Two friends are fishing on a river and their time is limited. For each, the probability of catching a fish is p < 1. The probability that somebody will catch two fish is zero and the results of fishing for each are independent. The two friends agree to the following. If each catches a fish, each will bring one home. If only one is lucky, they will toss a coin to determine who will come home with the only fish. Does their agreement increase the likelihood for each to bring home a fish, or should the friends just arrange a joint dinner with what they caught? First guess the answer, then verify it by computing the probability of bringing home a fish for each friend separately