You and two of your “friends” get into a dispute and decide to solve it with a three-way duel. Pistols are selected.
Friend A is a crack shot and never misses. Friend B hits the target 2/3 of the time. You are not quite as good as the others and hit your target 1/3 of the time. It is decided that you will take the fist shot, Friend B (2/3) will take the second shot (if alive) and Friend A (perfect shot) will go last (again if still alive). This rotation will continue until there is one person left alive. On each turn, one shot only is allowed. As stated, you are going first.
Where should you take your first shot at to have the greatest chance of winning the duel?
(I might add that all the people involved in the duel are extremely rational and selfish — they always perform the actions that maximize their own chances. -SR)
Source: http://users.tru.eastlink.ca/~brsears/math/oldprob.htm (with solution)
Think about it. The answer is surprising.