Gomoku is a strategy game played on the Go board. Two players, black and white, alternate placing pieces on the intersections of the grid to form five-in-a-row. It has often been used to test tree search algorithms, including Monte-Carlo Tree Search (MCTS). Due to its simplicity, it is possible to introduce variations to the rules slightly without affecting the core mechanics and strategies for the game. In this paper, we focus on the board size (traditionally 15 \(\,\times \,\) 15) and introducing a dynamic boundary for moves (traditionally unbounded). Both of these qualities greatly change the size of each move’s action space. We contribute 9 variants of Gomoku with different combinations of board sizes and dynamic boundaries, in order to provide a set of settings ranging across action space sizes. We calculated the action space sizes per moves for each board, and implemented a new variant of MCTS that uses ancestor-based alpha-beta bounds in the selection phase. We ran this against the classical MCTS in order to demonstrate the effects of the action space changes.

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A Gomoku Game-Testbed for Monte-Carlo Tree Search Algorithms

  • Lisa Liu,
  • Kelvin Yu

摘要

Gomoku is a strategy game played on the Go board. Two players, black and white, alternate placing pieces on the intersections of the grid to form five-in-a-row. It has often been used to test tree search algorithms, including Monte-Carlo Tree Search (MCTS). Due to its simplicity, it is possible to introduce variations to the rules slightly without affecting the core mechanics and strategies for the game. In this paper, we focus on the board size (traditionally 15 \(\,\times \,\) 15) and introducing a dynamic boundary for moves (traditionally unbounded). Both of these qualities greatly change the size of each move’s action space. We contribute 9 variants of Gomoku with different combinations of board sizes and dynamic boundaries, in order to provide a set of settings ranging across action space sizes. We calculated the action space sizes per moves for each board, and implemented a new variant of MCTS that uses ancestor-based alpha-beta bounds in the selection phase. We ran this against the classical MCTS in order to demonstrate the effects of the action space changes.