Solving 7×7 Hex with domination, fill-in, and virtual connections

Authors:
Ryan Hayward;Yngvi Björnsson;Michael Johanson;Morgan Kan;Nathan Po;Jack van Rijswijck
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;School of Computer Science, Reykjavik University, Iceland;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada
Venue:
Theoretical Computer Science - Advances in computer games
Year:
2005

Citing 1
Cited 3

The Game of Hex: An Automatic Theorem Proving Approach to Game Programming

Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence

Solving 8×8 Hex

IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Automatic strategy verification for Hex

CG'06 Proceedings of the 5th international conference on Computers and games
A move generating algorithm for hex solvers

AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence

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Abstract

We present an algorithm that determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm recursively searches the game-tree, combining fixed and dynamic game-state virtual connection composition rules to find a winning virtual connection for one of the two players. The search is enhanced by pruning the game-tree according to two new Hex game-state reduction results: under certain conditions, (i) some moves dominate others, and (ii) some board-cells can be "filled-in" without changing the game's outcome.The algorithm is powerful enough to solve arbitrary 7 × 7 game-states. In particular, we use it to determine the outcome of a 7 × 7 Hex game after each of the 49 possible opening moves, in each case finding an explicit proof-tree for the winning player.