RB_CH04_Q016. (***) Mr 30 Mr 60 Mr 90 duel survival

(***) Your name is Mr. 90. You are standing in a field with two opponents: Mr. 30 and Mr. 60. Each of you has a gun and unlimited ammunition. Each of you is in clear sight of the others and well within firing range. The goal is to maximize the probability of survival. Unfortunately, you are not a very good shot. If you take a shot at one of your opponents, you have only a 10% chance of killing him. Mr. 30 is a better shot; he has a 30% chance of killing whomever he shoots at. Mr. 60 is even better; he has a 60% chance of killing his target. You take turns shooting in a pre-arranged order: first you, then Mr. 30, then Mr. 60, and then through this cycle again and again until only one person remains. You get to shoot first. At whom do you shoot?