Puzzle # 303 - "Good, Bad and Ugly"
I am spending my vacation in the American frontier. Inspired by 'The good, the bad and the ugly' I decide to play the cowboy game. There are ten contestants including me and every contestant is given a gun. The other nine players are the Blondie, Tuko, Mr. Anderson, Dexter, Gimmy, Vincent, Charlie, Red John and Santenza and their probabilities of hitting the target are 1, 0.9, 0.85, 0.8, 0.75, 0.6, 0.3, 0.3, and 0.3 These players have a reputation of being ruthless and let no attack go unavenged. As I am new to the game, my probability of hitting the target is 0.3. I get to fire first for every round followed by the players in the given order. If I survive a round, I get to start the next round as well. On the other hand, if I get eliminated in any round, the person with the next highest probability gets to start in my place. This continues till only one person is left. Every person is supposed to fire only once per round and the person hit by a bullet is eliminated from the game. A round gets over the moment anybody is eliminated. What is the maximum amount of rounds that I can play for? Assume that every player is intelligent.