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Can Chess be Solved?

We solve more and more of chess every day. It's finally reaching the tipping point that people see how it's turning into checkers.

There's already a lot out there on this. We even have AI coaching bots now!

We solve more and more of chess every day. It's finally reaching the tipping point that people see how it's turning into checkers. There's already a lot out there on this. We even have AI coaching bots now!

@Zenchess said in #8:

Actually, 'in theory' not all complete information games can be solved.

That depends on how you define 'in theory'! If we can present a solution, ignoring some current practical limitations, then the game can be solved 'in theory'.

The brute force method (charting all possible positions move by move) is clearly a way of solving chess. It does not require a lot of computing power, all you need to do is to determine all possible moves in the current position, and repeat that for every new position. The only obstacle is storage space - 10^120 is indeed an intimidating number.

However, to mo my knowledge, no one has tried to prove a theoretical limit to storage space. Until that's done, and the limit is below 10^120, chess is solvable in theory.

For all practical purposes though, we can safely assume that chess will not be solved, at least not in our lifetime!

@Zenchess said in #8: > Actually, 'in theory' not all complete information games can be solved. That depends on how you define 'in theory'! If we can present a solution, ignoring some current practical limitations, then the game can be solved 'in theory'. The brute force method (charting all possible positions move by move) is clearly a way of solving chess. It does not require a lot of computing power, all you need to do is to determine all possible moves in the current position, and repeat that for every new position. The only obstacle is storage space - 10^120 is indeed an intimidating number. However, to mo my knowledge, no one has tried to prove a theoretical limit to storage space. Until that's done, and the limit is below 10^120, chess is solvable in theory. For all practical purposes though, we can safely assume that chess will not be solved, at least not in our lifetime!

@Gyllenstierna said in #12:

That depends on how you define 'in theory'! If we can present a solution, ignoring some current practical limitations, then the game can be solved 'in theory'.

The brute force method (charting all possible positions move by move) is clearly a way of solving chess. It does not require a lot of computing power, all you need to do is to determine all possible moves in the current position, and repeat that for every new position. The only obstacle is storage space - 10^120 is indeed an intimidating number.

However, to mo my knowledge, no one has tried to prove a theoretical limit to storage space. Until that's done, and the limit is below 10^120, chess is solvable in theory.

For all practical purposes though, we can safely assume that chess will not be solved, at least not in our lifetime!

Yes, but I wasn't talking about chess. I was talking about all complete information games. Whether chess will be solved is debatable, but saying that we can solve any complete information game, no matter how complex, would be infinitely difficult and would require infinite computation, because you can always make a game with more game states

@Gyllenstierna said in #12: > That depends on how you define 'in theory'! If we can present a solution, ignoring some current practical limitations, then the game can be solved 'in theory'. > > The brute force method (charting all possible positions move by move) is clearly a way of solving chess. It does not require a lot of computing power, all you need to do is to determine all possible moves in the current position, and repeat that for every new position. The only obstacle is storage space - 10^120 is indeed an intimidating number. > > However, to mo my knowledge, no one has tried to prove a theoretical limit to storage space. Until that's done, and the limit is below 10^120, chess is solvable in theory. > > For all practical purposes though, we can safely assume that chess will not be solved, at least not in our lifetime! Yes, but I wasn't talking about chess. I was talking about all complete information games. Whether chess will be solved is debatable, but saying that we can solve *any* complete information game, no matter how complex, would be infinitely difficult and would require infinite computation, because you can always make a game with more game states

@Zenchess said in #13:

Yes, but I wasn't talking about chess. I was talking about all complete information games. Whether chess will be solved is debatable, but saying that we can solve any complete information game, no matter how complex, would be infinitely difficult and would require infinite computation, because you can always make a game with more game states

From a practical point of view, you're absolutely right, but there's i huge difference between a practical solution and a theoretical one. I believe that chess is easily solvable in theory, but not at all in practice (at least not for a very long time).

My point is that we shouldn't worry so much about chess theory, but see the game from a practical point of view. We shouldn't strive for 'perfect play', but to play the best moves we can muster from our own knowledge and abilities.

@Zenchess said in #13: > Yes, but I wasn't talking about chess. I was talking about all complete information games. Whether chess will be solved is debatable, but saying that we can solve *any* complete information game, no matter how complex, would be infinitely difficult and would require infinite computation, because you can always make a game with more game states From a practical point of view, you're absolutely right, but there's i huge difference between a practical solution and a theoretical one. I believe that chess is easily solvable in theory, but not at all in practice (at least not for a very long time). My point is that we shouldn't worry so much about chess theory, but see the game from a practical point of view. We shouldn't strive for 'perfect play', but to play the best moves we can muster from our own knowledge and abilities.

Hans Berliner, the former Correspondence Chess World Champion, once said that chess would be solved. He had this idea of "perfect play" and decided that 1.d4 was the best opening move. He completely dismissed 1.e4, saying the only good move after 1.e4 e5 would be 2.f4—the King's Gambit—and according to him, that was just nonsense. He even talked to Bobby Fischer about it, trying to convince him that 1.d4 was better than 1.e4. Berliner also thought that after 1.Nf3, Black could just copy White's moves and the game would be a draw.

While reading his book, I started thinking: What would happen if chess really got solved? Honestly, I don’t think it would change much for humans, but it would probably be the end of computer chess. Any solution would be insanely long, and if it's a draw, someone would have to memorize the whole thing, including every possible sideline. No human could ever do that. Checkers was solved, and people still play it, so I guess the same would happen with chess.

That said, I do think the overall level of play would go up since the first 20-30 moves of the "solution" would probably become standard opening theory.

Hans Berliner, the former Correspondence Chess World Champion, once said that chess would be solved. He had this idea of "perfect play" and decided that 1.d4 was the best opening move. He completely dismissed 1.e4, saying the only good move after 1.e4 e5 would be 2.f4—the King's Gambit—and according to him, that was just nonsense. He even talked to Bobby Fischer about it, trying to convince him that 1.d4 was better than 1.e4. Berliner also thought that after 1.Nf3, Black could just copy White's moves and the game would be a draw. While reading his book, I started thinking: What would happen if chess really got solved? Honestly, I don’t think it would change much for humans, but it would probably be the end of computer chess. Any solution would be insanely long, and if it's a draw, someone would have to memorize the whole thing, including every possible sideline. No human could ever do that. Checkers was solved, and people still play it, so I guess the same would happen with chess. That said, I do think the overall level of play would go up since the first 20-30 moves of the "solution" would probably become standard opening theory.

The number of possible chess positions is way lower than 10^120. A trivial upper bound is 64!/32! which is less than 10^54, if you shuffle all the squares and then account for the fact that all empty squares are equal. (this is not technically an upper bound because of promotions, however, to promote you need to capture first which increases the number of empty squares which more than makes up for the extra options gained from promotion)

The current best estimate for number of positions as computed using Monte Carlo methods is more on the order of 10^46. So in principle, this is possible to compute with the entire resources of the universe. However, since humanity will probably not utilize every atom in the Solar system for solving chess, it still seems unlikely to me that chess would be solved.

As for the 10^120 number, that is the estimate of number of possible games of reasonable length. This is a way higher number than the number of positions because there are transpositions in chess. But if you are only interested in solving chess and build a giant tablebase then you don't need to care about that and merely consider each position.

The number of possible chess positions is way lower than 10^120. A trivial upper bound is 64!/32! which is less than 10^54, if you shuffle all the squares and then account for the fact that all empty squares are equal. (this is not technically an upper bound because of promotions, however, to promote you need to capture first which increases the number of empty squares which more than makes up for the extra options gained from promotion) The current best estimate for number of positions as computed using Monte Carlo methods is more on the order of 10^46. So in principle, this is possible to compute with the entire resources of the universe. However, since humanity will probably not utilize every atom in the Solar system for solving chess, it still seems unlikely to me that chess would be solved. As for the 10^120 number, that is the estimate of number of possible games of reasonable length. This is a way higher number than the number of positions because there are transpositions in chess. But if you are only interested in solving chess and build a giant tablebase then you don't need to care about that and merely consider each position.

What would happen is chess would go the way of checkers, only checkers didn't have a big industry surrounding publishing, teaching, and coaching. It would become a homework exercise rather than anything creative. Odds are they'd have to change the rules or seriously speed up time controls but the game as we know it would perish, and to some extent, already has. Top players are 2100 once they leave their engine prep it seems.

@Mephistochess99 said in #15:

Hans Berliner, the former Correspondence Chess World Champion, once said that chess would be solved. He had this idea of "perfect play" and decided that 1.d4 was the best opening move. He completely dismissed 1.e4, saying the only good move after 1.e4 e5 would be 2.f4—the King's Gambit—and according to him, that was just nonsense. He even talked to Bobby Fischer about it, trying to convince him that 1.d4 was better than 1.e4. Berliner also thought that after 1.Nf3, Black could just copy White's moves and the game would be a draw.

While reading his book, I started thinking: What would happen if chess really got solved? Honestly, I don’t think it would change much for humans, but it would probably be the end of computer chess. Any solution would be insanely long, and if it's a draw, someone would have to memorize the whole thing, including every possible sideline. No human could ever do that. Checkers was solved, and people still play it, so I guess the same would happen with chess.

That said, I do think the overall level of play would go up since the first 20-30 moves of the "solution" would probably become standard opening theory.

What would happen is chess would go the way of checkers, only checkers didn't have a big industry surrounding publishing, teaching, and coaching. It would become a homework exercise rather than anything creative. Odds are they'd have to change the rules or seriously speed up time controls but the game as we know it would perish, and to some extent, already has. Top players are 2100 once they leave their engine prep it seems. @Mephistochess99 said in #15: > Hans Berliner, the former Correspondence Chess World Champion, once said that chess would be solved. He had this idea of "perfect play" and decided that 1.d4 was the best opening move. He completely dismissed 1.e4, saying the only good move after 1.e4 e5 would be 2.f4—the King's Gambit—and according to him, that was just nonsense. He even talked to Bobby Fischer about it, trying to convince him that 1.d4 was better than 1.e4. Berliner also thought that after 1.Nf3, Black could just copy White's moves and the game would be a draw. > > While reading his book, I started thinking: What would happen if chess really got solved? Honestly, I don’t think it would change much for humans, but it would probably be the end of computer chess. Any solution would be insanely long, and if it's a draw, someone would have to memorize the whole thing, including every possible sideline. No human could ever do that. Checkers was solved, and people still play it, so I guess the same would happen with chess. > > That said, I do think the overall level of play would go up since the first 20-30 moves of the "solution" would probably become standard opening theory.
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@CoachedByABot said in #17:

What would happen is chess would go the way of checkers, only checkers didn't have a big industry surrounding publishing, teaching, and coaching. It would become a homework exercise rather than anything creative. Odds are they'd have to change the rules or seriously speed up time controls but the game as we know it would perish, and to some extent, already has. Top players are 2100 once they leave their engine prep it seems.

It would be much better if chess were never solved, and I hope it never will be. In my opinion, we shouldn’t even try. There’s no point in ruining a game that has brought people joy for centuries just to prove how smart we are. Correspondence chess has already been ruined—what was once a stage for human creativity has turned into nothing more than an engine competition. That should be warning enough.

@CoachedByABot said in #17: > What would happen is chess would go the way of checkers, only checkers didn't have a big industry surrounding publishing, teaching, and coaching. It would become a homework exercise rather than anything creative. Odds are they'd have to change the rules or seriously speed up time controls but the game as we know it would perish, and to some extent, already has. Top players are 2100 once they leave their engine prep it seems. It would be much better if chess were never solved, and I hope it never will be. In my opinion, we shouldn’t even try. There’s no point in ruining a game that has brought people joy for centuries just to prove how smart we are. Correspondence chess has already been ruined—what was once a stage for human creativity has turned into nothing more than an engine competition. That should be warning enough.

Focus on cooperative checkmates rather than competitive forced checkmates. Solve chess by using a help mate perft approach.
If you solve all the help mates at depth 4, you can then move onto solve all help mates at depth 5 and so on. So we can say it's solved to what depth so far?

Solving chess by brut space is to broad of a task. The task needs to be broken down into chunks, like captures. At the moment how many help mates are there at depth 8? To get the answer generate all possible positions after 8 plies (4 moves per side). https://www.chessprogramming.org/Perft_Results

Even with the cooperative challenge of solving all helpmates, it remains computationally infeasible to imagine we can solve every line that is less than 8848.5 moves deep.
https://www.reddit.com/r/chess/comments/168qmk6/longest_possible_chess_game_88485_moves/?rdt=57246

We need to be contempt with the average length of a chess game as depth to solve.
https://en.wikipedia.org/wiki/List_of_world_records_in_chess

Due to the complexity of solving a task, the aim of a move must know it's final mating pattern destination. Engines are not there yet. They don't aim at exchanging pieces to create an endgame scenario. If we or engines keep avoiding the destination, than it will take for ever to reach. Engines don't play with the concern of ending the game with insufficient material to mate, but humans should. The goal is what ? Definitely not perfect play, because that's a draw destination.

Focus on cooperative checkmates rather than competitive forced checkmates. Solve chess by using a help mate perft approach. If you solve all the help mates at depth 4, you can then move onto solve all help mates at depth 5 and so on. So we can say it's solved to what depth so far? Solving chess by brut space is to broad of a task. The task needs to be broken down into chunks, like captures. At the moment how many help mates are there at depth 8? To get the answer generate all possible positions after 8 plies (4 moves per side). https://www.chessprogramming.org/Perft_Results Even with the cooperative challenge of solving all helpmates, it remains computationally infeasible to imagine we can solve every line that is less than 8848.5 moves deep. https://www.reddit.com/r/chess/comments/168qmk6/longest_possible_chess_game_88485_moves/?rdt=57246 We need to be contempt with the average length of a chess game as depth to solve. https://en.wikipedia.org/wiki/List_of_world_records_in_chess Due to the complexity of solving a task, the aim of a move must know it's final mating pattern destination. Engines are not there yet. They don't aim at exchanging pieces to create an endgame scenario. If we or engines keep avoiding the destination, than it will take for ever to reach. Engines don't play with the concern of ending the game with insufficient material to mate, but humans should. The goal is what ? Definitely not perfect play, because that's a draw destination.