  The game of Hex has two players who take turns placing stones of their
respective colors on the hexagons of a rhombus-shaped hexagonal grid. Black
wins by completing a crossing between two opposite edges, while White wins by
completing a crossing between the other pair of opposite edges. Although
ordinary Hex is famously difficult to analyze, Random-Turn Hex--in which
players toss a coin before each turn to decide who gets to place the next
stone--has a simple optimal strategy. It belongs to a general class of
random-turn games--called selection games--in which the expected payoff when
both players play the random-turn game optimally is the same as when both
players play randomly. We also describe the optimal strategy and study the
expected length of the game under optimal play for Random-Turn Hex and several
other selection games.
