3 friends Xymen, Yelena, and Zara are having a 3-way paintball duel. Xymen is a poor shot, hitting his target with a probability of 1/3. Yelena is very accurate, hitting her target 2/3 of the time. Zara is a marksman, hitting her target every single time. The rules of the duel are: In turn, each person will have one chance to shoot at a target of their choice. Once someone is hit, he/she is out. The last person standing wins. Since he is the worst, Xymen goes first, followed by Yelena, and then Zara. What is Xymen's best strategy, and what is his chance of winning following it?
