Re: [Phys-l] Monty Hall problem (was: Marilyn)

[chuck britton <cvbritton@mac.com>]

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.
.
At 5:17 AM -0700 1/5/11, John Denker wrote:
> Hey Folks --
>
> Most of the recent postings about the Monty Hall problem
> (and Marilyn's treatment thereof) have utterly missed the
> point.
>
> We must consider
>   A) "THE" Monty Hall problem writ large, which comprises
>   B) quite a number of variations.
>
> The optimal strategy for "THE" game is very sensitive to
> the details of the rules, including what Monty is required
> and/or allowed to do, and whether he is your ally or your
> adversary.  The usual statement of "THE" Monty Hall problem
> is severely underspecified.  Therefore this problem is a
> poster child for ill-posed problems.
>
> There are right ways and wrong ways to handle ill-posed
> problems!  This is important!  This is something people
> ought to learn in school ... but usually don't.  This
> falls in the category of "critical thinking skills".
> Such things are all-too-often not listed on the syllabus,
> but they are IMHO far more important than most of the
> things that are listed.
>
>   http://www.av8n.com/physics/ill-posed.htm
>
> If you want to get some idea for how to handle such a
> problem, treating it as an underspecified problem, see
> see the table about 2/3rds of the way down in the article
>   http://en.wikipedia.org/wiki/Monty_Hall_problem
> (Search the page for the word "unspecified".)
>
> I mention this because several recent postings have referred
> in a general way to "THE" Monty Hall problem and/or to
> Marilyn's "original" posting on the subject ... all of
> which are grossly underspecified.  As such the correct
> answer must be a _solution set_ rather than a singleton
> solution.  To say the same thing another way:  I insist
> that for any underspecified problem, it is seriously
> *wrong* to give a simple numerical answer -- or yes/no
> answer -- without saying what conditions and assumptions
> lead to that answer ... or (better!) (much better!)
> doing a case-by-case analysis with a different numerical
> answer for each case.
>
> Marilyn's statement that "Very few [of her readers] raised
> questions about ambiguity" is (a) a sad reflection on her
> readership, and (b) an example of arrogant lawyering that
> does not excuse the fact that she did not address the
> ambiguities either, not until much later, and not
systematically even then.