Author: Uri Blass
Date: 14:37:44 05/14/01
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On May 14, 2001 at 15:44:28, Dann Corbit wrote: >On May 14, 2001 at 14:51:16, J. Wesley Cleveland wrote: >[snip] >>I thought that is what we were discussing. If you have a hash table large enough >>to store every position found in the search, then you do not need total path >>information with each position, which means you could solve chess by considering >>"only" about 10^25 positions. So, if Moore's law holds up, we could solve chess >>by the end of the century, rather than by the end of the universe. > >Not a chance. Let's ignore the complication of things like the half-move clock >for now. We shall also ignore the fact that you can ignore all the draw rules >except for material count, and that it may be beneficial to do so at times. > >One of the fields of the hash position is depth. You will not know the answer >to the true value of the position until the position has reached either >won/loss/draw. Since chess has a depth of nearly 12000 plies, that implies a >search so long and so deep that even if it were purely a binary choice you would >never solve it. Just consider 2^10000 [about 2e3010] (which is absurdly >smaller than the chess tree). Take the square root of that. Hmmmm. > >Having 10^50 positions in a hash table is useless unless you have analyzed them >clear to the end. The end is so far away that it is laughable to consider that >we might possibly get there. I do not know if 10^25 is practically enough to solve chess but I am not sure that it is not. The point is that you may analyze only part of the legal positions in order to solve chess. Instead of solving chess you can solve the following game that has the same solution as chess but less positions. The rules are the same as chess with the following modifications: 1)Moves that give the opponent to play a forced mate of at most 3 moves are illegal. 2)A side who has no leagl moves in this game and has legal moves by the chess rules is losing the game. There are clearly less position in this game (for example the position after 1.f3 e5 2.g4 is illegal byt the rules) Now you can replace the mate in at most 3 moves by the words a win without doubt and you can say that moves that give the opponent a win without doubt are illegal when win without doubt can be calculated in a short time. There are a lot of positions that can be described as a win without doubt. Example every position when the weaker side has only a king and no stalemate chances when the stronger side has 2 connected pawns that the king has no chance to capture. This no chance can be evaluated by a smart evaluation. The 50 move rule is not relevant because you need full 100 plies after you get a position with only a king for the weaker side. Uri
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