Quick typo note (unless I’m really misreading something): in your setups, you refer to coins that are biased towards tails, but in your analyses, you talk about the coins as though they are biased towards heads.
One is the “cold pool”, in which each coin comes up 1 (i.e. heads) with probability 0.1 and 0 with probability 0.9. The other is the “hot pool”, in which each coin comes up 1 with probability 0.2
n random coins with heads-probability 0.2
We started with only 0.2n tails
full compression would require roughly .59n tails, and we only have about (0.1+0.2)n=0.3n
This is super interesting!
Quick typo note (unless I’m really misreading something): in your setups, you refer to coins that are biased towards tails, but in your analyses, you talk about the coins as though they are biased towards heads.
Oh shit, that’s actually a pretty serious oversight. I’m effectively missing negative signs all over the place. Thanks for catching it!
Fixed now, and it did change the numbers.