Lets do then. Player 1 randomizes (1/3, 1/3, 1/3). Player 2 randomizes (1, 0, 0). Does player 1 want to deviate? Yes! Randomizing is not the best strategy if player 2 is going to be playing the same pure strategy all the time, player 1 would be better off if she were to play the best response to whatever (1, 0, 0) is. -> Not an equilibrium.