Can approach RPS (Rock, Paper, Scissors) strategy as a relatively simple case of classic von Neumann-Morgenstern two person game theory. That theory follows from the classic duality result in linear programming.<p>The main result for players Red and Blue for RPS is: Red plays each of Rock, Paper, Scissors with probability 1/3rd and independent of everything else in the known universe. Can do this by using, say, an ordinary die with six sides. Then just from the strong law of large numbers, in the long run Red and Blue will both break even, no matter what Blue did, does, or will do.<p>To win, Red needs some means of predicting Blue's play -- no good predictions, no winning. I.e., for Red to win, Blue has to be predictable in some sense.