Please do.
I will put it on a web page. But I need some time. My job keeps me very busy right now.
But I'm not sure I
will post the statistical analysis (it was almost ten hand writen pages,
and I'm not sure I still have them).
Have You performed an empirical test for collisions?
No, analysis was analytic. I've used the scheme in different ways, and since I knew were was the defect I put extra code to protect from the defect. This proved to be usefull... I was able to catch collisions at low rate in practice, but this rate would have been unacceptable if I had not been able to detect them.

The defect is as follow: if you have 2 different board configurations, the probability that they have the same hash key can be as low as 1/256 (for a 64-bit key) if the difference between the 2 configurations has self symmetries. Anti Huima's scheme had the same defect, except the probability was 1. That's why I've been able to isolate it: I always had collisions between the same positions, and it didn't depend on the way random bits were generated.

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