Journal of Korea Game Society (한국게임학회 논문지)

Korea Game Society (한국게임학회)
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The Best Sequence of Moves and the Size of Komi on a Very Small Go Board, using Monte-Carlo Tree Search

몬테카를로 트리탐색을 활용한 초소형 바둑에서의 최상의 수순과 덤의 크기

  • Lee, Byung-Doo (Department of Baduk Studies, Division of Sports Science, Sehan University)
  • 이병두 (세한대학교 체육학부 바둑학과)
  • Received : 2018.07.09
  • Accepted : 2018.10.07
  • Published : 2018.10.20
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Abstract

Go is the most complex board game in which the computer can not search all possible moves using an exhaustive search to find the best one. Prior to AlphaGo, all powerful computer Go programs have used the Monte-Carlo Tree Search (MCTS) to overcome the difficulty in positional evaluation and the very large branching factor in a game tree. In this paper, we tried to find the best sequence of moves using an MCTS on a very small Go board. We found that a $2{\times}2$ Go game would be ended in a tie and the size of Komi should be 0 point; Meanwhile, in a $3{\times}3$ Go Black can always win the game and the size of Komi should be 9 points.

바둑은 최상의 착점을 찾기 위해 컴퓨터가 완전탐색을 하여 모든 가능한 착점들을 탐색할 수 없는 가장 복잡한 보드게임이다. AlphaGo 이전에 모든 강력한 컴퓨터바둑 프로그램들은 게임트리 내 매우 큰 분기수와 국면평가에서의 어려움을 극복하기 위해 몬테카를로 트리탐색(Monte-Carlo Tree Search)을 사용해 왔다. 본 논문에서는 MCTS를 활용하여 초소형 바둑에서의 최상의 수순과 덤의 크기를 알고자 했다. 2줄바둑에서의 게임결과는 빅이 되었으며 덤의 크기는 0집, 반면에 3줄바둑에서는 흑이 항상 승리하고 덤의 크기는 9집이 되어야 함을 알아냈다.

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References

  1. B.D. Lee, "The first move in the game of $9{\time}9$ Go, using non-strategic Monte-Carlo Tree Search", Journal of Korea Game Society, Vol. 17, No. 3, pp. 63-70, 2017. https://doi.org/10.7583/JKGS.2017.17.3.63
  2. B. Abramson, "The Expected-Outcome Model of Two-Player Games", PhD thesis, Columbia University, 1987.
  3. B. Brugmann, "Monte Carlo Go", Technical report, Syracuse University, 1993.
  4. R. Coulom, "The Monte-Carlo Revolution in Go", Japanese-French Frontiers of Science Symposium, 2008.
  5. M. Enzenberger and M. Muller, "Fuego - An Open-Source Framework for Board Games and Go Engine Based on Monte Carlo Tree Search", Technical report, University of Alberta, 2008.
  6. D. Silver, et al., "Mastering the game of Go with deep neural networks and tree search", Journal of Nature, Vol. 529, Issue 7587, pp. 484-489, 2016.
  7. T. Song, "Monte Carlo Tree Search and Its Application in AlphaGo", from https://stlong0521.github.io/20160409%20-%20MCTS.html, 2017.
  8. Sense's Library, "Small board Go", from https://senseis.xmp.net/?SmallBoardGo, 2018.
  9. S.H. Jung, et al., "Modern Baduk theory", Dacom Press, 2016.
  10. Wikipedia, "Komidashi", from https://en.wikipedia.org/wiki/Komidashi, 2018.
  11. Wikipedia, "Scoring", from https://ko.wikipedia.org/wiki/%EA%B3%84%EA%B0%80, 2018.
  12. Wikipedia, "Seki", from https://ko.wikipedia.org/wiki/%EB%B9%85_(%EB%B0%94%EB%91%91), 2018.
  13. H. Baier and M.H.M. Winands, "Monte-carlo Tree Search and Minimax Hybrids", Computer Games, Vol. 504, pp. 45-63, 2014.
  14. M.H.M. Winands and Y. Brornsson, "Evaluation Function Based Monte-Carlo LOA", from http://www.ru.is/-yngvi/pdf/WinandsB09.pdf, 2017.
  15. S. Gelly, et al., "The Grand Challenge of Computer Go: Monte Carlo Tree Search and Extensions", Communications of the ACM, Vol. 55, No. 3, pp. 106-113, 2012. https://doi.org/10.1145/2093548.2093574
  16. E. Powley, et al., "Heuristic move pruning in monte carlo tree search for the strategic card game lords of war", In Computational Intelligence and Games (CIG) of IEEE, pp. 1-7, 2014.