An optimal MOO strategy

Abstract

We calculated a fixed strategy that minimizes the average number of guesses (minimum strategy) for the number-guessing game MOO by exhaustive search. Although the minimum strategy for a similar game, mastermind, has been reported, this study seems to be the first to find the minimum strategy for MOO with a larger search space. When two players play against each other in MOO, the minimum strategy is not always the strongest fixed strategy. First, we compute a fixed strategy that has the maximum winning rate when played against the minimum strategy. Then we confirm that there is no fixed strategy with a winning rate exceeding 0.5 against this strategy. This result shows that MOO is a game with the strongest fixed strategy.