This paper deals with 2-player zero-sum repeated games in which player 1 receives a bonus at stage t if he repeats the action he played at stage t-1. We investigate the optimality of simple strategies for player 1. A simple strategy for player 1 consists of playing the same mixed action at every stage, irrespective of past play. Furthermore, for games in which player 1 has a simple optimal strategy, we characterize the set of stationary optimal strategies for player 2.