Summary: We study learning processes for finite strategic-form games, in which players use the history of past play to forecast play in the current period. In a generalization of fictitious play, we assume only that players asymptotically choose best responses to the historical frequencies of opponents’ past play. This implies that if the stage-game strategies converge, the limit is a Nash equilibrium. In the basic model, plays seems unlikely to converge to a mixed-strategy equilibrium, but such convergence is natural when the stage game is perturbed in the manner of Harsanyi’s purification theorem.