We take a machine learning approach to the problem of predicting initial play in strategicform games, with the goal of uncovering new regularities in play and improving the predictions of existing theories. The analysis is implemented on data from previous laboratory experiments, and also a new data set of 200 games played on Mechanical Turk. We first use machine learning algorithms to train prediction rules based on a large set of game features. Examination of the games where our algorithm predicts play correctly, but the existing models do not, leads us to introduce a risk aversion parameter that we find significantly improves predictive accuracy. Second, we augment existing empirical models by using play in a set of training games to predict how the models’ parameters vary across new games. This modified approach generates better out-of-sample predictions, and provides insight into how and why the parameters vary. These methodologies are not special to the problem of predicting play in games, and may be useful in other contexts.