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Internal states in a computer GO program are typically organized as a game tree. While simple and convenient, the game tree organization may result in more tree nodes than actual internal states because duplicated tree nodes exist to represent the same gaming state. Modern computer GO programs use the UCT algorithm to conduct game tree search. Duplicated nodes in the game tree representation would make the UCT algorithm less effective. This paper proposes an approach to represent gaming internal states as a directed graph efficiently, and presents a modification of the UCT algorithm to work on the directed graph representation. Furthermore, this paper describes an approach to make the directed game graph persistent so that historical data can be reused to improve the accuracy of the UCT algorithm.