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Showing posts from September, 2013

### The Good, the Bad and the Weird: Duels and the Gentleman's Draw

As I mentioned in the previous article "The Good, the Bad and the Weird: Duels, Truels and Utility Functions", a classic probability puzzle involves a 3-way duel (called a "truel"). A, B and C are to fight a three-cornered pistol duel. All know that A's chance of hitting his target is 0.3, C's is 0.5, and B never misses. They are to fire at their choice of target in succession in the order A, B, C, cyclically (but a hit man loses further turns and is no longer shot at) until only one man is left unit. What should A's strategy be? There's a subtle issue involved in these types of problems in that we don't know how each participant values each outcome. If we allow duelists to deliberately miss there are $$2^3-1=7$$ possible outcomes; each person may or may not be shot and at least one person will not be shot. Even if deliberate missing isn't allowed, there are still 3 possible outcomes. A, for example, could conceivably value B winning more t…