[ExI] who should white shoot?

[Lee Corbin]

For what it's worth, as I recall this old probability problem
succumbs to a fairly straightforward analysis that does not
involve infinite series. (Or if infinite series are involved they're
extremely simple, i.e., must have been geometric.)

Lee

----- Original Message ----- 
From: "spike" <spike66 at att.net>
To: "'ExI chat list'" <extropy-chat at lists.extropy.org>
Sent: Thursday, August 28, 2008 9:06 PM
Subject: Re: [ExI] who should white shoot?


> 
>> Avant, let me clarify the question.  Each player has 
>> arbitrarily many bullets.  Any hit anywhere instantly slays 
>> the unfortunate gunslinger.  They start with Mr. White, then 
>> they take turns with Brown following White and Black to 
>> follow Brown, continuing the murderous game until a single 
>> prole walks away with two cooling corpses behind... spike 
> 
> 
> Given below is what I think is the answer, but I would like if some calculus
> hipster would check my numbers, as my own frail skills in McLaurin and
> Taylor series have grown tragically feeble with the passing of time.  So
> much time that my high school calculus book is written in Sumerian cuneiform
> with Roman numerals.  But I think I nailed this one.  Think more if you
> wish, then scroll down.
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> Mr. White maximizes his chances of survival by shooting at no one,
> intentionally firing into the air.  Reasoning: if White shoots Brown, then
> only one target remains for Mr. Black, who never misses.  So White will not
> shoot at Brown.  White will not shoot at Black either, for if he slays
> Black, that sets up a duel between Brown and White in which Brown gets the
> first shot.  The probability of White winning such a duel is one in 8.
> (Calculus hipsters?  Lee?  Alex?)  If on the other hand White gets the first
> shot in a White/Brown  duel, White's chances of survival are 3 in 7.  So by
> firing into the air, White sets up a Black/Brown duel.  If Black wins that
> match, then White has 1 in 3 chance of surviving to old age.  If Brown wins
> that duel then White has the previously calculated 3 in 7 chance.  So White
> should fire his first shot into the air.
> 
> spike
> 
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