Newsgroups: sci.math, rec.puzzles
Followup-To: poster
From: hoey@ai.etl.army.mil (Dan Hoey)
Date: 11 Dec 90 19:27:46 GMT
Subject: Re: Monty Hall problem: a precise statement

bh...@nswc-wo.navy.mil (Brian R. Hunt) writes:

>Let me offer an attempt at a reasonably precise statement of a Monty
>Hall scenario in which the "switching wins 2/3 of the time" answer is
>correct.
>"You will play a game with a fellow named Monty Hall, and he has to
>play by the rules I'm about to describe....

and goes on to describe such a scenario.  The problem is that in the
real world we are never given a set of rules that Monty must follow.
Well, actually he says there's a prize behind one of those doors, so I
guess that's a rule.  And he says he'll give it to us if we pick it.
But this bit about being given a second choice has never been
promised.  I suppose a contestant who has just been selected to play
the game might ask whether Monty is going to open an empty, unchosen
door and offer a chance to switch.  Monty might just say, ``you're not
the contestant we're looking for'' and take the next contestant.  The
audience is full of people who would like a chance to win a prize.

I've heard that Monty has an evil twin who sometimes stands in on the
show.  The evil twin offers you a choice of three doors, behind one of
which is a prize.  If you pick an empty door, he opens up the door
with the prize (or the door you chose, or both) and says, ``Hard
cheese, you lose.''  If you pick the door with the prize, he opens
one of the empty doors and offers you a chance to switch.  This is a
scenario in which switching never wins, and not switching wins one
third of the time.

Then there's Saint Monty, who offers you a choice of doors and only
offers you a chance to switch when you didn't pick the prize.  When
Saint Monty runs the show, switching wins every time, and not
switching wins one third of the time.

The problem is that you can't tell which Monty you've got.  Has anyone
got firm statistics on how often the contestants on Let's Make a Deal
got a second chance, correlated to the accuracy of their first guess?
Was there any correlation with the value of the prize?  Did Monty's
behavior change when the contestant had been through a few rounds,
perhaps in response to the contestant's strategy?

I solicit reliable answers to these questions via email.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil