In adversarial multiagent domains, security, commonly defined as the ability to deal with intentional threats from other agents, is a critical issue. This paper focuses on domains where these threats come from unknown adversaries. These domains can be modeled as Bayesian games; much work has been done on finding equilibria for such games. However, it is often the case in multiagent security domains that one agent can commit to a mixed strategy which its adversaries observe before choosing their own strategies. In this case, the agent can maximize reward by finding an optimal strategy, without requiring equilibrium. Previous work has shown this problem of optimal strategy selection to be NP-hard. Therefore, we present a heuristic called ASAP, with three key advantages to address the problem. First, ASAP searches for the highest-reward strategy, rather than a Bayes-Nash equilibrium, allowing it to find feasible strategies that exploit the natural first-mover advantage of the game. Second, it provides strategies which are simple to understand, represent, and implement. Third, it operates directly on the compact, Bayesian game representation, without requiring conversion to normal form. We provide an efficient Mixed Integer Linear Program (MILP) implementation for ASAP, along with experimental results illustrating significant speedups and higher rewards over other approaches.