Are you ready for the answer to the cowboy's dilemma?

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?

Reach for the sky!  Actually, shoot the sky.  Your best chance is not to shoot at either cowboy.  Really really.

There are actually three possibilities:

1. Shoot the 100% cowboy.
2. Shoot the 50% cowboy.
3. Shoot anywhere else.

Your chances of surviving the duel are best with door #3.  I'll give a detailed analysis later...

Update: here's a detailed analysis.