OPTIMAL STRATEGY IN “GUESS WHO?”: BEYOND BINARY SEARCH

Abstract

“Guess Who?” is a popular two player game where players ask “Yes”/“No” questions to search for their opponent's secret identity from a pool of possible candidates. This is modeled as a simple stochastic game. Using this model, the optimal strategy is explicitly found. Contrary to popular belief, performing a binary search is not always optimal. Instead, the optimal strategy for the player who trails is to make certain bold plays in an attempt catch up. This is discovered by first analyzing a continuous version of the game where players play indefinitely and the winner is never decided after finitely many rounds.