TL;DW: an extremely convoluted explanation of the optimal strategy for Guess Who.

Let’s call

• “pool” - the number of characters a player did not rule out as not being the right character. For example, if there are 20 chars and you ruled 8 out, then your pool is 12. Your pool is “a”, your opponent’s pool is “b”.
• “bid” - the number of characters in the pool that a question applies to. For example, if your pool is 12, you ask “do they have a beard?”, and there are 4 bearded characters there, then the bid is 4. And if your opponent asks “does he look like a bitch?”, whatever you do, do not include Marsellus Wallace into the bid.

So. If I got this right, your bid should be either a/2 or b-1, whichever is the smallest. That’s it.