Be sure you read The Monty Hall Problem
before you read this node...
Monty Hall himself, presented the problem with the original Monty Hall Problem. The original problem, as proposed by Marilyn vos Savant is mathematically sound, but there is a loophole.
Monty Hall presented a series of trials exploiting this loophole.
Note: The following text originally appeared in the New York Times, January 21, 1991.
On the first (trial), the contestant picked Door 1.
"That's too bad," Mr. Hall said, opening Door 1. "You've won a goat."
"But you didn't open another door yet or give me a chance to switch."
"Where does it say I have to let you switch every time? I'm the master of the
show. Here, try it again."
On the second trial, the contestant again picked Door 1. Mr. Hall opened Door
3, revealing a goat. The contestant was about to switch to Door 2 when Mr. Hall
pulled out a roll of bills.
"You're sure you want Door No. 2?" he asked. "Before I show you what's behind
that door, I will give you $3,000 in cash not to switch to it."
"I'll switch to it."
"Three thousand dollars," Mr. Hall repeated, shifting into his famous
cadence. "Cash. Cash money. It could be a car, but it could be a goat. Four
"I'll try the door."
"Forty-five hundred. Forty-seven. Forty-eight. My last offer: Five thousand
"Let's open the door."
"You just ended up with a goat," he said, opening the door.
Mr. Hall continued: "Now do you see what happened there? The higher I got,
the more you thought the car was behind Door 2. I wanted to con you into
switching there, because I knew the car was behind 1. That's the kind of thing I
can do when I'm in control of the game. You may think you have probability going
for you when you follow the answer in her column, but there's the pyschological
factor to consider."
He proceeded to prove his case by winning the next eight rounds. Whenever the
contestant began with the wrong door, Mr. Hall promptly opened it and awarded
the goat; whenever the contestant started out with the right door, Mr. Hall
allowed him to switch doors and get another goat. The only way to win a car
would have been to disregard Ms. vos Savant's advice and stick with the original
door, defying the Monty Hall Problem Solution.
Was Mr. Hall cheating? Not according to the rules of the show, because he did have the option of not offering the switch, and he usually did not offer it.