Optimal play in Guess Who? 2 June 2026

Available for all to read: Optimal Play in Guess Who?

The game Guess Who? has a board of 24 faces and you must guess which character your opponent has selected using yes/no questions to narrow down the suspects, such as "Does your person have white hair?". The authors of this paper suggest you can narrow down the suspects more quickly by asking questions with an embedded paradox. This means there are three possible outcomes - your opponent might answer yes, they might answer no, or the paradox occurs and their head explodes - a third response which reveals something about the character you're trying to guess. 

It's a bit of fun in game theory making use of mathematical logic and paradoxes. The authors also explain how their ideas could be used as an introduction to game theory for an interested sixth form student, perhaps at an extra-curricular event or club. 

The paper is open access and free for all to read.  

The preprint caused media interest when it was posted last summer, see for example:

• Scientist shares formula to win Guess Who and there's questions you must avoid (Manchester Evening News)
• Mathematicians have worked out the optimal strategy for Guess Who? (New Scientist)