We study a new equilibrium concept in non-cooperative games, where players follow a behavioral rule called best-reply matching. Under this rule a player matches the probability of playing a pure strategy to the probability that this strategy is a best reply. Kosfeld, Droste, and Voorneveld [Games and Economic Behavior 40 (2002) 270] show that best-reply matching equilibria are stationary states in a simple model of social learning, where newborns adopt a best-reply to recent observations of play. In this paper we analyze best-reply matching in more detail and illustrate the concept by means of well-known examples. For example in the centipede game it is shown that players will continue with large probability.