  Given a skew-symmetric matrix, the corresponding two-player symmetric
zero-sum game is defined as follows: one player, the row player, chooses a row
and the other player, the column player, chooses a column. The payoff of the
row player is given by the corresponding matrix entry, the column player
receives the negative of the row player. A randomized strategy is optimal if it
guarantees an expected payoff of at least 0 for a player independently of the
strategy of the other player. We determine the probability that an optimal
strategy randomizes over a given set of actions when the game is drawn from a
distribution that satisfies certain regularity conditions. The regularity
conditions are quite general and apply to a wide range of natural
distributions.
