Welcome to the home page of the computer Hex research group. We --- Kenny Young, Kelly Li, Broderick, Phil, Ryan, Jakub (and previously Aja, David, Jack, Mike, Morgan, Nathan Po, Maryia, Martha, Leah, Yngvi, Geoff Ryan, and Robert Budac) --- build Hex players and solvers. The group informally dates from 1999, when Jack, who wrote Queenbee, started an MSc with Jonathan. Current projects include MoHex, and Solver. Previous projects include Wolve, Mongoose and Queenbee.
Hex is a two-player game invented by Piet Hein in 1942 while a student at Niels Bohr's Institute for Theoretical Physics, and subsequently and independently by John Nash in 1948 while a mathematics graduate student at Princeton. The game was originally called Nash or John, with the latter name at the same time crediting its inventor and referring to the fact that it was frequently played on the tiled floors of bathrooms (Gardner 1959, pp. The name Hex was invented in 1952, when a commercial version was issued by the game company Parker Brothers. Hex is played on a diamond-shaped board made up of hexagons. The game is usually played on a boards of size 11 on a side, for a total of 121 hexagons, as illustrated above.
Since the state space of most games is a directed graph, many game-playing systems detect repeated positions with a transposition table. This approach can reduce search effort by a large margin. However, it suffers from the so-called Graph History Interaction (GHI) problem, which causes errors in games containing repeated positions. This paper presents a practical solution to the GHI problem that combines and extends previous techniques. Because our scheme is general, it is applicable to different game tree search algorithms and to different domains. As demonstrated with the two algorithms αβ and df-pn in the two games checkers and Go, our scheme incurs only a very small overhead, while guaranteeing the correctness of solutions.
The game of Hex is a two-player game with simple rules, a deep underlying mathematical beauty, and a strategic complexity comparable to that of Chess and Go. The massive game-tree search techniques developed mostly for Chess, and successfully used for Checkers, Othello, and a number of other games, become less useful for games with large branching factors like Go and Hex. We offer a new approach, which results in superior playing strength. This approach emphasizes deep analysis of relatively few game positions. In order to reach this goal, we develop an automatic theorem proving technique for topological analysis of Hex positions. We also discuss in detail an idea of modeling Hex positions with electrical resistor circuits. We explain how this approach is implemented in Hexy - the strongest known Hex-playing computer program, able to compete with best human players.