Suppose Alice and Bob play the following game. Alice has N dollars and Bob has M dollars, with 0 < N; M. They flip a fair coin. If it comes up heads, Bob gives Alice a dollar; if it comes up tails, Alice gives Bob a dollar. They play until one of them loses all their money. Calculate the probability that Alice wins, and calculate the probability that Bob wins. What is the probability that the game goes on forever without a winner