# Tricky Extra-Credit Decision Theory Question

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

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

They are not equally good shots.

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

The three decide that they will take turns shooting. Prof. Plum will shoot first. Then Mr. Green will shoot, if he hasn't been shot. Then Col. Mustard will shoot, if he hasn't been shot. Then Prof. Plum, Mr. Green, and Col. Mustard will keep taking turns until only one of them is unscathed. That one will be the winner!

Prof. Plum has the first shot. Where should he aim, to maximize the probability that he will win?

For double super credit, complete this sentence: If Prof. Plum uses his best strategy, his probability of winning is at least ______.

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