In this game, you play Rock paper scissors 30 times against the same opponent. In each round, you both simultaneously choose either rock, paper or scissors. If you choose the same option, you draw. Otherwise, paper wins over rock, scissors over paper, and rock over scissors. The winner gets one point, the loser loses one point.
Enter a probability with which to play each of the three options. Your opponent will be able to guess these probabilities, and plays an optimal strategy against it.
Find out your optimal strategy against this cunning opponent.