NetNews Usenet Archive 1992 #31/NN_1992_31.iso/spool/alt/folklore/science/4506

Internet Message Format | 1992-12-25 | 3.9 KB

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From: [e-mail] (Carl J Lydick)
Newsgroups: alt.folklore.science
Subject: Re: Monty Hall/Shell Game..
Date: 26 Dec 1992 04:38:52 GMT
Organization: HST Wide Field/Planetary Camera
Lines: 59
Distribution: world
Message-ID: <[e-mail]>
References: <[e-mail]> <[e-mail]>,<[e-mail]>
Reply-To: [e-mail]
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In article <[e-mail]>, [e-mail] (Jerry M. Cox) writes:
>Odds are that I could stand a review course in probability. But hear me
>out anyway :-) If the contestant selects one door of three and that was
>all there was to it then the odds of initially selecting the winning door
>are one out of three. I have no problem with that, but I don't think
>this describes the situation. If Monty is *always* going to reveal a
>goat behind one of the doors, that door is removed from consideration.
>The final choice then becomes a choice between one of two doors. If
>Monty *always* removes one of the doors from consideration, then the
>final choice (as well as the initial choice) is between a door with a
>car behind it, and a door with the "other" (the one Monty doesn't show)
>goat behind it. The odds of picking the car are 50/50 whether you switch
>or not because Monty is *always* going to take away one of the losing
>choices.

But YOUR choice of a door will, two times out of three, limity Monty's choice
of a door:  If you picked a door with a goat behind it, then Monty CANNOT open
that door.  So the underlying symmetry opon which your argument rests is
broken, two times out of three (i.e., when you pick a door with a goat).  Hence
your analysis doesn't apply.

>If he said "You can have the door you picked or the TWO doors that you
>didn't pick", and didn't reveal anything about the two doors, then I
>would agree that the best thing to do would be to switch. But, Monty
>changes the odds when he shows you one of the goats behind one of the
>two doors. He removes that door from consideration completely.

Then consider the following hypothetical offer from Monty:
    You can either keep the door that you picked, OR you can pay me a goat
    and have both of the other two doors.
The payoffs for that offer are identical to the payoffs from the original
problem.

>Unless
>you would like to take the goat Monty just showed you, you are left with
>a one out of two choice. He equivalently says to you: "You can have the
>car or the goat that I didn't show you", or "You can have the door you
>initially chose or the door I didn't show you". That sounds like 50/50
>odds to me.

>To sum up the initial choice is not a one of three choice between
>a car or goat #1 or goat #2. The initial (and final) choice is between a
>car and one of the 2 goats. The other goat will be removed as a choice
>by Monty.

That's right.  Which is what causes you to win 2 times out of three by
switching.  If Monty randomly opened a door, it wouldn't alter the odds of your
winning by switching.  You'd still have a 1/3 chance of winning.  But Monty
CAN'T randomly open a door:  He's GOT to pick a door that does not have a goat
and that you did  not pick.  2/3 of the time, he's got only one choice, and
his pick tells you which door has the prize.
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: [e-mail] | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.