Fictitious play is an algorithm for computing Nash equilibria of matrix games. Recently, machine learning variants of fictitious play have been successfully applied to complicated real-world games. This paper presents a simple modification of fictitious play which is a strict improvement over the original: it has the same theoretical worst-case convergence rate, is equally applicable in a machine learning context, and enjoys superior empirical performance. We conduct an extensive comparison of our algorithm with fictitious play, proving an optimal O(1/t) convergence rate for certain classes of games, demonstrating superior performance numerically across a variety of games, and concluding with experiments that extend these algorithms to the setting of deep multiagent reinforcement learning.