1. ## Three duelers

So, I started this problem and then realized i was doing it wrong. Now I don't really know how i'm supposed to do it. Can anyone help me out.

There are 3 shooters, A, B, & C, and they are in a duel to the last person standing. They are going to go in a cyclic oder: A first, then B, then C, then back to A. As soon as one person is hit, he is out of the duel. A is a poor shot (1/3 chance of hitting), B is better (2/3 chance), and C always hits his mark. Sounds like A's chances of winning are rather low. A takes his first shot: how should he choose his target?

A can choose B or C and it is still a 1/3 chance of hitting them. I would assume you want to get rid of your toughest target first, so he should go after C, but I think this theory is probably wrong. Any help would be great!

2. Maybe I'm missing something, but, assuming that A MUST fire at one of them, I would hope that the right answer is that he shoots at C considering, if he shot at B and hit him, C would proceede to shoot A 100% of the time.

Though, to be honest, it looks like A might be best served by intentionally missing the first shot, since B and C look to be strategically obligated to fire at each other; this guarantees A will be heads up against the survivor of the first round. A would win more than 1/3rd of the time with this strategy, ironically allowing him to win more than his fair share of duels while C, the perfect shot, will win LESS than 1/3rd of the time.