Finding an evolutionary solution to the game of MasterMind with good scaling behavior Juan J. Merelo, Antonio M. Mora 1 , Carlos Cotta, Antonio J. Fern´andez-Leiva 2 1 Dept. Computer Architecture and Technology + CITIC University of Granada (jmerelo|amorag)@geneura.ugr.es 2 Dept. of Computer Sciences and Languages University of M´ alaga (ccottap|afdez)@lcc.uma.es Keywords: MasterMind, oracle games, puzzles, evolutionary algorithms, pa- rameter optimization Abstract. The main research issue in the game of MasterMind is to find a method that minimizes the number of turns needed to find the solution. But another venue is to find a method that scale well when the size of the search space is increased. In this paper we will present a method that uses evolutionary algorithms to find fast solutions to the game of MasterMind that scale better with problem size than previously described methods; this is obtained by just fixing one parameter. We prove its scalability by testing it over a wide range of MasterMind problem sizes. 1 Introduction and state of the art MasterMind [2] is a puzzle in which one player A hides a combination of κ symbols and length ‘, while the other player B tries to discover it by playing combinations using the same alphabet and length. The answers from player A to every combination include the number of symbols in the combination that are in the correct position and the number of colors that have been guessed correctly. Player B then xplays a new combination, until the hidden one is found. The objective of the game is to play repeatedly minimizing the number of turns needed to find the solution. Most MasterMind algorithms so far [3, 4] use the concept of eligible, pos- sible or consistent combinations: those that, according to responses by player A, could still be the hidden combination or, in other words, those that match the played combinations as indicated by the answer. Exhaustive methods [2, 5] would eliminate all non-consistent solutions and play a consistent one, while non-exhaustive methods would sample the set of consistent solutions and play one of them. Those solutions are guaranteed to reduce the search space at least by one, but obviously different combinations have a different reduction capabil- ity. This capability is reflected by a score. However, scores are heuristic; there is