It is well-known that laboratory subjects often do not play mixed strategy equilibrium games according to the equilibrium predictions. However, little is known about the role of cognition in these strategic settings. We conduct an experiment where subjects play a repeated hide and seek game against a computer opponent. Subjects play with either fewer available cognitive resources (under a high cognitive load) or with more available cognitive resources (under a low cognitive load). Surprisingly, we …find evidence that subjects under a high load earn more than subjects under a low load. However, we also …find that subjects under a low cognitive load exhibit a greater rate of increase in earnings across rounds, thus suggesting more learning. Further, while we observe that subjects do not mix in the predicted proportions and that their actions exhibit serial correlation, we do not find strong evidence these are related to their available cognitive resources. This suggests that the standard laboratory deviations from equilibrium are not associated with the availability of cognitive resources. Our results shed light on the extent to which cognitive resources affect (and do not affect) behavior in games with a mixed strategy equilibrium.