> Produce a table of all possible sequences of length 1,000 with k heads and 1,000-k tails. > Look up the position of your actual realized sequence in that table. The index of that position is a uniform random integer in a range from 1 to the size of the table.

I don’t see why it would be. The normal way to produce such a table is as hhh…hh, hhh…ht, hhh…th, … ttt…ht, ttt…th, ttt…tt. If heads is more likely than tails, the index is more likely to be in the lower half than the upper half.

Reading https://blog.cloudflare.com/ensuring-randomness-with-linuxs-..., I also don’t think that’s how Linux’ entropy pool works.