2. You are playing a (zero sum) game of rock, paper, scissors. Your friend can play any of the 3 strategies rock, paper, or scissors. She doesn't know your deepest secret, however, that you have papyrophobia. You are so afraid of paper you won't even play it in this game. Given that you only play rock or scissors, and that the probability of picking rock is $x$, what is the optimal value for $x$? Justify this answer with calculations. What would the value of the game be (the maximin or the expected value given your friend had the least convenient approach for you)? It is fair to assume winning gives 1 point, tying gives 0 points, and losing give -1 points.