This is a logic puzzle I first read in "Games" magazine when I was a kid. The solution is all over the web, of course, and some of the regulars here have probably heard it before -- let's give others a chance to try to figure it out before anyone posts the answer, though.
You, Mr. Goode, and Mr. Best have been having a heated dispute over a matter of great consequence, and not being able to come to a resolution, you've decided to settle the matter with a duel -- or, more precisely, a truel, since there are three of you. However, you've also decided that since you're all gentlemen, you're going to try to kill each other like civilized people.
The three of you are each going to take turns firing, one at a time. The truel will continue until there is only one survivor. You are the worst marksman of the three, hitting your target only 33% of the time. Mr. Goode is a better shot, hitting his target 66% of the time. Mr. Best, however, never misses -- he hits his target 100% of the time. (For the sake of simplicity, we will assume that a hit is a kill.)
In an attempt to level the playing field somewhat, you all agree that turns will be taken starting with the worst marksman first, then proceeding to the next best marksman, and so on. This means, of course, that you're the one who starts the truel.
Who do you aim at with your first shot?