Solving 7×7 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. © 2004 by Springer Science+Business Media New York.