Random-Turn Hex and Other Selection Games

Overview. The game of Hex , invented independently by Piet Hein in 1942 and John Nash in 1948 [9], has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid (see Figure 1). A player wins by completing a path connecting the two opposite sides of his or her color. Although it is easy to show that player I has a winning strategy, it is far from obvious what that strategy is. Hex is usually played on an 11× 11 board (e.g., the commercial version by Parker Brothers® and the Computer Olympiad Hex Tournament both use 11× 11 boards), for which the optimal strategy is not yet known. (For a book on practical Hex strategy see [3], and for further information on Hex see [23], [7], [1], or [6].)