Author: Pat King
Date: 05:50:53 09/22/98
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On September 21, 1998 at 19:32:37, James Robertson wrote: >I sent a message to Robert Hyatt with the same question, and he said that the >odds of turning up two positions with the same number is almost nil. Almost. I use a 16 bit index and 16 bit signature, so the chance of two positions having the same index and signature is 2^-32 (assuming my hashing algorithms are doing a good job of uniformly distributing the keys). The odds of a search not containing a mistake are therefore (1-2^-32)^n, where n is the number of nodes searched. To have a 50% chance of an error, you'd need to search about 3e+09 nodes. With null-move, that's about 20 plies. And is the error in a place likely to affect the outcome of the search? Probably not. So we can sleep well at night knowing that at least mistakes in recalling hash nodes are not a serious problem! Pat PS Since 1-2^32 is so close to 1, there's probably a fair amount of error in that 3e+09 estimate, but you can stand a LOT of error in this case and still have the argument hold up!
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