Author: Robert Hyatt
Date: 20:53:26 11/22/03
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On November 21, 2003 at 23:05:38, K. Burcham wrote: > >Chris, thank you for information. This clears up some of my thoughts. > >a follow up question. > >"It is possible that this advice would not work for another chess program, for >example one that "clears" its hash table before it starts thinking. In this >case, clearing 1Gb of hash table when playing bullet games would lead the >program to use almost all its time for "clearing the hash table". > >this is what I understand from your information. >if we are in a tournament with Tiger and permanent brain is on, then we can say >that with x amount of hash, if we use more than this then Tiger will have hash >collisions. > >If we are in a tournament with another program why would it ever clear its hash >during the game? it would seem this would be valuable information for the >search. > >kburcham This is a bad assumption. First, a "collision" is what happens when two hash signatures from different positions, match exactly. With 64 bit hashing, the probability is near zero that this happens during a game. Making the hash table bigger doesn't really make this probability higher. Because even though it is really a bit higher when you are able to keep more possible positions, if P is low enough to start with, 2P is _still_ low... The question is, what is the probability that a position will produce a duplicate hash signature that matches a different position already stored in the table? The bigger the table, the higher the probability, but _only_ if you have a high probability for collisions in the first place... 64 bits is roughly 4,000,000,000 squared, or 16,000,000,000,000,000,000 unique hash signatures (2^64) taken from roughly 2^168 unique chess positions. With good random numbers that is enough unique signatures that the probability is _very low_. And then you have the issue that even if you do have a collision here and there the probability is almost 0.00 that it will actually effect the search result. make it as big as you can stand without paging.
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