A finite population of agents playing a 2 ×2 symmetric game evolves by adaptive best response. The assumption that players make mistakes is dropped in favour of one where players differ, via payoff heterogeneity. Arbitrary mutations are thus replaced with an economically justified specification. The depth as well as the width of basins of attraction is important when determining long-run behaviour. With vanishing noise and balanced payoff variances, the risk dominant equilibrium is selected. Unbalanced variances may result in the selection of other equilibria, including the payoff dominant. The ergodic extrema correspond exactly to the Baysian Nash equilibria of the underlying trembled stage game. This enables an analysis of the ergodic distribution for non-vanishing noise and larger populations.