MJ: Professor Mickey Rosa's Game Show Problem: Thoughts please

[MJ]

During class, Professor Mickey Rosa asks Ben what he thinks about a game show scenario which goes something like this:

There are 3 doors. Behind 1 of the doors is a car, and a goat is behind each of the remaining 2 doors. Once you select the door that you think the car is behind, then the host will open one of the 2 remaining doors to reveal a goat. At this point, the contestant has a choice to switch doors or remain with his initial selection. With only 2 doors to choose from, is the probability of selecting the door with the car behind it improved by switching doors? Why or why not?

This is perhaps the coolest math problem I have ever seen. I totally fell for it! I spent 45 minutes trying to convince my friend of the correct answer.

MJ

[Norm Wattenberger]

See the below:

Monty Hall problem

[MJ]

You are a sharp guy, were you able to come up with the correct answer the first time you encountered this problem? It is just so damn counterintuitive!

[Norm Wattenberger]

Unfortunately, I saw the answer before I had a chance to think about it. There have been discussions of this problem on BJ forums in the past.

[young gun]

This is a very interesting problem. I believe that mathematicians argued about it for some time before a conclusion was reached.

The irony as this was depicted in the movie is that they got it wrong. If you don't know that the host is going to open a door with a goat in it, then switching is useless. Since Micky didn't say that the host was going to open a door showing a goat, Ben didn't increase his chances by switching. Additionally, Micky's question of how do you know the host isn't using reverse psychology can not be dismissed if you don't know the host's intentions.

[Don Schlesinger]

> This is a very interesting problem. I believe that
> mathematicians argued about it for some time before a
> conclusion was reached.

> The irony as this was depicted in the movie is that
> they got it wrong. If you don't know that the host is
> going to open a door with a goat in it, then switching
> is useless. Since Micky didn't say that the host was
> going to open a door showing a goat, Ben didn't
> increase his chances by switching.

The host always opens a door with a goat behind it! It's a given of the problem. What sense would it make for the host to open a door with the car behind it?! How stupid with that be.

I don't remember if it was stated or implied, but it was clear (at least to me), that the purpose of opening a door was to reveal the presence of a goat, thereby helping the player, whether he realized it or not (by switching).

Don

[young gun]

> The host always opens a door with a goat behind it!
> It's a given of the problem. What sense would it make
> for the host to open a door with the car behind it?!
> How stupid with that be.

It's a given of the problem if the the professor says that the host will show you a door with a goat. That's one of the reasons this problem is interesting. If you don't know what the host will do, then switching doesn't help, and can hurt if the host is using reverse psychology. Ben doesn't explain this at all, he just says he would switch because of variable change, whatever that is. I wouldn't call that a correct answer, since the host's intentions are left unsaid.

[Don Schlesinger]

> It's a given of the problem if the the professor says
> that the host will show you a door with a goat. That's
> one of the reasons this problem is interesting. If you
> don't know what the host will do, then switching
> doesn't help, and can hurt if the host is using
> reverse psychology. Ben doesn't explain this at all,
> he just says he would switch because of variable
> change, whatever that is. I wouldn't call that a
> correct answer, since the host's intentions are left
> unsaid.

I have to see it again, to see if it's really true that he didn't tell you that the host already knows where the car is. But, clearly, he has to.

On the real program, which I imagine you are much too young to remember, the players knew that Hall knew where the car was, and, of course, when he indicated a door, it never had the main prize behind it, which would be pointless. If you watched the show 1,000 times, and 1,000 times, the host always revealed a door with a goat -- or a lesser prize -- it should have become clear that he always knew where the car was and was helping the contestant. But, many didn't understand.

Clear?

Don

[Dog Hand]

MJ,

My sister Joan has two children. You meet one of them and find he's a boy. Assuming male & female children are born with equal probability, what are the odds that her other child is a girl?

Dog Hand

[Don Schlesinger]

... answering dog's question, above, try this one:

"A woman says, 'I have two children and one is named John.' We can assume nobody named John is a girl and no woman gives the same name to more than one child. What is the probability that the woman's other child is a boy (that is, that she has two boys)?"

(Oh, Dog already asked, basically, the same question, above. Or, DID he?? :-))

Don

[young gun]

I just felt Ben's answer was inadequate and didn't demonstrate an understanding of the situation, yet Micky gave decided he was a star based on his answer.

To me, the most interesting part of this problem is not that it's counterintuitive/paradoxical, it's that you need to know the host's intentions, not his actions, in order to confidently switch. I can't think of a great relationship of this problem to blackjack, but it definitely relates to poker, i.e. if your opponent bets every flop, turn, etc. when checked to, then his bet means nothing and his range is the same as it was before he bet his hand.

[Don Schlesinger]

About 30 people have read both posts (probably a lot of duplication) and not one person will take a shot at answering either question?

What a bunch of cowards! :-)

Don

[Daily Dubble]

> About 30 people have read both posts (probably a lot
> of duplication) and not one person will take a shot at
> answering either question?

> What a bunch of cowards! :-)

> Don

But I viewed it 3 times