A key issue for a device involved in a competitive game is to be able to match the ability of the opponent, thus making the game interesting. When the game is played by a human player against a machine, this should be able to adapt online to the opponent's ability, which may change during the game. When the playing machine is a robot, and the game involves physical activity, adaptation should consider the player's ability, but also other aspects directly related to the physical nature of the game. Adaptation could be obtained either intrinsically, by designing the interaction, or explicitly, by modeling aspects of the opponent that can enable to estimate performance, behaviors, and strategies. We present in this paper different approaches to design the two types of adaptation, together with two competitive, physically interactive robogames exploiting them.