Occasional?
Chess will never be solved, here's why
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@6936
"First thing you need to do is understand what "solve chess" means."
++Ultra-weakly solved means that the game-theoretic value of the initial position has been determined,
weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition, and
strongly solved is being used for a game for which such a strategy has been determined for all legal positions.
The only meaningful to discuss for Chess is weakly solving.
For all practical purpose Chess is already ultra-weakly solved,
and the game-theoretic value of the initial position is a draw.
Strongly solving Chess would generate a 32-men table base
and need to determine a strategy for all 10^44 legal positions, that is too much.
That leaves weakly solving, and that needs 10^17 relevant positions,
which present computers can calculate in 5 years, like GM Sveshnikov said.
Just like weakly solving Checkers, pruning is allowed. Schaeffer calculated only 19 of the 300 tournament openings, eliminating 200 by transposition and 81 by pruning.
Just like weakly solving Losing Chess the 'best first' heuristic is allowed.
Just like weakly solving Connect Four it is allowed and beneficial to incorporate game knowledge. That is also what Prof. van den Herik wrote.
Dec 30, 2022
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#5225
You don't understand what Schaeffer did. He would tell you where you are going wrong if he had the chance.
Dec 30, 2022
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#5226
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.
Dec 30, 2022
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#5227
RemovedUsername333 wrote:
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
Spot on. @tygcx seems never to have got far enough in the mathematical sciences to understand what a proof is.
Dec 30, 2022
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#5228
tygxc wrote:
Just like weakly solving Checkers, pruning is allowed. Schaeffer calculated only 19 of the 300 tournament openings, eliminating 200 by transposition and 81 by pruning.
He only used valid methods. The key fact was that once the 19 openings had been solved, the solutions of the others were valid corollaries, achieved with very little additional computation. This involved two things - proving that each side could force a position which was already known to be a draw. With this, all other lines from the 281 other openings became irrelevant to the weak solution.
To confirm this from a University of Alberta article:
<<Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.>>
Just like weakly solving Losing Chess the 'best first' heuristic is allowed.
You really should be able to understand this part. A strategy for white only needs to deal with all legal moves for black in positions reached (an omitted move leads to a position with an uncertain value) but needs to deal with (i.e. select) just one move for white at each juncture . "Best first" means trying the move that looks best as a candidate for the strategy and seeing if that will do. Primarily this is about positions that are winning for the strategy side. These positions can then be ignored by the other strategy (as there has either been a mistake made to reach them or the second side has nothing to prove - achieving a loss is simple!
As the University of Alberta article says :
<<Instead, Schaeffer and his colleagues used a technique called ”best first” to prioritize searching various positions and lines of play. At a given position in the game there are several possible moves that can be made. Instead of exploring all of these moves to their final outcomes using deep search, Schaeffer's team used Chinook to provide a measure of what the strongest line of play would be—what would most likely result in a win in the fewest moves. This line of play was evaluated first. If it did result in a win, then there was no need to search any other parallel lines of play, because the entire line was already known to result in a strong win. A win in such an instance is not a characteristic of perfect play by both sides; perfect play means that each side will try to win in as few moves as possible, or delay losing in as many moves as possible. Since a win was achieved so quickly, it means the losing side made a mistake and did not play perfectly. Entire lines of play branching from various positions were eliminated this way, vastly reducing the number of lines that had to be deeply explored. By applying such a technique, Schaeffer’s team was able to solve checkers using the least amount of effort. 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.>>
@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.
Dec 30, 2022
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#5230
tygxc wrote:
@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.
Would that be this Stockfish ...
Ply count 0, Black to play, White to mate in 46
or this one?
Ply count 68, White to play and mate in 16
@6947
"Would that be this Stockfish"
++ Stockfish is to calculate from the initial position to a 7-men endgame table base draw.
Dec 30, 2022
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#5232
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.
Dec 30, 2022
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#5233
tygxc wrote:
@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.
TENTATIVELY.
They picked a candidate move, then attempted to PROVE it led to a win. If so, it was good enough. On many occasions it was surely not (Even Chinook was not perfect, although it was likely a lot more accurate than the latest Stockfish).
"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?
You seem to have forgotten to provide a proof. This is a far, far worse failing that turning up for a chess game and claiming a draw without moving.
"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.
No, I have to reluctantly accept you are simply too stupid to understand that this is not close to being an example. It would be necessary to provide a proof with not the slightest uncertainty (not a single unevaluated move by black).
"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.
He took approximately the 2/3 power of the number of moves to correctly prove the result.
You assert that 2/5 power of the number of moves is adequate to provide a blatantly inadequate attempt at proving the result, leaving vast numbers of moves by the opposing side of a strategy not determined (based on what everyone knows are uncertain evaluations).
Dec 30, 2022
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#5234
Elroch wrote:
...
It would be necessary to provide a proof with not the slightest uncertainty (not a single unevaluated move by black).
...
White? (Editor's gone doolally again.)
Dec 30, 2022
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#5235
MARattigan wrote:
Elroch wrote:
...
It would be necessary to provide a proof with not the slightest uncertainty (not a single unevaluated move by black).
...
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).
Dec 30, 2022
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#5236
@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.
Dec 30, 2022
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#5237
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.
Dec 31, 2022
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#5240
tygxc wrote:
A full bishop up, no compensation of any kind is a win. When everything else is the same a bishop is enough to win
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.
If people wish to engage in a circular discussion of this (or any) topic, delving into minutia of any aspect, that is their choice. They may well find it entertaining and informative.
Anyone who finds this a waste of time has the simple option of not bothering to follow this thread.