We study a simple model of similarity-based global cumulative imitation in symmetric games with large and ordered strategy sets and a salient winning player. We show that the learning model explains behavior well in both field and laboratory data from one such “winner-takes-all” game: the lowest unique positive integer game in which the player that chose the lowest number not chosen by anyone else wins a fixed prize. We corroborate this finding in three other winner-takes-all games and discuss under what conditions the model may be applicable beyond this class of games. Theoretically, we show that global cumulative imitation without similarity weighting results in a version of the replicator dynamic in winner-takes-all games.