Solving 7x7 Hex: Virtual Connections and Game-State Reduction

Abstract

We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination. 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.

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3 Excerpts

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