Abstract: This talk addresses the solution of large zero-sum matrix games using randomized methods. We formalize a procedure -- termed the Sampled Security Policy (SSP) algorithm -- by which a player can compute policies that, with high probability, guarantees a certain level of performance against an adversary engaged in a random exploration of the game's decision tree. The SSP Algorithm has applications to numerous combinatorial games in which decision makers are faced with a number of possible options that increases exponentially with the size of the problem. In this talk we focus on an applications in the area of network security, where system administrators need to consider multi-stage, multi-host attacks that may consist of long sequences of actions by an attacker in their attempt to circumvent the system defenses. In practice, this leads to policy spaces that grow exponentially with the number of stages involved in an attack. Bio: Brief bio at http://www.ece.ucsb.edu/~hespanha/