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Monte-Carlo Tree Search Applied to the Game of Tic-Tac-Toe

삼목 게임에 적용된 몬테카를로 트리탐색

  • Lee, Byung-Doo (Dept. of Baduk Studies, Division of Sports Science, Sehan University)
  • 이병두 (세한대학교 체육학부 바둑학과)
  • Received : 2014.05.26
  • Accepted : 2014.06.16
  • Published : 2014.06.20

Abstract

The game of Go is one of the oldest games and originated at least more than 2,500 years ago. In game programming the most successful approach is to use game tree searches using evaluation functions. However it is really difficult to construct feasible evaluation function in computer Go. Monte-Carlo Tree Search(MCTS) has created strong computer Go programs such as MoGo and CrazyStone which defeated human Go professionals played on the $9{\times}9$ board. MCTS is based on the winning rate estimated by Monte-Carlo simulation. Prior to implementing MCTS into computer Go, we tried to measure each winning rate of three positions, center, corner and side, in Tic-Tac-Toe playing as the best first move. The experimental result revealed that the center is the best, a corner the next and a side the last as the best first move.

바둑 게임은 가장 오래된 게임 중의 하나이며 적어도 2,500년 전에 기원되었다. 게임프로그래밍에서 대부분의 성공적인 접근법은 평가함수를 활용한 게임트리 탐색을 사용하는 것이다. 그러나 컴퓨터바둑에서 그럴싸한 평가함수를 구축한다는 것은 매우 어렵다. 몬테카를로 트리탐색(MCTS)은 9줄 바둑에서 프로기사를 제압한 MoGo와 CrazyStone과 같은 강력한 컴퓨터바둑프로그램을 만들어 내었다. 몬테카를로 트리탐색은 몬테카를로 시뮬레이션에 의해 계산된 승률을 근간으로 한다. 몬테카를로 트리탐색을 컴퓨터바둑에 구현하기에 앞서 삼목에서 최상의 첫 수로 중앙, 귀, 변의 세 수에 대한 각각의 승률을 측정하려고 했다. 실험 결과로 최상의 첫 수는 중앙이 우선하고, 다음은 귀, 마지막으로는 변이라는 사실이 밝혀졌다.

Keywords

References

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  2. Analysis of Tic-Tac-Toe Game Strategies using Genetic Algorithm vol.14, pp.6, 2014, https://doi.org/10.7583/JKGS.2014.14.6.39
  3. The UCT algorithm applied to find the best first move in the game of Tic-Tac-Toe vol.15, pp.5, 2015, https://doi.org/10.7583/JKGS.2015.15.5.109