🤖 AI Summary
This paper investigates optimal questioning strategies in the two-player deduction game “Guess Who?”. Challenging the conventional wisdom that binary search is universally optimal, we formulate a stochastic game model and employ dynamic programming combined with continuous-limit analysis to rigorously prove that, under asymmetric states (e.g., when one player lags), aggressive strategies—characterized by high-risk, high-information-gain questions—significantly increase the trailing player’s reversal probability, outperforming binary search. We derive a globally explicit optimal strategy, quantify win-rate gains across game states, and characterize asymptotic behavior under infinite rounds using optimal stopping theory. This work corrects a longstanding misconception regarding strategy optimality and establishes a theoretical paradigm and computational framework for designing counter-strategies for disadvantaged players in incomplete-information games.
📝 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.
