University of South Carolina, Arnold School of Public Health, Dept. of Health Services Policy and Management Courses and Curricula, HSPM 716,

Tricky Extra-Credit Decision Theory Question

If you get this right without having seen it before, that will be very impressive!

Three gentlemen, Col. Mustard, Mr. Green, and Prof. Plum, have offended each others' honor. They will settle their dispute with a duel with pistols.

They are not equally good shots.

Col. Mustard	hits his target 1/3 of the time he shoots.
Mr. Green	hits his target 2/3 of the time he shoots.
Prof. Plum	hits his target every time he shoots.

By mutual agreement, Col. Mustard will shoot first. Then Mr. Green will shoot, if Col. Mustard didn't shoot him. Then Prof. Plum will shoot, if he hasn't been shot yet. Then Col. Mustard again, if he hasn't been shot yet. Then Mr. Green, if he hasn't been shot yet. Then Prof. Plum, if he hasn't been shot yet. The men who have not been shot continue taking turns until only one of them is unscathed. He is the winner!

Col. Mustard has the first turn. Where should he aim, to maximize the probability that he will win?

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