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I heard about an estimate how many legal positions there are in a chess game. There are roughly ${10}^{40}$.

Is it realistic that this amound of positions can be checked in the near future ?

Or is the only hope to solve chess to find some amazing properties to cut the tree of possibilities drastically ?

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Solving a game can mean (at least) three different things: (1) knowing the result from the starting position, (2) plus knowing a strategy that gives the optimal result for a player whatever his opponents moves are, or (3) knowing the optimal moves and the result in every legal position. Which one do you mean (altough the answer may be "no" in any case)? –  JiK Dec 20 '13 at 13:30
Pesonally, I would be content with (1), but probably (1) will imply (2) because a nonconstructive proof would be a miracle. –  Peter Dec 20 '13 at 13:42

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It should be noted that the vast majority of those $10^{40}$ legal positions are so unbalanced and so "absurd" that would never occur in any game between knowledgeable players not playing totally random moves. As such they're basically irrelevant for the problem of "solving chess". Nevertheless the number of "reasonable" positions and games is so huge that after more than 150 years of grandmaster games, the question is still very open, although one may argue that the game is about even.

For all practical purposes chess has been solved, at least in the weaker sense that the chess engine running in my tablet can beat any human player, past, living and most likely also future.

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It is right that solving chess does not require to know the value of all positions. It would be sufficient to find a particular line forcing a draw or a win. I also agree that the resulting number of positions is too big, and that the game probably is theoretically draw. But I do not fully agree to the last statement : It is widely believed that NO human can beat the current engines, but it is impossible to prove this statement, but that is not the point. Even if it is true, then I would not agree that chess is solved only because machines play better then human beings. –  Peter Mar 9 at 10:45
A computer can prove numbers to be prime which are far too big that human beings could hope to do so in a reasonable amount of time. But this does not mean, that goldbach's conjecture is solved. –  Peter Mar 9 at 10:48

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