Development of An O(n)-Round Strategy for the Magnus-Derek Game

Abstract

The Magnus-Derek game, a two-player game played on a round table with n positions, is investigated further. The players jointly control the movement of a token. One player, Magnus, aims to maximize the number of positions visited while minimizing the number of rounds. The other player, Derek, attempts to minimize the number of visited positions. We provide a new Magnus approach that allows him to visit the most spots in 3(n - 1) rounds, which is the optimum number of rounds up to a constant factor.