Draft:Bpow49

The following problem was suggested by Alexander Freuman. Many Thanks!

Several years ago, three suitors from three countries were vying for the hand of a lovely maiden. They agree to fight a pistol duel under the following conditions:

The three draw lots to determine who fires first, second, and third, then take their places at the corners of an equilateral triangle. They will fire single shots in turn and continue in the same cyclic order until two of them are dead. At each turn the man firing may aim wherever he pleases. All three duelists know that Monsieur Toujours always hits his target, Señor Casisiempre is 80% accurate, while Sir Soso is 50% accurate.

Assuming that each gentleman adopts his best strategy, and that none is killed by a wild shot not intended for him, what are the exact survival probabilities for each of the men?

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.