Three people are in a duel. The first is an olympic shooter, the second is an average shooter, and the third is a drunk. They will take turns taking shots, with the drunk going first, the average shooter going second, and the olympian going third. If the olympian aims at someone, then he will hit them. If the average shooter aims at someone, he will hit them half of the time. If the drunk aims at someone, then he will hit them only ten percent of the time. Once someone is hit, they are out of the game, with the winner being whoever is the last remaining participant. Who should the drunk aim for on his first shot?
Hint, consider the various two person games first, then once you have those values solve the three person games.