: The Truel : as opposed to the duel

: This is a mathematical puzzle, which I recently saw on the A Word A Day mailing
: list.

: You're involved in a duel, but with three people, hence a truel. You face two
: other competitors, and all of you are armed with guns which will kill an opponent
: if the shot hits. Each of you is allowed to fire a single shot at a time, and may fire
: at one of your remaining opponents. However, not everyone is an equally good shot:
: you're the worst of the three, hitting only once out of every three shots fired; the
: next person hits once out of every two shots; and the last person is an expert,
: hitting with every shot fired. The shots are fired in reverse order of accuracy,
: so you get the first shot, and the expert-shot gets the last shot of each round.

: The trilemma : How do you maximize your chances of surviving this conflict?

: Note: Your options are restricted to choosing what to do with your gun at each
: turn. You may not make friends with either of your opponents (there has been
: some bitter feud), nor may you run away (you'll be shot in the back as a coward),
: etc.

: To the answer