You’re a cowboy, and get involved in a three way pistol duel with two other cowboys. You are a poor shot, with an accuracy of only 33%. The other two cowboys shoot with accuracies of 50% and 100%, respectively. The rules of the duel are one shot per cowboy per round. The shooting order is from worst shooter to best shooter, so you get to shoot first, the 50% guy goes second, and the 100% guy goes third, then repeat. If a cowboy is shot he’s out for good, and his turn is skipped. Where or who should you shoot first?
Leave your guesses in the comments. I’ll post the answer later this week
Update: I posted the answer below the fold.
Assuming that shooting yourself is not an option (you’ve never been much of a masochist), the best option is to shoot into the air (or the ground).
If all of the other cowboys are logical players, as well, the scenario will unfold something like this:
1) You shoot into the air
2) The second cowboy shoots at the third cowboy. Why? Well, If the third cowboy is logical as well, he’ll shoot the greatest threat to himself on his turn (and kill him with 100% certainty). That’s going to be the second cowboy, who only misses half the time, as opposed to you, Mr. Couldn’t-hit-the-broad-side-of-a-barn.
Knowing this, the second cowboy has to shoot at the third cowboy. From there, there are two possible outcomes:
3a) The second cowboy kills the third cowboy. Then, it’s you against the second cowboy, and you get the first shot.
3b) The second cowboy misses the third cowboy. Then, the third cowboy kills the second. So now it’s you against Mr. 100%, but at least you get the first shot.