Optimal Strategy in "Guess Who?": Beyond Binary Search

TL;DR

This paper models 'Guess Who?' as a stochastic game and finds the explicit optimal strategy, revealing that binary search is not always optimal and that bold plays can be advantageous for trailing players.

Contribution

It introduces a stochastic game model for 'Guess Who?' and derives the explicit optimal strategy, challenging the common binary search approach.

Findings

Optimal strategy explicitly derived

Binary search not always optimal

Bold plays benefit trailing players

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 \emph{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.