Morris: Trial/Trual/Whatever
When two men get up ridiculously early to fire pistols at each other we call it a duel. Personally I prefer to lie in.
But what is the right term when three men skip breakfast to fire pistols at each other?
In a cold, misty field near the outskirts of Paris the sun peers over the horizon to see three men face each other with pistols. Xavier is an expert shot, he never misses. Jean-Christophe is a very good shot, he will get you four times out of five. Francois only has a fifty/fifity chance of hitting his target.
They each take turns to fire their pistol.
What is the best strategy for each of them and what odds would you give for the last man standing?
After the bodies had been cleared away I started to wander home only to hear the referee say ‘Maintenant, M. Galois et ami’
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Brian Tristam Williams said,
November 27, 2009 at 3:07 am
I believe it’s called a “duel.” :p
Stephen Morris said,
November 27, 2009 at 5:46 am
Good point, so maybe truel?
I’ve corrected the spelling in the post now, it did say dual.
Blaine said,
November 28, 2009 at 9:31 am
Is there an implied order to the shooters?
Stephen Morris said,
November 28, 2009 at 6:05 pm
Blaine, I haven’t specified the order or who starts. You should think about what difference that makes.
PF said,
December 3, 2009 at 3:57 pm
I haven’t attempted to think it all through, but if I’m Francois and get to go first, I’m shooting into the ground. The next guy will certainly not take a shot at me, since I’m not much of a threat. In fact, the next shooter will likely kill the third man, and then either the match is over (everyone gets at most one shot) or I get a chance to shoot at the only person still standing.
OTOH, if I should take a shot on the first try and hit my opponent, the next man up only has me as a potential target, and I’m probably toast.
PF said,
December 3, 2009 at 5:06 pm
I think I’ve got it, but… anyway, I think the chances of each surviving are
Francois: 232/443 (~0.524)
Xavier: 43/150 (~0.287)
Jean-Christophe: 128/675 (~0.190)
I assumed the rational behavior that when all three are still standing, Francois will shoot at neither of them, for the reason stated in my last post, and that Xavier and Jean-Christophe will aim at each other so as to take out the most dangerous opponent.
How did I do, coach?
Stephen Morris said,
December 5, 2009 at 1:00 pm
Just posted the solution as a follow up post, http://mathfactor.uark.edu/2009/12/morris-follow-up-trieltruelwhatever/