1
Let’s Make a Deal.
Years ago in America, there was a wildly popular game show on TV called
Let’s Make a Deal
with
host Monty Hall. If you have seen this show, no description is needed; if you have never seen it,
no accurate description is believable.
One of the games went as follows. Monty would be among the audience, questioning his
current contestant. On the stage were three ‘doors’ or ‘curtains,’ labeled 1, 2 and 3. Monty would
state, “Behind one door is a brand new car, but behind each of the other two doors is a goat.” (Note:
For the sake of this discussion, a goat is a gag gift of no value while a car has immense value to
the contestant.) “Select a door,” Monty continued, “and win the prize behind it.”
At this point, the contestant would select a door. For sake of this discussion, suppose that the
contestant selects door 1. Now you might guess that door 1 would be opened and the contestant
would leave with the gift revealed. But that would be wrong. Instead, Monty would have one of
the remaining doors opened, let’s say door 3, and behind the door is revealed a goat.
Monty would then say to the contestant, “You may have the prize behind door 1 or you may
switch and take the prize behind door 2. What will you do? Stay or switch?”
Since 1986 (this and the following biographical info are taken from Wikipedia), Marilyn vos
Savant has written a column, called
Ask Marilyn
that appears in
Parade
magazine. Her credentials
for having a column includes that she was listed in the
Guinness Book of World Records
under
highest IQ. In addition, I have read her column more than a few times and have found her to be
clever and entertaining.
In September, 1990, Marilyn analyzed the question I posed above. She stated that the better
strategy is to switch. Many persons, including a number of math professors, wrote that she was
wrong. In particular, the math professors stated that there was no advantage to either switching
or staying. In this presentation, I will take the math professors’ advice to be to stay. They can’t
possibly object to my doing this b/c their position is that it does not matter what the contestant