Motivated by authentication, intrusion and spam detection applications we consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the learner has a sample from a target distribution and the goal is to construct a classifier capable of distinguishing observations from the target distribution from observations emitted from an unknown other distribution. The ideal SCC classifier must guarantee a given tolerance for the false-positive error (false alarm rate) while minimizing the false negative error (intruder pass rate). Viewing SCC as a two-person zero-sum game we identify both deterministic and randomized optimal classification strategies for different game variants. We demonstrate that randomized classification can provide a significant advantage. In the deterministic setting we show how to reduce SCC to two-class classification where in the two-class problem the other class is a synthetically generated distribution. We provide an efficient and practical algorithm for constructing and solving the two class problem. The algorithm distinguishes low density regions of the target distribution and is shown to be consistent.