From: carl@SOL1.GPS.CALTECH.EDU (Carl J Lydick)
Newsgroups: rec.puzzles
Subject: Re: Monty Hall Puzzle RIP
Date: 20 Dec 1992 22:28:21 GMT
Organization: HST Wide Field/Planetary Camera
Distribution: world
Reply-To: carl@SOL1.GPS.CALTECH.EDU
NNTP-Posting-Host: sol1.gps.caltech.edu

In article <92353.100332SHERE@SLACVM.SLAC.STANFORD.EDU>, <SHERE@SLACVM.SLAC.STANFORD.EDU> writes:
=Alright, I've had just about all bickering I can stand on this
=Monty Hall drivel and I'm going to put it to bed.  You folks are so
=busy outsmarting yourselves that this should be called the Monty
=Python Puzzle; however, if you cut through the pseudo-intellectual
=double talk about probabilities and how they may, or may not,
=change after being shown a door and put together a simple chart
=detailing each possible permutation of how the game can progress
=you will have the following:
=
=      Permutation:  A B C D E F G H I J K L M N O P Q R S T U V W X
=
=Prize behind door:  1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3
=Originally choose:  1 1 1 1 2 2 3 3 1 1 2 2 2 2 3 3 1 1 2 2 3 3 3 3
=       Door shown:  2 2 3 3 3 3 2 2 3 3 1 1 3 3 1 1 2 2 1 1 1 1 2 2
=   Change or Stay:  S C S C S C S C S C S C S C S C S C S C S C S C
=     Final choice:  1 3 1 2 2 1 3 1 1 2 2 3 2 1 3 2 1 3 2 3 3 2 3 1
=      Win or Lose:  W L W L L W L W L W W L W L L W L W L W W L W L
=
=You will note that out of the twenty-four permutations of this game
=you can win exactly twelve ways, six ways by staying with your
=original choice (ACKMUW) and six ways by changing your mind
=(FHJPRT). You can also lose exactly twelve ways, six ways by
=staying with your original choice (EGIOQS) and six ways by changing
=your mind (BDLNVX).  Now everybody, repeat after me; half the time
=we stay with our original choice we win, half the time we change
=our minds we win, half the time we win, PERIOD!  You have no
=problems with the fact that if Monty reveals what is behind one of
=the doors and then lets you choose between the two remaining that
=your chances are fifty-fifty.  Yet this is exactly what's happening
=here!  The only difference is SEMANTICS!  Whether you "change your
=mind" or "stay with your original choice" you are STILL CHOOSING
=BETWEEN ONE OF TWO DOORS.  FIFTY-FIFTY.

Sorry, but what gives you the badly mistaken impression that the
above-described scenarios are equally likely?

Here's another application of your deductive strategy at work:

Tomorrow morning, the sun either will rise, or it won't rise.  There are
exactly two cases, and in one half of them the sun rises, and in one half of
them, the sun doesn't rise.  Therefore, there's a 50% chance that the sun won't
rise tomorrow morning.  QED.

NOW DO YOU SEE WHAT'S WRONG WITH YOUR SO-CALLED "REASONING"?
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | 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.