Adopting a mixed response strategy in competitive situations can prevent opponents from exploiting predictable play. What drives stochastic action selection is unclear given that choice patterns suggest that, on average, players are indifferent to available options during mixed-strategy equilibria. To gain insight into this stochastic selection process we examined how motor preparation was allocated during a mixed-strategy game. If selection processes on each trial reflect a global indifference between options then there should be no bias in motor preparation ('unbiased preparation hypothesis'). If, however, differences exist in the desirability of options on each trial then motor preparation should be biased towards the preferred option ('biased preparation hypothesis'). We tested between these alternatives by examining how saccade preparation was allocated as human subjects competed against an adaptive computer opponent in an oculomotor version of the game 'matching pennies'. Subjects were free to choose between two visual targets using a saccadic eye movement. Saccade preparation was probed by occasionally flashing a visual distractor at a range of times preceding target presentation. The probability that a distractor would evoke a saccade error and, when it failed to do so, the probability of choosing each of the subsequent targets quantified the temporal and spatial evolution of saccade preparation, respectively. Our results show that saccade preparation became increasingly biased as the time of target presentation approached. Specifically, the spatial locus to which saccade preparation was directed varied from trial to trial and its time course depended on task timing.