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.