Summary: We examine an evolutionary process based on an explicit model of choice in which agents occasionally make mistakes in choosing their strategies. If the application size is sufficiently large, then the deterministic replicator dynamics provides a good approximation of the behavior of the system over finite time periods. The limiting behavior of the process is captured by combinatorial techniques introduced by Freidlin and Wentzell and popularized by Young and Kandori, Mailath, and Rob. We find conditions under which the limiting distribution selects the risk-dominant equilibrium in a \(2\times 2\) game and conditions under which the payoff-dominant equilibrium is selected.