Much of the history of game theory has been dominated by the problem of indeterminacy. The very search for better versions of rationality, as well as the long list of attempts to refine Nash equilibrium, can be seen as answers to the indeterminacy that has accompanied game theory through its history. More recently, the experimental approach to game theory has attempted a more radical solution: by directly generating a stream of behavioral observations, one hopes that behavioral hypotheses will be sharper, and predictions more accurate. This article looks at several attempts to address indeterminacy, including the shift to evolutionary models. However, because its goal is to establish whether rational choice models are inescapably doomed to produce indeterminate outcomes, it pays much more attention to the experimental turn in game theory, the difficulty it encounters, and the promising results obtained by more realistic models of rationality that include a social component.