We are developing a robot that can play an outdoor game with children. In realizing such a robot, the person detection and tracking methods play an important role. In this paper, we propose methods for improving person detection and tracking using a laser range finder (LRF). A problem facing player detection using an LRF during play is that detection of a player's body sometimes fails because of the posture of the player. Thus, we propose two improvements of the conventional person detection algorithm. One is to determine the body boundary when an arm overlaps the body, and the other is to choose the most probable object as the body among the detected objects. Another problem is how to track players who are hidden by other players. We introduce a new algorithm to robustly track a player even when the player is behind other players. We conducted three experiments. In the first experiment, we investigate the performance improvement by the proposed player detection algorithm. The second experiment proves that the proposed player-tracking algorithm can robustly track a player even after the LRF has lost that player. In the last experiment, we conduct the game Darumasan ga Koronda using the developed system and confirm that the system can perform the game without large problems.