We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies, and allows switching between these states. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that always follows its part of the unique mixed strategy Nash equilibrium profile. Estimated results show significant mixed strategy play and non-stationary dynamics. We also explore the ability of the model to forecast action choice.