Optimal strategies for random tournament games Original Research Article

Given a tournament T, the tournament game is: Two players independently pick a node of T. If both pick the same node, the game is tied. Otherwise, the player whose node is at the tail of the arc connecting the two nodes wins. Fisher and Ryan showed that this game has a unique optimal strategy. For a tournament game on a random n node tournament, we find the probability that the optimal strategy uses k nodes with nonzero probability.