Game-Theoretic Search in Physical Systems with an Application to the Sport of Curling

Game-theoretic reinforcement-learning systems have achieved strong results in board and card games, but extending them to physical sports requires reasoning over continuous actions, stochastic execution, and nontrivial physics. We introduce a search-and-distillation framework for the sport of mixed doubles curling, using a physics simulator with iterative empirical-game optimization. A graph transformer jointly represents shot selection and position value: a Gaussian-mixture policy models distinct continuous shot modes, a distributional value head predicts end-score outcomes, and an auxiliary latent-dynamics objective encourages world-model-like physics understanding. Starting from human match data, we iteratively compute a meta-Nash mixture over existing policies, search for an approximate best response against that mixture, and distill accepted search decisions and realized returns into the next policy. Under human-like imperfect execution noise, the final policy beats open-weight language-model agents by +0.96 points per end. Against frontier agentic models, which are becoming powerful across diverse games, our policy wins by +0.19 points per end. In blind paired comparisons on 30 held-out positions, two U.S. national (Olympic) curling team staff members judged the policy's shots comparably to recorded human actions, selecting the policy as more optimal in 26 of 60 judgments (43%). These results demonstrate a practical framework for combining empirical-game reasoning, continuous-action search, and physical simulation in stochastic sports.