Skip to main content
Top

2015 | OriginalPaper | Chapter

Comparative Study of Monte-Carlo Tree Search and Alpha-Beta Pruning in Amazons

Authors : Hikari Kato, Szilárd Zsolt Fazekas, Mayumi Takaya, Akihiro Yamamura

Published in: Information and Communication Technology

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The game of Amazons is a combinatorial game sharing some properties of both chess and Go. We study programs which play Amazons with strategies based on Monte-Carlo Tree Search and a classical search algorithm, Alpha-Beta pruning. We execute several experiments to investigate the effect of increasing the number of searches in a Monte-Carlo Tree Search program. We show that increasing the number of searches is not an efficient method to strengthen the program for Amazons. On the other hand, augmenting the algorithms with a choice of several evaluation functions fulfills has great influence on playing strength.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Allis, L.V.: Searching for Solutions in games and Artificial Intelligence. Ph.D. thesis, Maastricht, Rrijksuniversiteit Limburg (1995) Allis, L.V.: Searching for Solutions in games and Artificial Intelligence. Ph.D. thesis, Maastricht, Rrijksuniversiteit Limburg (1995)
2.
go back to reference Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Mach. Learning 47(2–3), 235–256 (2002)CrossRefMATH Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Mach. Learning 47(2–3), 235–256 (2002)CrossRefMATH
3.
go back to reference Avetisyan, H., Lorentz, R.J.: Selective search in an Amazons program. In: Schaeffer, J., Müller, M., Björnsson, Y. (eds.) CG 2002. LNCS, vol. 2883, pp. 123–141. Springer, Heidelberg (2003) CrossRef Avetisyan, H., Lorentz, R.J.: Selective search in an Amazons program. In: Schaeffer, J., Müller, M., Björnsson, Y. (eds.) CG 2002. LNCS, vol. 2883, pp. 123–141. Springer, Heidelberg (2003) CrossRef
4.
go back to reference Berlekamp, E.R.: Sums of \(N \times 2\) Amazons. Institute of Mathematical Statistics Lecture Notes - Monograph Series, vol. 35 (2000) Berlekamp, E.R.: Sums of \(N \times 2\) Amazons. Institute of Mathematical Statistics Lecture Notes - Monograph Series, vol. 35 (2000)
5.
go back to reference Buro, M.: Simple Amazons endgames and their connection to Hamilton circuits in cubic subgrid graphs. In: Marsland, T., Frank, I. (eds.) CG 2001. LNCS, vol. 2063, pp. 250–261. Springer, Heidelberg (2002) CrossRef Buro, M.: Simple Amazons endgames and their connection to Hamilton circuits in cubic subgrid graphs. In: Marsland, T., Frank, I. (eds.) CG 2001. LNCS, vol. 2063, pp. 250–261. Springer, Heidelberg (2002) CrossRef
6.
go back to reference 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) CrossRef 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) CrossRef
7.
go back to reference Coulom, R.: Computing Elo ratings of move patterns in the game of Go. ICGA J. 30, 198–208 (2007) Coulom, R.: Computing Elo ratings of move patterns in the game of Go. ICGA J. 30, 198–208 (2007)
8.
go back to reference Gelly, S., Wang, Y., Munos, R., Teytaud, O.: Modification of UCT with patterns in Monte-Carlo Go. Technical Report PR-6062, INRIA (2006) Gelly, S., Wang, Y., Munos, R., Teytaud, O.: Modification of UCT with patterns in Monte-Carlo Go. Technical Report PR-6062, INRIA (2006)
9.
go back to reference Hensgens, P.: A Knowledge-based Approach of the Game of Amazons. Master’s thesis, Maastricht University (2001) Hensgens, P.: A Knowledge-based Approach of the Game of Amazons. Master’s thesis, Maastricht University (2001)
10.
go back to reference Hoki, K., Muramatsu, M.: Efficiency of three forward-pruning techniques in Shogi: futility pruning, null-move pruning, and late move reduction (LMR). Entertainment Comput. 3, 51–57 (2012)CrossRef Hoki, K., Muramatsu, M.: Efficiency of three forward-pruning techniques in Shogi: futility pruning, null-move pruning, and late move reduction (LMR). Entertainment Comput. 3, 51–57 (2012)CrossRef
11.
go back to reference Kaneko, T.: Evaluation functions of computer Shogi programs and supervised learning using game records. J. Jpn. Soc. Artif. Intell. 27, 75–82 (2012) Kaneko, T.: Evaluation functions of computer Shogi programs and supervised learning using game records. J. Jpn. Soc. Artif. Intell. 27, 75–82 (2012)
12.
go back to reference Kloetzer, J., Iida, H., Bouzy, B.: The Monte-Carlo approach in Amazons. In: Computer Games Workshop, pp. 185–192, Amsterdam, The Netherlands (2007) Kloetzer, J., Iida, H., Bouzy, B.: The Monte-Carlo approach in Amazons. In: Computer Games Workshop, pp. 185–192, Amsterdam, The Netherlands (2007)
13.
go back to reference Kloetzer, J., Iida, H., Bouzy, B.: A comparative study of solvers in Amazons endgames. In: IEEE 2008 Symposium on Computational Intelligence in Games, Perth, Australia (2008) Kloetzer, J., Iida, H., Bouzy, B.: A comparative study of solvers in Amazons endgames. In: IEEE 2008 Symposium on Computational Intelligence in Games, Perth, Australia (2008)
14.
go back to reference Kloetzer, J., Iida, H., Bouzy, B.: Playing Amazons endgames. ICGA J. 32, 140–148 (2009)CrossRef Kloetzer, J., Iida, H., Bouzy, B.: Playing Amazons endgames. ICGA J. 32, 140–148 (2009)CrossRef
15.
go back to reference Kloetzer, J.: Experiments in Monte-Carlo Amazons. IPSJ SIG Technical Report, vol. 2010-GI-24 No. 6, pp. 1–4 (2010) Kloetzer, J.: Experiments in Monte-Carlo Amazons. IPSJ SIG Technical Report, vol. 2010-GI-24 No. 6, pp. 1–4 (2010)
16.
go back to reference Kloetzer, J.: Monte-Carlo opening books for Amazons. In: 7th Conference on Computer and Games (2010) Kloetzer, J.: Monte-Carlo opening books for Amazons. In: 7th Conference on Computer and Games (2010)
19.
go back to reference Kocsis, L., Szepesvári, C.: Bandit based Monte Carlo planning. In: 17th European Conference on Machine Learning (ECML 2006), pp. 282–293 (2006) Kocsis, L., Szepesvári, C.: Bandit based Monte Carlo planning. In: 17th European Conference on Machine Learning (ECML 2006), pp. 282–293 (2006)
20.
go back to reference Kozelek, T.: Methods of MCTS and the game Arimaa. Master’s thesis, Charles University in Prague (2009) Kozelek, T.: Methods of MCTS and the game Arimaa. Master’s thesis, Charles University in Prague (2009)
22.
go back to reference Matsubara, H., Iida, H., Grimbergen, R.: Chess, Shogi, Go, natural developments in game research. ICCA J. 19, 103–112 (1996) Matsubara, H., Iida, H., Grimbergen, R.: Chess, Shogi, Go, natural developments in game research. ICCA J. 19, 103–112 (1996)
23.
go back to reference Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995) CrossRefMATH Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995) CrossRefMATH
Metadata
Title
Comparative Study of Monte-Carlo Tree Search and Alpha-Beta Pruning in Amazons
Authors
Hikari Kato
Szilárd Zsolt Fazekas
Mayumi Takaya
Akihiro Yamamura
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-24315-3_14

Premium Partner