THE GAME OF HEX: THE HIERARCHICAL APPROACH

The game of Hex is a beautiful and mind-challenging game with simple rules and a strategic complexity comparable to that of Chess and Go. Hex positions do not tend to decompose into sums of independent positions. Nevertheless, we demonstrate how to reduce evaluation of Hex positions to topological analysis of a hierarchy of simpler positions, and we develop corresponding recursive calculus. 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, the Gold Medallist of the 5th Computer Olympiad in London, August 2000.