In this study, we propose a novel algorithm for an air-hockey robot to select an optimal attack motion according to the behavior of a human opponent. The attack motion of the robot is optimized during an air hockey game by two-step look ahead prediction. First, we explain how to calculate state values in continuous games like air-hockey. Second, we model the human and robot behaviors and propose a value function to be used in the optimization. Then, we show experimental data of simulations and analysis results of the robot behaviors generated from the calculated value.