A bag is filled with a given quantity of red and blue marbles. In each turn, a
player reaches into the bag and removes 1, 2, or 3 marbles. The player looks to see
the color of the marbles, and announces how many of each color marble were removed. The last player to remove a red marble from the bag loses. You are given ints red and blue, the number of red and blue marbles initially in the bag. Before play begins, a friend removes several of the marbles from the bag, at random, without showing either of you, given in int removed.
Assuming you go first, and each player makes the optimal choice of number of
marbles to remove, calculate the probability that you win the game.