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.
Arthur
On Dec 20, 2007, at 10:49 AM, Jacques Basaldúa wrote:
<snip>
The idea is that any of the board the can be transformed by mirror
rot from a given
board will produce the same set 8 hashes, just in a different
order. Because the
hashes are (with high probability) unique, one hash represents a
board and the canonical hash represents the class of 8 boards
produced by mirror/rot.
It is true: Another board in the class -> same set of 8 hashes ->
same canonical hash.
It is almost certain (prob = 1/2^64 per check): A different board -
> a different set
of 8 hashes -> different canonical hash.
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