Advertisement

New Winning and Losing Positions for 7×7 Hex

  • Jing Yang
  • Simon Liao
  • Miroslaw Pawlak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2883)

Abstract

In this paper we apply a decomposition method to obtain a new winning strategy for 7x7 Hex. We also show that some positions on the 7x7 Hex board, called trivial positions, are never occupied by Black among all of the strategies in the new solution. In other words, Black can still win the game by using the strategies described in this paper even if White already has pieces placed on those positions at the start of the game. Considering the symmetry properties of a Hex board for both players, we also derive 14 losing positions for Black’s first move on a 7x7 Hex board.

Keywords

Decomposition Method Local Pattern Markov Decision Process Winning Strategy Large Board 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yang, J., Liao, S., Pawlak, M.: A decomposition method for finding solution in game Hex 7x7. In: International Conference On Application and Development of Computer Games in the 21st Century, pp. 96–111 (2001)Google Scholar
  2. 2.
    Stewart, I.: Hex marks the spot. Scientific American, 100–103 (2000)Google Scholar
  3. 3.
    Yang, J., Liao, S., Pawlak, M.: Another solution for Hex 7x7. Technical report, University of Manitoba, Department of Electrical and Computer Engineering (2002), http://www.ee.umanitoba.ca/~jingyang/TR.pdf
  4. 4.
    Boutilier, C., Dean, T., Hanks, S.: Decision-theoretic planning: Structural assumptions and computational leverage. Journal of Artificial Intelligence Research 11, 1–94 (1999)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Anshelevich, V.: The game of Hex: An automatic theorem proving approach to game programming. In: Seventeenth National Conference of the American Association for Artificial Intelligence (AAAI 2000), pp. 189–194. AAAI Press, Menlo Park (2000)Google Scholar
  6. 6.
    Beck, A., Bleicher, M., Crowe, D.: Excursions into Mathematics. Worth Publishers (1969)Google Scholar
  7. 7.
    Rijswijck, J.: Queenbee’s home page (2000), http://www.cs.ualberta.ca/~queenbee/
  8. 8.
    Singh, S., Cohn, D.: How to dynamically merge Markov decision processes. In: Jordan, M., Kearns, M., Solla, S. (eds.) Advances in Neural Information Processing Systems, vol. 10, The MIT Press, Cambridge (1998)Google Scholar
  9. 9.
    Meuleau, N., Hauskrecht, M., Kim, K., Peshkin, L., Kaelbling, L., Dean, T., Boutilier, C.: Solving very large weakly coupled Markov decision processes. In: Fifteenth National Conference of the American Association for Artificial Intelligence (AAAI 1998), pp. 165–172. AAAI Press, Menlo Park (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jing Yang
    • 1
  • Simon Liao
    • 2
  • Miroslaw Pawlak
    • 1
  1. 1.Electrical & Computer Engineering DepartmentUniversity of ManitobaCanada
  2. 2.Business Computing DepartmentUniversity of WinnipegCanada

Personalised recommendations