We consider stochastic dynamics for the Matching Pennies game, which behave, in expectation, like the best-response dynamics (i.e., the continuous fictitious play). Since the corresponding vector field is not continuous, we cannot apply the deterministic approximation results of Benaïm and Weibull [M. Benaïm, W. Weibull. 2003. Deterministic approximation of stochastic evolution in games. Econometrica 71, 873-903]. Nevertheless, we prove such results for our dynamics by developing the notion of a "leading coordinate."