Author: Uri Blass
Date: 21:35:37 05/14/01
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On May 14, 2001 at 21:10:52, J. Wesley Cleveland wrote: >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. > >What you are ignoring, is that with alpha-beta, one side is always making its >best move which will eliminate (virtually) all of these extrodinarily deep >lines. I agree that 2^10000 is not the right number and the number that I am interested is the number of positions because you do not need to search the same position twice but I am still interested to know how many positions programs need to search in order to solve the following position without tablebases(the position happened in Fritz-Junior match and Deep Fritz missed a win because it did not use the right tablebases. [D]8/4b2B/k7/6n1/8/8/4K1R1/8 w - - 0 1 I do not think that sqrt of the size of the relevant tablebases is enough In this case 10^6 positions were clearly enough to solve the position and it means that searching x plies forward could take clearly less than 2x seconds with the hardware of Deep Fritz. Deep Fritz searched for 105 seconds and only got 17 plies so it seems that your math of sqrt is wrong or that Deep Fritz has a bug. Uri
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