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The Truel

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#22672
Fun:*** (2.83)
Difficulty:*** (2.38)
Category:Probability
Submitted By:brianz****
Corrected By:eighsse

 

 

 



Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 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. All three competitors know one another's shooting odds. If you are Mr. Black, where should you shoot first for the highest chance of survival?


Hint

Think from the points of view of Mr. Gray and Mr. White, not just Mr. Black.
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