In Stackelberg games, a "leader" player first chooses a mixed strategy to commit to, then a "follower" player responds based on the observed leader strategy. Notable strides have been made in scaling up the algorithms for such games, but the problem of finding optimal leader strategies spanning multiple rounds of the game, with a Bayesian prior over unknown follower preferences, has been left unaddressed. Towards remedying this shortcoming we propose a first-of-a-kind tractable method to compute an optimal plan of leader actions in a repeated game against an unknown follower, assuming that the follower plays myopic best-response in every round. Our approach combines Monte Carlo Tree Search, dealing with leader exploration/exploitation tradeoffs, with a novel technique for the identification and pruning of dominated leader strategies. The method provably finds asymptotically optimal solutions and scales up to real world security games spanning double-digit number of rounds. Copyright © 2012, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.