Optimal Mastermind Strategy: Maximizing Information Entropy

This article explores an optimal strategy for playing Mastermind, leveraging information theory. The core idea is to always choose the guess with the highest entropy – the guess that provides the most information on average. By calculating the remaining possible codes after each guess and using the entropy formula, the optimal guess can be determined. Simulations show this strategy solves Mastermind in an average of 4.47 guesses, comparable to other algorithms and approaching the theoretical limit. The article also notes that calculating the remaining possible codes is an NP-complete problem, making the computational cost significant as code length and color options increase.