A gambler starting with an initial fortune of a units repeatedly plays an even money game against an adversary with an initial fortune of b. Each has an equal chance of winning each game. They continue the play until one is broke. What is the probability that the gambler with a units will eventually lose his initial stake before the other does? (As an equivalent formulation, we can remove any restriction from the opponents' initial stake and instead postulate that the gambler decides to quit upon losing a or winning b.)