Saturday, February 19, 2011

Game theory: The Truel

You may have seen the movie "The Good, The Bad and the Ugly". Here's a scene at the end of the movie

Suppose that you must participate in a three-way duel with two rivals. Each of you is given a pistol and unlimited ammunition. Unfortunately, you, Red, are the weakest shot — you hit your target only 1/3 of the time. Black is successful 2/3 of the time, and Gray hits everything he aims at.

It’s agreed that you will take turns: You’ll shoot first, then Black, then Gray, and you’ll continue in this order until one survivor remains. At whom should you shoot?

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