Learning to Play Mastermind Well Using the Anti-Mind with Feedback Algorithm

摘要

In a previous work we developed the Anti-Mind algorithm. The Anti-Mind program simulated a good player of the Mastermind game, discovering the secret code defined by the human operator (a sequence of four integers in the interval [0 5]) very quickly. Then we used the algorithm of Anti-Mind to help and correct a human operator trying to discover the secret code defined by the computer resulting in the Anti-Mind with Feedback algorithm. In this paper, we revisited this work and developed another faster implementation of the Anti-Mind with Feedback algorithm which has the drawback that it does not know the set of next good guesses, it just compares each guess with the previous moves and accepts it if it is coherent with all the previous moves. Nevertheless, we introduced an option to generate the set of good guesses, i.e., the guesses that are coherent with all the previous moves. This implementation allows generalizing the Mastermind game to more than four digits and more than six colours. We begin to define rigorously what we mean by a guess coherent with a previous move, next we define what is a good guess and, then, we enunciate five hypotheses about the Anti-Mind algorithm namely one that guarantees that if we always play a good guess we will find the code in a finite bounded number of guesses. We propose a strategy to play Mastermind with the maximization of repetions at the beginning of the game which reduces the cognitive overload to play well and validate it with the Anti-Mind with Feedback algorithm. Finally we compare the Anti-Mind algorithm with the Ant-Mind with maximization of repetitions of the guesses through intensive simulations and conclude that the original Anti-Mind algorithm has a better average performance in terms of the number of guesses to break the secret code.