Optimizing the Video Game Multi-Jump: Player Strategy, AI, and Level Design

This article initiates the mathematical study of multi-jumping in video games. We begin by proving a necessary, and frequently sufficient, condition for a multi-jump to be optimal, i.e., achieve the highest possible height after traveling a given horizontal distance. We then give strategies that can be used by human players and by AI to select successful multi-jumps in real time. We also show how a video game designer can build the ground around a platform to guarantee that the platform is reachable-or unreachable-by a multi-jump beginning at any point on the ground.