  For matrix games we study how small nonzero probability must be used in
optimal strategies. We show that for nxn win-lose-draw games (i.e. (-1,0,1)
matrix games) nonzero probabilities smaller than n^{-O(n)} are never needed. We
also construct an explicit nxn win-lose game such that the unique optimal
strategy uses a nonzero probability as small as n^{-Omega(n)}. This is done by
constructing an explicit (-1,1) nonsingular nxn matrix, for which the inverse
has only nonnegative entries and where some of the entries are of value
n^{Omega(n)}.
