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This article presents a model-based reinforcement learning (RL) scheme for a card game, "Hearts". Since this is a large-scale multi-player game with partial observability, effective state estimation and optimal control based on an environmental model are required. In our method, the learning agent is controlled by a one-step-ahead utility prediction using opponent agents' models. The computational intractability is overcome by the sampling method over a specific subspace. Simulation results show that our model-based RL method can produce an agent comparable to a human expert for this realistic problem.