[OscarCunningham]

One thing this doesn't take into account (and the paper acknowledges this) is that the characters are assigned by picking cards from a deck. So the two players cannot have the same character.

Taking this into account would make the game much more complicated, because it can introduce an element of bluff.

For a simple example, imagine that there are only 5 characters. On your first turn you know the opponent doesn't have the same card as you, so you've got 4 options remaining. You'd like to ask a question that splits them into 2+2, but if you do this then the card you're holding will make one of the groups into a 3. Your opponent will know that your card is one of the 3, so you've effectively given them a head start. Instead you might sometimes want to split the options 3+2 with your card in the 2, as a bluff.

How often you want to do this must be described by some Nash equilibrium probabilities. It would be interesting to set up a linear programming solver to find these exactly, but so far I haven't had time to set this up. I don't know if it would be practical to solve the full version of the game with 24 characters.

[alberth]

Is this accurate?

Doesn’t that strategy only work in games like Clue, where everyone is trying to uncover the same hidden character?

In Guess Who, you’re identifying your opponent’s character, not a shared one, so any misdirection only hurts you … because it doesn’t generate extra signal for your opponent, so there’s no strategic benefit to misleading them.

[OscarCunningham]

The problem is when you bisect an odd sized group. You necessarily have to make one half larger than the other. So you're not trying to misdirect, you're trying to avoid creating a signal. But to do this you have to sometimes put your character in the smaller half, which trades off against your other goal of shrinking the pool as fast as possible.

[baobun]

The signal is in observing the number of options your opponent eliminates after a guess.