Hex, Braids, the Crossing Rule, and XH-Search

  • Philip Henderson
  • Broderick Arneson
  • Ryan B. Hayward
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6048)


We present XH-search, a Hex connection finding algorithm. XH-search extends Anshelevich’s H-search by incorporating a new Crossing Rule to find braids, connections built from overlapping subconnections.


Step Stone Winning Strategy Deduction Rule Virtual Connection Form Carrier 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hein, P.: Vil de laere Polygon? Series of articles in Politiken newspaper (December 1942)Google Scholar
  2. 2.
    Nash, J.: Some games and machines for playing them. Technical Report D-1164, RAND (1952)Google Scholar
  3. 3.
    Reisch, S.: Hex ist PSPACE-vollständig. Acta Informatica 15, 167–191 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Anshelevich, V.V.: The game of Hex: An automatic theorem proving approach to game programming. In: AAAI/IAAI, pp. 189–194 (2000)Google Scholar
  5. 5.
    Anshelevich, V.V.: A hierarchical approach to computer Hex. Artificial Intelligence 134(1–2), 101–120 (2002)zbMATHCrossRefGoogle Scholar
  6. 6.
    Anshelevich, V.V.: Hexy wins Hex tournament. ICGA Journal 23(3), 181–184 (2000)Google Scholar
  7. 7.
    Arneson, B., Henderson, P., Hayward, R.B.: Wolve Wins Hex Tournament. ICGA 31(4) (2008)Google Scholar
  8. 8.
    Hayward, R.B.: Six wins Hex tournament. ICGA Journal 29(3), 163–165 (2006)Google Scholar
  9. 9.
    Melis, G., Hayward, R.: Six wins Hex tournament. ICGA Journal 26(4), 277–280 (2003)Google Scholar
  10. 10.
    Willemson, J., Björnsson, Y.: Six wins Hex tournament. ICGA Journal 27(3), 180 (2004)Google Scholar
  11. 11.
    Melis, G.: Six (2006),
  12. 12.
    Rasmussen, R., Maire, F.: An extension of the H-search algorithm for artificial Hex players. In: Australian Conference on Artificial Intelligence, pp. 646–657 (2004)Google Scholar
  13. 13.
    Yang, J.: Jing Yang’s web site (2003),
  14. 14.
    Yang, J., Liao, S., Pawlak, M.: A decomposition method for finding solution in game Hex 7x7. In: ADCOG, pp. 96–111 (2001)Google Scholar
  15. 15.
    Kohei, N.: Union-connections and a simple readable winning way in 7 ×7 Hex. In: Proceedings of 11th Game Programming Workshop, pp. 72–79 (2004)Google Scholar
  16. 16.
    Kohei, N.: Union-connections and straightforward winning strategies in Hex. ICGA Journal 28(1), 3–12 (2005)Google Scholar
  17. 17.
    Hayward, R.B.: A note on domination in Hex. Technical report, University of Alberta (2003)Google Scholar
  18. 18.
    Hayward, R.B., Björnsson, Y., Johanson, M., Kan, M., Po, N., van Rijswijck, J.: Solving 7 ×7 Hex: Virtual connections and game-state reduction. In: van den Herik, H.J., Iida, H., Heinz, E.A. (eds.) Advances in Computer Games. International Federation for Information Processing, vol. 263, pp. 261–278. Kluwer Academic Publishers, Boston (2003)Google Scholar
  19. 19.
    King, D.: Hall of hexagons - the game of Hex (2007),

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Philip Henderson
    • 1
  • Broderick Arneson
    • 1
  • Ryan B. Hayward
    • 1
  1. 1.Dept. of Computing ScienceUniversity of Alberta 

Personalised recommendations