Optimal guessing in ‘Guess Who’

Are you Richard? Are you Anne? We look at the strategic problem in the children’s guessing game Guess Who, which is a form of zero-sum symmetric game with perfect information. We discuss some preliminary strategic insights and formally derive an optimal strategy and win-probabilities for the game. We discuss the first-mover advantage in the game and other strategic aspects coming out of the optimal strategy. While the paper is based on the popular children’s game, our analysis generalises the actual game by allowing any initial game state with an arbitrarily large number of starting characters. With the aid of these mathematical results you can now comprehensively thrash your young children and be a terrible parent!