Abstract. Over the years, various research projects have attempted to develop a chess program that learns to play well given little prior knowledge beyond the rules of the game. Early on it was recognized that the key would be to adequately represent the relationships between the pieces and to evaluate the strengths or weaknesses of such relationships. As such, representations have developed, including a graph-based model. In this paper we extend the work on graph representation to a precise type of graph that we call a piece or square neighborhood. Specifically, a chessboard is represented as 64 neighborhoods, one for each square. Each neighborhood has a center, and 16 satellites corresponding to the pieces that are immediately close on the 4 diagonals, 2 ranks, 2 files, and 8 knight moves related to the square. Games are played and training values for boards are developed using temporal difference learning, as in other reinforcement learning systems. We then use a 2-layer regression ...