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Re: A game strategy.



Ludwick asks why this problem is confusing. Aside from the reason that many
people do not understand statistics, the primary problem in this case is not
understanding the rules. In the current discussion on this list people are
asking "what if Monty chooses at random" versus "what if Monty has to choose
a goat" and so forth.

Those may be interesting questions, but the actual game show we are talking
about did have rules. So my question is, what was the official set of rules
concerning this portion of "Let's Make a Deal?"

One thing confusing the issue is that the 3-door problem is not the only
type of game that was played on the Let's Make a Deal show. Therefore there
is no single set of rules for "the show," because there was no single type
of game on the show. In some games (deals) it appears Monty had a fair
amount of leeway whether to offer the contestant a particular deal, or not,
or offer some other deal. Also, the amount of time left on the show
determined how many deals were made or whether a particular contestant near
the end of the show got offered a deal or not.

However, the 3-door problem was a specific case that came into existance
fairly late in the history of the show. It is my understanding this portion
of the show had definite rules which did not allow Monty any freedom.
Specifically, it is my understanding that (1) Monty was required to open one
of the remaining doors after the contestant made the intial choice. Monty
could not choose to eliminate this portion of the game. For example,
suppose he knows the contestant has chosen the car, for some reason he likes
this particular contestent, so he chooses not to to offer a switch, thus
helping the contestant win. I believe that scenario was not allowed.
Additionally, this portion of the show came near the end, but they were sure
to allow enough time to make so it could be played clear through. If it got
done early, Monty could use the remaining time to make quick deals with the
audience. (2) Monty was required to open a door with a bad prize behind it.
He was not allowed to open no door, and he was not allowed to open the door
with the good prize. 3) After opening the appropriate door, the contestant
was always allowed the choice of sticking with the original pick or
switching to the other closed door.

I believe those are the rules to this particular portion of the show. If
someone has definitive information to the contrary I would like to hear it.
If we have to investigate many scenarios without knowing which is the actual
game being played, no wonder the question of whether to switch or not is
confusing. But once we know the actual rules, the solution becomes more
clear.


Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817