The Monty Hall Paradox - Interview with Monty Hall

For those that have never heard of it, there is a well known math problem, known as The Monty Hall Paradox, which sometimes stumps professional mathematicians.


I was surfing the net today and stumbled on a 20 year old New York Times article about the problem. The article includes an interview with Monty Hall himself.

Monty agrees with the math, but also gives the reason why you should NOT switch.

New York Times - Behind Monty Hall's Doors: Puzzle, Debate and Answer?
The "meat" of his answer is towards the bottom of page two, but read the whole thing.



FYI: There are at least four Wizard of Vegas threads that discuss The Monty Hall Paradox:
A question for the Wizard about the Monty Hall paradox
The Monty Hall Paradox
Dealing With Monte Hall
The Monty Hall Paradox explained, for once, in English

Quote: DJTeddyBear

For those that have never heard of it, there is a well known math problem, known as The Monty Hall Paradox, which sometimes stumps professional mathematicians.

"Professional mathematicians"? That's a bit of an overstatement, I am afraid.

Quote:

I was surfing the net today and stumbled on a 20 year old New York Times article about the problem. The article includes an interview with Monty Hall himself.

Monty agrees with the math, but also gives the reason why you should NOT switch.

I scanned the article quickly for that "reason", but this was the closest thing I could find:

Quote: Monty

"If the host is required to open a door all the time and offer you a switch, then you should take the switch," he said. "But if he has the choice whether to allow a switch or not, beware. Caveat emptor. It all depends on his mood.

It's far more intersting to read the entire article, but, from the bottom of page two:

Quote:

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.

I see. I always thought it was entirely obvious that the host from the problem does not have free will. Because if he does, there is simply no solution, at least, not in the realm of mathematics. Perhaps, a psychologist could come up with a theory, but I doubt that would be possible without having a whole lot more information about the person doing the show.

What is not mentioned in that article / interview, are three important details:

1 - On the show, there was never a three way choice with two 'zonk' prizes. Usually there was the good prize, a mediocre prize, and a zonk. Sometimes there were three prizes, two of which were mediocre.

2 - When Monty showed / eliminated one choice, the other choice was never a zonk. I.E. He either showed a zonk, or a mediocre when there were two of them.

3 - Some of the wording of the interview leads me to believe that Monty only made that reveal and second choice when the contestant picked the top prize.

It's basically just a silly question why has no definitive answer. What is certain is that if you don't pick the car, he can make you a loser immediately. So if he doesn't do so it's pretty dumb not to assume you have chosen the car and stick with the pick. Who can argue with that? Now, if you're an attractive woman, there might be reasons why he would act stupidly.

Quote: dm

Who can argue with that?

I can :)
It's not his car ... Why would he want you to lose? The show wants at least some of the players to win the cars every now and then, that's the whole point. He is not playing against you, at least, not all the time.

Why? Because he works for the show, and the show has to make money.

Sure, just like a casino, there needs to be some winners, but it also has expenses to pay for.

FYI: Often the product placement contract for a show like that specifies two numbers, one price if the product is given away, and a higher price if it is not.

The car would have to be a Ferrari to make a good dent in the show's profits.

But, humiliating the contestant by tricking him into a bad switch might well be better TV than showing a win.

Quote: weaselman

I can :)
It's not his car ... Why would he want you to lose? The show wants at least some of the players to win the cars every now and then, that's the whole point. He is not playing against you, at least, not all the time.

Can you read "silly question with no definitive answer"? So now you have to guess whether or not he's playing against you? Good luck. Sounds silly to me.

Let me ask this: let's say Monty had a bowl with a million numbers in it-1 to 1000000. The prize if you can pull with 1 draw the number 1 is a car. After you pull, but don't know what number you have, Monty then proceeds to remove 999,998 numbers that he checks the number on, and puts some back but removes some also. So finally there are only the number you are holding and one lone number in the bowl. So, do you think you then have a 50% chance of winning the car? What if he will let you switch? What do you do. If it's more likely he doesn't want you to win the car, then you are a fool if you switch. But with the if's, wgaf?