Logic 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?

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.

Here's the statistical breakdown, taken from the comments on the original post at Boing Boing.

Comments

Written by Ben -

I'd shoot at the 100% guy first. He's the best shot, so getting rid of him first is important. Also, the 50% guy might have the same strategy, and by not shooting at him first, he'll be less likely to shoot at you on the next shot. With both of you shooting at the 100% guy, you'll have a 5/6 chance of knocking out the 100% guy before he's even shot anyone. Even if the first two shots miss, the 100% guy would probably go at the 50% guy given that knocking him out would be more useful for him than knocking you out would be.

Written by Chris -

While your solution isn't horrible, it's not the optimal strategy for ensuring your survival.

Written by Ben -

Dammit. I wouldn't last long in the Wild West.

Written by Keith -

The best way to assure your survival is to do what Bush refuses to do---pull out. If you fail to shoot first, the duel is over and every cowboy lives to ride another day. Or you could graze yourself with the first shot which under the rules would get you out of the duel for good. And you could live to see another rodeo. If you must fire a shot, I think the best strategy is to shoot into the ground and let the other two fire (hopefully) at each other. I think this will increase your odds of survival, but not assure them as in my first two scenarios.

Written by christy -

Well....I would have probably gotten shot while they were waiting for me to decide what to do, but after careful consideration, I guess I would shoot myself (in the foot) and eliminate myself. Can I collect disability?

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