Author: Sune Fischer
Date: 03:03:37 12/09/01
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On December 08, 2001 at 22:30:31, Wylie Garvin wrote: >Hi all, > > Disclaimer, my math/logic may be broken! I would welcome feedback on this >message. There's been some discussion on this board of zobrist keys w.r.t. >hamming distances etc. I want to have a look at it from a different angle. > > We have two goals for our zobrist keys: >(1) minimize the probability of a collision for two arbitrary positions, and >(2) spread the keys evenly across the keyspace (I guess this only matters for >the bottom N bits for some N=24 or something). > > NOTE: for the moment, I'm going to assume that each table entry is equally >likely to be XORed into an arbitrary zobrist key. > > Now (1) is essentially saying the key should retain as much information as >possible; in other words, the probability P(n) of bit n being a 1 in a zobrist >key should be about 0.5. This assumption about P(n)=0.5 is not quite clear IMO. We want to avoid they collide, but is this the same as having random keys? That is the problem, and I think you are assuming what we want to prove (??). Given 100 Zobrist tables of random keys, some tables will have better "non-collide" properties than others tables. So randomizing could also backfire and give us a _very_ bad table (in principle). The question is: will "the Hamming trick" improve on these odds or not? Like there is a perfect chess game (we need to solve chess to find it), there is probably a "best" Zobrist table, one that we should all be using and read in from a file. Since we don't have that table, we just make an educated guess. -S.
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