An optimal MOO strategy

TL;DR

This paper determines the optimal fixed guessing strategy for the number-guessing game MOO using exhaustive search, establishing it as a game with a strongest fixed strategy and analyzing its properties.

Contribution

It is the first to find the minimum strategy for MOO with a larger search space and to analyze the game's fixed strategies and their effectiveness.

Findings

The minimum strategy minimizes average guesses in MOO.

No fixed strategy beats a 0.5 winning rate against the maximum winning rate strategy.

MOO has a strongest fixed 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.