How many options to shoot?
Mr. Black, Mr. Gray, and Mr. White are fighting in a duel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot \(\dfrac13\) of the time, gets to shoot first. Mr. Gray, who hits his shot \(\dfrac23\) of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, whom should you shoot first for the highest chance of survival?