  We prove that in a normal form n-player game with m actions for each player,
there exists an approximate Nash equilibrium where each player randomizes
uniformly among a set of O(log(m) + log(n)) pure strategies. This result
induces an $N^{\log \log N}$ algorithm for computing an approximate Nash
equilibrium in games where the number of actions is polynomial in the number of
players (m=poly(n)), where $N=nm^n$ is the size of the game (the input size).
  In addition, we establish an inverse connection between the entropy of Nash
equilibria in the game, and the time it takes to find such an approximate Nash
equilibrium using the random sampling algorithm.
