Found this one in my son's puzzle book.
You are a cyborg in a death match with two other cyborgs. All three of you have identical blasters, and one single shot from these blasters will destroy any of you. You have a 33% (read as 1/3) chance of hitting your target per shot. The next cyborg has a 50% chance. The next cyborg will always hit his target.
In this match the cyborgs take turns shooting, one shot per round. The weakest accuracy (you) goes first, on up to the strongest. If a cyborg is eliminated he won't get another turn. You are all logical and will try to win.
What is your optimum first move? With this move what are your odds of being the final survivor?