In repeated games with Nash equilibria in mixed strategies, players optimize by playing randomly. Players are boundedly rational in their randomization e�orts. Arguably, they have no internal randomization facility and they fashion external randomization aids from the environment. By conditioning on past play, boundedly rational players exhibit a pattern. The pattern is characterized by cognitive limitations variously called local representativeness, the law of small numbers or the gambler’s fallacy. I find one such pattern—balance then runs—in re-analysis of existing data for matching pennies experiments. While players and play are heterogeneous, the pattern makes prediction plausible. I implement prediction with a non-linear autoregression. Model 1 is a statistically and substantively significant tool for predicting behavior in matching pennies. There is evidence for two other behavioral models, both of which require some sort of sophistication—including a model of the opponent as boundedly rational.
