Abstract Curling is an adversarial two-player game with a continuous state and action space, and stochastic transitions. This paper focuses on one aspect of the full game, namely, finding the optimal “hammer shot”, which is the last action taken before a score is tallied. We survey existing methods for finding an optimal action in a continuous, lowdimensional space with stochastic outcomes, and adapt a method based on Delaunay triangulation to our application. Experiments using our curling physics simulator show that the adapted Delaunay triangulation’s shot selection outperforms other algorithms, and with some caveats, exceeds Olympic-level human performance.