> 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.
The parent comment was saying that when you fix the number of heads to be k in advance, the set of head positions you get is random. That sounds correct.
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.