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This paper describes a methodology for quickly learning to play games at a strong level. The methodology consists of a novel combination of three techniques, and a variety of experiments on the game of Othello demonstrates their usefulness. First, structures or topologies in neural network connectivity patterns are used to decrease the number of learning parameters and to deal more effectively with the structural credit assignment problem, which is to change individual network weights based on the obtained feedback. Furthermore, the structured neural networks are trained with the novel neural-fitted temporal difference (TD) learning algorithm to create a system that can exploit most of the training experiences and enhance learning speed and performance. Finally, we use the neural-fitted TD-leaf algorithm to learn more effectively when look-ahead search is performed by the game-playing program. Our extensive experimental study clearly indicates that the proposed method outperforms linear networks and fully connected neural networks or evaluation functions evolved with evolutionary algorithms.