Critical Section

cowboys dilemma analyzed again

Friday,  01/11/08  11:02 PM

shoot self in footYesterday I analyzed the cowboy's dilemma.  Via email, Shawn Hillis suggested a simpler explanation of the counter-intuitive solution:

If you shoot at and hit the 50% guy, then you are dead on the very next shoot when 100% shoots at you.  So you either want to shoot at 100% or miss purposely.  Let's call the odds of you dying if you miss 'm'.  If you shoot at 100%, you'll either hit or miss.  The odds of you dying with a miss is the same as if you missed on purpose, m.  Let's call the odds of you dying if you hit, h.  So the odds of you dying if you aim at 100% are m + h, which both h & m > 0.  Thus, since h + m > m, you want to miss to minimize the odds of you dying.

He also suggested a nice refinement, allow each duelist to optionally shoot themselves in the foot.  If they're successful then they're injured, and they withdraw from the duel.  I haven't worked this out, but I suspect if you're a bad shot, shooting yourself in the foot might be a good option.

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