The goal of this paper is to describe an adaptive robot game, which motivates elderly people to do a regular amount of physical exercise while playing. One of the advantages of robot based games is that the initiative to play can be taken autonomously by the robot. In this case, the goal is to improve the mental and physical state of the user by playing a physical game with the robot. Ideally, a robot game should be simple to learn but difficult to master, providing an appropriate degree of challenge for players with different skills. In order to achieve that, the robot should be able to adapt to the behavior of the interacting person. This paper presents a simple ball game between a single player and a mobile robot platform. The algorithm has been validated using simulation and real world experiments.