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Subject: Re: Look at zobrist keys from information-theoretic point of view.

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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