OT: The Monty Hall Problem

[ritari330]

Okay, I'm curious in seeing what you think your odds are in this situation.

Suppose you're on a game show and you're given the choice of three doors and will win what is behind the chosen door. Behind one door is a car; behind the others, goats. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one at random. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

What are your odds if you switch doors? And what are the odds if you don't switch doors?

And if you need help imagining it: The Monty Hall page

 

[TOX1]

If you win the car and you run over the goats with it, does that disqualify you?

 

[ritari330]

If you win the car and you run over the goats with it, does that disqualify you?

yes, they reuse the goats

 

[juliansteed]

You want to switch to make your odds 2/3. However on the movie "21", if you switch or stay it woulkdn't matter. The odds would have been 50/50 despite what the movie says because Kevin Spacey's character did not explain the problem properly.

 

[Destroydacre]

You want to switch to make your odds 2/3. However on the movie "21", if you switch or stay it woulkdn't matter. The odds would have been 50/50 despite what the movie says because Kevin Spacey's character did not explain the problem properly.

hehe


But yes you do switch. 2/3 of the time you will pick wrong. Then they eliminate the other wrong one so only 2 are left. Since 2/3 of the time you will pick wrong, by switching you have a 2 in 3 chance of changing to the good prize.

 

[ritari330]

I was trying to explain this to my sister and mother, they didn't understand it though...

Edit: 3,800!

 

[juliansteed]

I was trying to explain this to my sister and mother, they didn't understand it though...

Edit: 3,800!

If you want them to understand then show them this:

YouTube - The Monty Hall Problem

But apologize in advance for the annoying voice/accent.


Do NOT show them this:

YouTube - "21" explains the Monty Hall problem

In this clip Spacey leaves out a very important detail. That beng that the host will always reveal a goat after you pick and before offering you a chance to switch. Without this knowledge we don't know that he didn't just show door #3 at random. Thus making your odds 50/50 either way. He does stress that the host knows where it is but that's still not good enough. That alone just leaves us to speculate what the hosts intentions are and brings psychology into play which is not the intent of the problem.

 

[Destroydacre]

If you want them to understand then show them this:

YouTube - The Monty Hall Problem

But apologize in advance for the annoying voice/accent.


Do NOT show them this:

YouTube - "21" explains the Monty Hall problem

In this clip Spacey leaves out a very important detail. That beng that the host will always reveal a goat after you pick and before offering you a chance to switch. Without this knowledge we don't know that he didn't just show door #3 at random. Thus making your odds 50/50 either way. He does stress that the host knows where it is but that's still not good enough. That alone just leaves us to speculate what the hosts intentions are and brings psychology into play which is not the intent of the problem.

I wrote a very simple monty hall program in java a few years ago and coded it so that the user would pick a door and then the prize would be assigned to one of the other two doors so the chances of winning was only 50/50. The intelligence level of the class wasn't particularly high and they couldn't figure out why it was coming out 50/50 instead of 67/33 when they ran it a few hundred times. It was somewhat amusing.

 

[juliansteed]

I wrote a very simple monty hall program in java a few years ago and coded it so that the user would pick a door and then the prize would be assigned to one of the other two doors so the chances of winning was only 50/50. The intelligence level of the class wasn't particularly high and they couldn't figure out why it was coming out 50/50 instead of 67/33 when they ran it a few hundred times. It was somewhat amusing.

Well at least they were intelligent enough to understand why it should have been 67/33 and not 50/50. But yeah after a few hundred times if the results were approximately 50/50 they should have realized that it wasn't the true Monte Hall Problem.

 

[dare2be]

I've seen actual HS and college math professors argue against the 2/3 answer, saying it was 50/50. The key element in the problem is that Monty always *knows* where the prize is and *always* reveals a losing door. Otherwise, then it would end up being 50/50.

This is a good read and debate on the problem:

Marilyn vos Savant | The Game Show Problem

 

[ritari330]

If you want them to understand then show them this:

YouTube - The Monty Hall Problem

But apologize in advance for the annoying voice/accent.


Do NOT show them this:

YouTube - "21" explains the Monty Hall problem

In this clip Spacey leaves out a very important detail. That beng that the host will always reveal a goat after you pick and before offering you a chance to switch. Without this knowledge we don't know that he didn't just show door #3 at random. Thus making your odds 50/50 either way. He does stress that the host knows where it is but that's still not good enough. That alone just leaves us to speculate what the hosts intentions are and brings psychology into play which is not the intent of the problem.

yeah, when I saw 21, and it actually didn't make sense then. Now, I'm reading this book called "The Curious Incodent of the Dog in the Nightime" and it explained it much beter. Actually had the right "rules" of the equation in it

 

[loki604]

yeah, when I saw 21, and it actually didn't make sense then. Now, I'm reading this book called "The Curious Incodent of the Dog in the Nightime" and it explained it much beter. Actually had the right "rules" of the equation in it

Good book.

If anyone is interested, another interesting problem: Birthday problem - Wikipedia, the free encyclopedia

 

[SLY]

What comes twice in a week, but once in a year?

 

[puckhead]

What comes twice in a week, but once in a year?

"e"

 

[SLY]

yea thats an easy one, just figured id throw it out there. kinda hard to stump people online.

 

[juliansteed]

I've seen actual HS and college math professors argue against the 2/3 answer, saying it was 50/50. The key element in the problem is that Monty always *knows* where the prize is and *always* reveals a losing door. Otherwise, then it would end up being 50/50.

This is a good read and debate on the problem:

Marilyn vos Savant | The Game Show Problem

I've only read the original problem being asked and a hand full of the responses. As I suspected, the cause of the debate comes from the wording of the problem. Just as it is the case in the movie "21" and an episode of "Numb3rs", the problem was poorly explained because it does not make it clear that the host will always reveal a goat behind 1 of the 2 remaining doors before offering you a chance to switch. They are assuming that you are familiar with the game show hosts patterns. But if you're not, then you have no way of knowing that the host decided to show you what was behind a certain door because there is a 2/3 chance that door was his only option to reveal because the car is behind the other unselected door. For all you know he chose that door at random and for the next contestant might reveal the car, or might reveal what's behind the selected door etc. Surprisingly, none of the responses I have read that say the odds are 50/50 mention this. They just insist that the person is wrong and that it would be 50/50.

 

[dare2be]

Surprisingly, none of the responses I have read that say the odds are 50/50 mention this. They just insist that the person is wrong and that it would be 50/50.

What's even more surprising to me is that there have been no arguments from people here like I experienced with co-workers the last time I was presented with this problem a few years ago. We have a smart bunch here.

The fact that there is so much contention over the problem and its wording, and even when the wording is properly and accurately presented, fascinates me. Here is another page with an online "debate":

The Straight Dope: On "Let's Make a Deal," you pick Door #1. Monty opens Door #2--no prize. Do you stay with Door #1 or switch to #3?

EDIT: I have found that the best explanation that convinces even the most stubborn critic is:

"You can have the door you picked, or you can have both of the other doors, one of which I will open for you. Which do you choose?"

 

[ritari330]

Darn, I wanted people to disagree over this, now it's just a thread over how and why other explinations are wrong

 

[dare2be]

Darn, I wanted people to disagree over this, now it's just a thread over how and why other explinations are wrong

Agreed, it would've been fun...perhaps the ones who disagree are smart enough to keep their mouths shut

 

[SLY]

I'm definitely not super smart or anything, but even a tart should understand that scenario.