My brain asplodes!

[elfs]

I've been trying to figure out The Monty Hall Paradox. So far, the Bayes Theorem explanation holds the most weight and makes the most sense, but moving out of the purely mathematical aspects of Bayesian math to the real world makes my brain asplode.

There's a lovely simulator with tallies on-line as well.

Comments

[asell.livejournal.com]

AAAAAAAAAHHHHHHHH! THis makes no sense! (BTW, I'm just some random person from Customers_Suck)

[asell.livejournal.com]

(OOPS, I mean I found you in a geographic search... ) >.< how embarassing

[elfs.livejournal.com]

Not a problem! Welcome!

[kenshardik]

I remember showing this article to my father, a mathematician, when it was published. He disagreed with Savant, while I agreed with her. He got VERY upset with me because he felt that my not agreeing with him was a major sign of disrespect. (My father had a temper and would get angry quickly if he thought you were ignoring his advice or disagreed with something where he had knowledge.) He eventually came to the same conclusion as stated in the article - that if the host doesn't know where the car is, then the odds are the same, but if the host does know, then you should switch.

It's still one of those "dark memories" of a time when my father was pissed off at me. He died before I ever got a chance to tell him what a prick he could be at times like that, and how hurtful his reactions were. Ah well, at least I have spiffy tattoos now.

[elfs.livejournal.com]

The puzzle doesn't work if the host doesn't know where the car is, because the objective of the host is to get you to pick the car. If the host always has to open one door (remember, that's the distraction that confuses everyone), he has to know that the door he's opening is not the one with the car behind it. That's what it took me forever to grok.

Sorry about your dad. Maybe someday I'll reconcile with mine, too. At least I haven't gotten any tattoos, and I took out my dick piercing years ago.

[dossy.livejournal.com]

Have you read this? Does any of that help?

I think the explanation at Wikipedia makes it very clear (to me) -- the section labeled "The solution" -- in two out of three situations, switching results in the win condition. So, you're more likely to win if you switch. What more is there?

[whipartist.livejournal.com]

OK, so it goes like this.


Clearly, you have a 1/3 chance of picking right the first time, which means that there's a 2/3 chance that the prize is in one of the two doors you didn't pick, right?

You choose one door. You're then essentially given the option to choose BOTH of the other doors. Even if Monty opens one door and shows you a goat, there's a 2/3 chance that the prize is in the combination of the two doors that you didn't pick the first time.

Monty's showing you a goat behind one door is a red herring. It doesn't change the probabilities one bit-- it's still 1/3 A, 2/3 B + C.

[elfs.livejournal.com]

Oh, I got it after reading the Baysian equation. That made sense to me and I was able to agree that the equation adequately maps the problem. It's just not intuitively obvious at first why the door opening is a red herring.

[whipartist.livejournal.com]

The door opening is a red herring because Monty has knowledge. If he didn't, and just chose a door randomly, it would change the equation.

[whipartist.livejournal.com]

BTW, was this triggered by my comment from the other day?

[elfs.livejournal.com]

Yeah, it was.

[norikos-author.livejournal.com]

AH!

You're then essentially given the option to choose BOTH of the other doors.

That's what I was missing. I'd never been unable to understand _why_ it worked.

[antonia-tiger.livejournal.com]

Here's a bucket.

It's so much easier to clean up if you stick your head in it before your brain explodes.

[atheorist.livejournal.com]

It's much easier if you imagine

1. Monty shuffles a deck of cards and spreads it out
2. You pick one card and say "This is the queen of spades."
3. Monty turns over 50 cards that are not the queen of spades.

Switch or not?

[lisakit.livejournal.com]

From a mathematical sense I can see how it makes sense to switch, but, like you say, it just doesn't compute in a "real world" sense.

And using the similator I got the car 6 out of 10 times; by always choosing the same door the second time.

[lisakit.livejournal.com]

Oh yah:

I think what's confusing people is the fact that we're talking about the initial choice here. If you have the intention of switching on the second choice then the first choice has a 2/3 probability of winning.

However, most people are inclined to think "that's in the past" and focus only on the second choice which, by itself, does have a probability of 1 in 2.

[neowolf2.livejournal.com]

It becomes clearer if you consider the case with N doors, in which the host opens N-2 of them (for some N much greater than 3).

[ewhac.livejournal.com]

Yes, discussing ten doors makes the issue clearer than talking about three.

You pick one door; you have a 1/10 chance of winning. Monty has a 9/10 chance of winning.

Then Monty opens 8 doors with nothing behind them. The odds have not changed; You still have a 1/10 chance of winning and Monty 9/10. Then he asks if you want to change your choice.

You could pick any one of the other nine doors. But, having opened eight of the losing ones, you know which ones not to pick. In other words, Monty's overwhelming 9/10 chance has been conflated to a single door, making your choice obvious.