[tripletao]

> If, say, you do the assignment from a 256 bit random number such that 4 of the possible assignments are twice as likely as the others under your randomization procedure

Your numbers don't make sense. Your number of assignments is way fewer than 2^256, so the problem the author is (mistakenly) concerned about doesn't arise--no sane method would result in any measurable deviation from equiprobable, certainly not "twice as likely".

With a larger number of turkeys and thus assignments, the author is correct that some assignments must be impossible by a counting argument. They are incorrect that it matters--as long as the process of winnowing our set to 2^256 candidates isn't measurably biased (i.e., correlated with turkey weight ex television effects), it changes nothing. There is no difference between discarding a possible assignment because the CSPRNG algorithm choice excludes it (as we do for all but 2^256) and discarding it because the seed excludes it (as we do for all but one), as long as both processes are unbiased.

[topaz0]

typo -- meant to say 8 bit random number i.e. having 256 possibilities, convenient just because the number of assignments was close to a power of 2. If instead you use a 248-sided die and have equal probabilities for all but 4 of the assignments, the result is similar but in the other direction. Of course there are many other more subtle ways that your distribution over assignments could go wrong, I was just picking one that was easy to analyze.

[tripletao]

Ah, then I see where you got 4 assignments and 2x probability. Then I think that is the problem the author was worried about and that it would be a real concern with those numbers, but that the much smaller number of possibilities in your example causes incorrect intuition for the 2^256-possibility case.