New Winning and Losing Positions for 7×7 Hex
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.
KeywordsDecomposition Method Local Pattern Markov Decision Process Winning Strategy Large Board
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- 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.Stewart, I.: Hex marks the spot. Scientific American, 100–103 (2000)Google Scholar
- 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
- 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.Beck, A., Bleicher, M., Crowe, D.: Excursions into Mathematics. Worth Publishers (1969)Google Scholar
- 7.Rijswijck, J.: Queenbee’s home page (2000), http://www.cs.ualberta.ca/~queenbee/
- 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.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