An old chestnut
goes like this:
Three men fight a duel (a truel) with pistols as follows:
The men take turns, firing one shot each turn at any target, until there is only one man left standing.
All three men know that man A always hits his target, man B hits his target half the time, and man C hits his target 3/10 of the time.
Assume all shots that hit are fatal, so shot men always drop out of the truel. Also assume that each man is a perfect logician, and adopts the strategy most likely to let him win.
They draw lots for starting order, and C goes first. What does C do?