The Mirrored Road into the Interior

So on Boingboing there was a Puzzle from that's how it happened.


The three way pistol duel puzzle

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?

My answer/reasoning behind the cut. I think my logic is good so I didn't crunch the numbers, but it wouldn't be hard to do so.


You should shoot the 100 percent guy first. In any longer version of the puzzle, any given position should shoot the highest percentage person who isn't them available.

Let's call our people Alice, Bob, and Carol.
Alice shoots to hit at 33%, Bob at 50%, and Carol is a crack shot at 100%

That means each round runs Alice to Bob to Carol.

In the first round, if Alice shoots and misses, it doesn't matter who she shoots at, but if she shoots at Bob and hits, then Carol only has one possible target, Alice, and Alice dies. If Bob shoots at Alice and hits, then again, Carol's only target is Bob. Carol should, of course, shoot at whoever has the best chance of hitting her each round.

If everyone follows my rule above, then Alice has a 16.5% chance of being killed in the first round. Bob has a 33% chance of being killed in the first round, and Carol has a (I think...) 66 percent chance of being killed in the first round.