Re: [Phys-l] Monty Hall problem

[John Denker <jsd@av8n.com>]

As Daniel Patrick Moynihan was fond of saying:
  Everybody is entitled to their own opinions, but
  they are not entitled to their own facts.

It seems Moynihan's principle is being upheld less and less
all the time.


On 01/05/2011 08:20 AM, chuck britton wrote:
> ASK MARILYN
> By Marilyn Von Savant
> The Monty Hall Problem
> You're on a TV game show. In front of you are three doors: there's a
> great prize behind one door, and nothing behind the other two. You
> choose a door. Then the host (Monty Hall) opens one of the two doors
> you didn't choose to show that there is nothing behind that door. It
> would be bad for the TV ratings if he opened the prize door: you'd
> know you had lost and the game would be over; so Monty knows where
> the prize is, and he always opens a door that doesn't have a prize
> behind it (Monty is Canadian, so you know you can trust him). You're
> now facing two unopened doors, the one you originally picked and the
> other one, and the host gives you a chance to change your mind: do
> you want to stick with the door you originally chose, or do you want
> to switch to what's behind the other door?
>
> In what way is Marilyn's statement of the problem ill-posed,
> ambiguous, underspecified, etc.
> The contestants optimal strategy seems clear to me.

Let's call that version "B".


Well, according to Marilyn's own site,
  http://www.marilynvossavant.com/articles/gameshow.html
the following is the original statement of the problem (in its entirety) 
and the original answer (in its entirety).  

> > Game Show Problem
> >
> > (This material in this article was originally published in PARADE magazine in 1990 and 1991.)
> >
> > Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?
> >
> > Craig F. Whitaker
> > Columbia, Maryland
> >
> > Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here's a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what's behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You'd switch to that door pretty fast, wouldn't you?

Now, maybe this web site is lying, but at least I can say that 
I have chosen a seemingly-authoritative source and quoted it 
accurately.  Also I reckon that (a) she is in control of the 
site, (b) she is not likely to lie about what was said, since 
that would immediately be detected.

Also, unless the archives are lying to me, version "B" was not
posted in the recent "Ask Marilyn" thread.  Hint:  search for
the critical word "trust".  So the various people who have been
blissfully answering "THE" question did not have, so far as I 
can tell, any grounds for assuming that version "B" was "THE" 
question that should be answered.

So, those are the facts that as they appear to me.  If any of
those facts are incorrect, I would be delighted to learn some 
better facts.

==============================

It would make an interesting Crime Scene Investigation project
for some student to track down where version "B" came from, and
when.