Solving breakthrough with Race Patterns and Job-Level Proof Number Search

  • Abdallah Saffidine
  • Nicolas Jouandeau
  • Tristan Cazenave
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7168)


breakthrough is a recent race-based board game usually played on a 8×8 board. We describe a method to solve 6×5 boards based on (1) race patterns and (2) an extension of (JLPNS).

Using race patterns is a new domain-specific technique that allows early endgame detection. The patterns we use enable us to prune positions safely and statically as far as 7 moves from the end.

For the purpose of solving Breakthrough we also present an extension of the parallel algorithm (JLPNS), viz. when a PN search is used as the underlying job. In this extension, partial results are regularly sent by the clients to the server.


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  1. 1.
    Allis, L.V.: Searching for Solutions in Games an Artificial Intelligence. Phd thesis, Vrije Universitat Amsterdam, Department of Computer Science, Rijksuniversiteit Limburg (1994)Google Scholar
  2. 2.
    Allis, L.V., van der Meulen, M., van den Herik, H.J.: Proof-Number Search. Artificial Intelligence 66(1), 91–124 (1994)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Breuker, D.M.: Memory versus Search in Games. Phd thesis, Universiteit Maastricht (1998)Google Scholar
  4. 4.
    Brockington, M.: Asynchronous Parallel Game-Tree Search. Phd thesis, University of Alberta (1997)Google Scholar
  5. 5.
    Cazenave, T., Jouandeau, N.: On the parallelization of UCT. In: Proceedings of the Computer Games Workshop, pp. 93–101 (2007)Google Scholar
  6. 6.
    Chaslot, G.M.J.-B., Winands, M.H.M., van den Herik, H.J.: Parallel Monte-Carlo Tree Search. In: van den Herik, H.J., Xu, X., Ma, Z., Winands, M.H.M. (eds.) CG 2008. LNCS, vol. 5131, pp. 60–71. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Enzenberger, M., Müller, M.: A Lock-Free Multithreaded Monte-Carlo Tree Search Algorithm. In: van den Herik, H.J., Spronck, P. (eds.) ACG 2009. LNCS, vol. 6048, pp. 14–20. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Feldmann, R., Mysliwietz, P., Monien, B.: Game tree search on a massively parallel system, In: Advances in Computer Chess 7, pp. 203–219 (1993)Google Scholar
  9. 9.
    Finnsson, H., Björnsson, Y.: Game-tree properties and mcts performance. In: Proceedings of the IJCAI Workshop on General Intelligence in Game-Playing Agents (GIGA 2011), pp. 23–30 (2011)Google Scholar
  10. 10.
    Handscomb, K.: 8×8 game design competition: The winning game: Breakthrough... and two other favorites. Abstract Games Magazine 7, 8–9 (2001)Google Scholar
  11. 11.
    Kaneko, T.: Parallel depth first proof number search. In: AAAI (2010)Google Scholar
  12. 12.
    Kishimoto, A., Schaeffer, J.: Distributed game-tree search using transposition table driven work scheduling. In: Proceedings International Conference on Parallel Processing, pp. 323–330. IEEE (2002)Google Scholar
  13. 13.
    Kishimoto, A., Kotani, Y.: Parallel and/or tree search based on proof and disproof numbers. In: Game Programming Workshop in Japan, pp. 24–30 (1999)Google Scholar
  14. 14.
    Nagai, A.: A new and/or tree search algorithm using proof number and disproof number. In: Complex Games Lab Workshop, pp. 40–45. ETL, Tsukuba (1998)Google Scholar
  15. 15.
    Nagai, A.: Df-pn algorithm for searching AND/OR trees and its applications. Ph.D. thesis (2002)Google Scholar
  16. 16.
    Saito, J.-T., Winands, M.H.M., van den Herik, H.J.: Randomized Parallel Proof-Number Search. In: van den Herik, H.J., Spronck, P. (eds.) ACG 2009. LNCS, vol. 6048, pp. 75–87. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Schadd, M.P.D., Winands, M.H.M., Uiterwijk, J.W.H.M., van den Herik, H.J., Bergsma, M.H.J.: Best Play in Fanorona leads to Draw. New Mathematics and Natural Computation 4(3), 369–387 (2008)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Schaeffer, J., Björnsson, Y., Burch, N., Kishimoto, A., 0003, M.M., Lake, R., Lu, P., Sutphen, S.: Solving checkers. In: IJCAI, pp. 292–297 (2005)Google Scholar
  19. 19.
    Schaeffer, J., Burch, N., Bjornsson, Y., Kishimoto, A., Müller, M., Lake, R., Lu, P., Sutphen, S.: Checkers is solved. Science 317(5844), 1518 (2007)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Skowronski, P., Björnsson, Y., Winands, M.: Automated Discovery of Search-Extension Features. In: van den Herik, H.J., Spronck, P. (eds.) ACG 2009. LNCS, vol. 6048, pp. 182–194. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Wu, I.-C., Lin, H.-H., Lin, P.-H., Sun, D.-J., Chan, Y.-C., Chen, B.-T.: Job-Level Proof-Number Search for Connect6. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2010. LNCS, vol. 6515, pp. 11–22. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Abdallah Saffidine
    • 1
  • Nicolas Jouandeau
    • 2
  • Tristan Cazenave
    • 1
  1. 1.LAMSADEUniversité Paris-DauphineFrance
  2. 2.LIASDUniversité Paris 8France

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