Abstract
In recent years the Monte Carlo tree search revolution has spread from computer Go to many areas, including computer Hex. MCTS-based Hex players now outperform traditional knowledge-based alpha-beta search players, and the reigning Computer Olympiad Hex gold medallist is the MCTS player MoHex. In this paper we show how to strengthen MoHex, and observe that—as in computer Go—using learned patterns in priors and replacing a hand-crafted simulation policy by a softmax policy that uses learned patterns significantly increases playing strength. The result is MoHex 2.0, about 250 Elo points stronger than MoHex on the 11\(\times \)11 board, and 300 Elo points stronger on the 13\(\times \)13 board.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The Elo gain from win rate \(r\) is \(400*-\log ((1/r)-1)\).
References
Anshelevich, V.V.: Hexy wins Hex tournament. ICGA J. 23(3), 181–184 (2000)
Anshelevich, V.V.: A hierarchical approach to computer Hex. Artif. Intell. 134(1–2), 101–120 (2002)
Arneson, B., Hayward, R.B., Henderson, P.: Mohex wins Hex tournament. ICGA J. 32(2), 114–116 (2009)
Arneson, B., Hayward, R.B., Henderson, P.: Wolve 2008 wins Hex tournament. ICGA J. 32(1), 49–53 (2009)
Arneson, B., Hayward, R.B., Henderson, P.: Mohex wins Hex tournament. ICGA J. 33(3), 181–186 (2010)
Arneson, B., Hayward, R.B., Henderson, P.: Monte-Carlo tree search in Hex. IEEE Trans. Comput. Intell. AI Games 2(4), 251–258 (2010)
Björnsson, Y., Hayward, R.B., Johanson, M., van Rijswijck, J.: Dead cell analysis in Hex and the Shannon game. In: Bondy, A., Fonlupt, J., Fouquet, J.-L., Fournier, J.-C., Ramirez Alfonsin, J.L. (eds.) Graph Theory in Paris: Proceedings of a Conference in Memory of Claude Berge, pp. 45–60. Birkhäuser (2007)
Browne, C.: Hex Strategy: Making the Right Connections. A.K. Peters, Natick (2000)
Browne, C.: Connection Games: Variations on a Theme. A.K. Peters, Wellesley (2005)
Chaslot, G.M.J.-B., Winands, M.H.M., van den Herik, H.J., Uiterwijk, J.W.H.M., Bouzy, B.: Progressive strategies for monte-carlo tree search. New Math. Nat. Comput. (NMNC) 04(03), 343–357 (2008)
Coulom, R.: Efficient selectivity and backup operators in Monte-Carlo tree search. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.J. (eds.) CG 2006. LNCS, vol. 4630, pp. 72–83. Springer, Heidelberg (2007)
Coulom, R.: Computing “elo ratings” of move patterns in the game of go. ICGA J. 30(4), 198–208 (2007). http://remi.coulom.free.fr/Amsterdam2007/
Coulom, R.: Criticality: a monte-carlo heuristic for go programs (2009). http://remi.coulom.free.fr/Criticality/
Coulom, R.: CLOP: confident local optimization for noisy black-box parameter tuning. In: 13th Advances in Computer Games, pp. 146–157 (2011). http://remi.coulom.free.fr/CLOP/
Enzenberger, M., Müller, M., Arneson, B., Segal, R., Xie, F., Huang, A.: Fuego (2007–2012). http://fuego.sourceforge.net/
Ewalds, T.: Playing and solving havannah. Master’s thesis, University of Alberta (2012)
Gardner, M.: Recreational topology. In: The 2nd Scientific American Book of Mathematical Puzzles and Diversions, Chap. 7, pp. 78–88. Simon and Schuster, New York (1961)
Gelly, S., Silver, D.: Combining online and offline knowledge in UCT. In: Ghahramani, Z. (ed.) ICML. ACM International Conference Proceeding Series, vol. 227, pp. 273–280. ACM (2007)
Hayward, R.B.: Six wins Hex tournament. ICGA J. 29(3), 163–165 (2006)
Hayward, R.B.: Mohex wins Hex tournament. ICGA J. 36(3), 180–183 (2013)
Hayward, R.B., van Rijswijck, J.: Hex and combinatorics. Discrete Math. 306 (19–20), 2515–2528 (2006)
Hein, P.: Vil de laere Polygon? Politiken, 26 December 1942
Henderson, P.: Playing and Solving the Game of Hex. Ph.D. thesis, University of Alberta, Edmonton, Alberta, Canada (2010)
Huang, S.-C.: New Heuristics for Monte Carlo Tree Search Applied to the Game of Go. Ph.D. thesis, Nat. Taiwan Normal Univ., Taipei (2011)
Huang, S.-C., Coulom, R., Lin, S.-S.: Time management for Monte-Carlo tree search applied to the game of go. In: 2010 International Conference on Technologies and Applications of Artificial Intelligence (TAAI), pp. 462–466, November 2010
Kuhn, H.W., Nasar, S. (eds.): The Essential John Nash. Princeton University Press, Princeton (2002)
Nasar, S.: A Beautiful Mind: A Biography of John Forbes Nash. Jr, Simon and Schuster (1998)
Nash, J.: Some games and machines for playing them. Technical report D-1164, RAND, February 1952
Shannon, C.E.: Computers and automata. Proc. Inst. Radio Eng. 41, 1234–1241 (1953)
Wang, Y., Gelly, S.: Modifications of uct and sequence-like simulations for monte-carlo go. In: CIG, pp. 175–182. IEEE (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Huang, SC., Arneson, B., Hayward, R.B., Müller, M., Pawlewicz, J. (2014). MoHex 2.0: A Pattern-Based MCTS Hex Player. In: van den Herik, H., Iida, H., Plaat, A. (eds) Computers and Games. CG 2013. Lecture Notes in Computer Science(), vol 8427. Springer, Cham. https://doi.org/10.1007/978-3-319-09165-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-09165-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09164-8
Online ISBN: 978-3-319-09165-5
eBook Packages: Computer ScienceComputer Science (R0)