[incorrecthorse]

Board state itself becomes unique pretty quickly, so you would just end up with a gigantic lot of "moves" played only 1 time.

EDIT: so you could define "rare" moves as the biggest difference of occurrences between state N and state N+1.

[kristopolous]

I bet it becomes unique far far less often then most people think.

Computing the number of permutations is thoroughly unconvincing.

For instance, there's 20 possible first moves and of those only probably 2 are played 95% of the time. You can certainly compute what the rates open is and the rarest response that's actually played or the rarest response to the most common open