> > With 8 hashes per position, the chance of two different boards
> > producing a different set of hashes but
> > the same canonical hash is greater than 1/2^64, because there will be
> > a bias in the choice of canonical
> > hashes - toward numerically lower numbers, for instance.
> >
> > I think.
> 
> More importantly, how does it differ from 8/2^64 = 1/2^61?

If hash collisions are worrisome, you can always use
96-bit or 128-bit hashes. Modern x86s can do 8 parallel
loads, adds, subtracts, or stores of 16-bit numbers in
one step using SIMD, just like Antti Huima suggests in
http://fragrieu.free.fr/zobrist.pdf.

Michael Wing

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