The Monty Hall Problem

[Mike Teacher]

People, even math experts flood whoever brings this up, and it was brought up recently in the NY Times, and the author actually begs for people not to mail him telling him he's got it wrong: Interesting? Bone crushing boring? Who cares? Exactly...

=

The Monty Hall Problem:

Monty Hall shows you three doors, telling you theres a Car behind one of them and Goats behind the other two. Pick the door with the car and you win it.

You pick a door, say Door #1. Before Monty opens it, however, Monty shows you what was behind one of the doors you did not pick; Say Door #3. It opens, and there's one of the goats.

Monty now asks you, Would you like to stay with door #1, your original choice, or, switch, and take door #2?

=

The big question: What should you do? Stick with Door #1, or switch to Door#2?

Google-ers will be shot on sight.

[Gvac]

Switch.

Your original pick has a 33% chance of being right.

Door #2 has a 50% chance of succeeding.

[Hosp]

Google-ers will be shot on sight.

Good thing you said nothing about Wikipedia.

Never heard of this but it's really interesting.

[smiler grogan]

stick with your initial gut pick.I don't know why it's what came to mind first.

[Ritalin]

I'll switch, and if I don't win I'm going to pound lumps on Gvac for suggesting it.

Then I'm going to make him take the goat home.

[FUNKMAN]

i'll take earl for 200 alex

http://www.christianbaxter.com/blog/uploaded_images/fainting_goat-765279.jpg

[Brad_Rush]

Stick with door one.

Real Americans don't flip-flop.

[BeerBandit]

I think I remember something about that odds not changing because you now know what's behind one door. I still don't understand why, and I remember arguing with my math teacher about it. So I guess you should stick with you initial choice.

[cupcakelove]

Your first choice, 2 out of 3 times, will be a goat. So once you know the location of the other goat, switching will give you the car more often than not. Either way you're still leaving it up to chance, all you can do is play the odds so there really isn't any 'right' answer.

[DarkHippie]

it doesnt matter. the odds are now 50% for each door

[Sinestro]

They had a similar scene in the movie "21" when the teacher was discussing the same principle in the class.

[IMSlacker]

Switch.

Your original pick has a 33% chance of being right.

Door #2 has a 50% chance of succeeding.

I like Gvac's answer. Even though he can't solve a Rubik's Cube.

[cupcakelove]

it doesnt matter. the odds are now 50% for each door

Since you were more likely to have picked a goat the first time, the odds are not 50/50.

[Gvac]

I like Gvac's answer. Even though he can's solve a Rubik's Cube.

Don't make me smash you in the face with a yo yo!

[IMSlacker]

Don't make me smash you in the face with a yo yo!

You're totally contradicting your avatar.

[Gvac]

It's a whole Yin and Yang thing...the bull and the roses.

Hate and love.

Rubik's cube and yo yos.

[FUNKMAN]

fuck the doors and pick the broad



that's just crazytalk

[STC-Dub]

Didn't you cover this on the show before? You are better off going with the new door.

[Marc with a c]

the car is behind door number two.

if it wasn't you most likely would've been shown door number two first.

[nickeye]

* note that Monty knows where the car is, and CAN'T open the door with the car. It's an undeclared rule: He's not picking randomly, unless you happened to be right on the first try.

It helps to picture the same problem, except with 100 doors. You pick, say, door number 53. Monty opens 98 other doors, leaving your door and door number 34 still closed. It's kinda obvious that you want to switch, since you only had a 1 percent chance of being right on the first guess. And, again, Monty didn't have a choice about which ones to open; he had to leave the car door shut.

[sailor]

switch, of course. the math given by gvac is correct (but people hate math). it may help folks to visualize a million doors so that the problem becomes:

Monty Hall shows you a million doors, telling you there's a Car behind one of them and Goats behind the others. Pick the door with the car and you win it.

You pick a door, say Door #1. Before Monty opens it, however, Monty shows you what was behind 999,998 of the doors you did not pick; Say Doors #3-1,000,000. They open, and there's goats behind all of them.

Monty now asks you, Would you like to stay with door #1, your original choice, or, switch, and take door #2?

edit: damn you nickeye.

[Tall_James]

What if you just wanted the goat?

[midwestjeff]

What if you just wanted the goat?

And who wouldn't?

You can't fuck a car.

[cupcakelove]

And who wouldn't?

You can't fuck a car.

Hey speak for yourself.

[Marc with a c]

it might be easier to look at it with more doors, say one billion. so you pick door #1. before monty opens it he shows you doors 3-1,000,000,000 all with goats behind them.

monty now asks you, would you like to stay with door #1, your original choice, or, switch, and take door #2?

[Mike Teacher]

from the web:

Ms. Savant, who’s listed in the Guinness Book of World Records Hall of Fame for “Highest IQ” (228), answered “[Censored]” Because of the estimated 10,000 letters she received in response, she published a second article on the subject.

Due to the fervor created by Ms. Savant’s two columns, the New York Times published a large front page article which declared: “Her answer... has been debated in the halls of the C.I.A. and the barracks of fighter pilots in the Persian Gulf. It has been analyzed by mathematicians at M.I.T. and computer programmers at Los Alamos National Laboratory in New Mexico. It has been tested in classes ranging from second grade to graduate level at more than 1,000 schools across the country.”

[Ogre]

i'll take earl for 200 alex

http://www.christianbaxter.com/blog/uploaded_images/fainting_goat-765279.jpg

:lol::lol::lol::lol:

[Tall_James]

Marilyn Vos Savant is a know-it-all twat and Parade magazine makes Us Magazine look like the Utne Reader.

[FUNKMAN]

one thing i know for certain

if you pick the wrong door it could be baaaaaaaad



go funkman it's your birthday go funkman it's your birthday

[Gvac]

* note that Monty knows where the car is, and CAN'T open the door with the car. It's an undeclared rule: He's not picking randomly, unless you happened to be right on the first try.

It helps to picture the same problem, except with 100 doors. You pick, say, door number 53. Monty opens 98 other doors, leaving your door and door number 34 still closed. It's kinda obvious that you want to switch, since you only had a 1 percent chance of being right on the first guess. And, again, Monty didn't have a choice about which ones to open; he had to leave the car door shut.

HOLY SHIT!!! NICKEYE!!!

Where the hell have you been???

[DarkHippie]

Since you were more likely to have picked a goat the first time, the odds are not 50/50.

i dont understand why. Once the first goat is removed, there is one door with a car, and one with a goat.

[sailor]

i dont understand why. Once the first goat is removed, there is one door with a car, and one with a goat.

pretend there are a trillion doors...

[DarkHippie]

i looked it up and now i understand why. it might help to picture it as a shell game

[nickeye]

HOLY SHIT!!! NICKEYE!!!

Where the hell have you been???

Busy. I won 98 goats on a game show.

[Mike Teacher]

Busy. I won 98 goats on a game show.

The Price Is Right: Afghanistan ?

Goat or No Goat?

[nickeye]

The Price Is Right: Afghanistan ?

Goat or No Goat?

Win, Lose, or Straw

[PapaBear]

I haven't looked it up, and I can't see how it could possibly make any difference if you change your pick or not.

[King Hippos Bandaid]

Im going for the

http://cash4gamers.com/images/MysteryBox.gif

mystery box

[Thebazile78]

I haven't looked it up, and I can't see how it could possibly make any difference if you change your pick or not.

You should always switch doors, which is counterintuitive to what you'd normally do.

At the start of the problem, you have a 2 in 3 chance (66%) of picking a goat.
Monty Hall opens one of the doors you didn't pick and shows you a goat, reducing the number of doors you've got remaining to 2 and your odds of picking a goat over a car to 1 in 2 (50%), whereas, if you stick with your original choice, your odds are not the same because you only have a 1 in 3 chance (33%) of being right. Switching doors when you're given the option improves your odds to 1 in 2 if you were wrong to begin with.

The column (because it's part of John Tierney's "Findings" weekly column, which is often followed up with more information ... and lots of flaming... at his "TierneyLab" blog) in the Times from yesterday (4/8/08) (http://www.nytimes.com/2008/04/08/science/08tier.html?_r=1&ref=science&oref=slogin) is talking about the relationship betweent he "Monty Hall Problem" and the study of cognitive dissonance in experiments since 1956.

Within the column, there's a link to play the game ... you can play as many times as you like and have a concrete representation of how your odds change when you switch doors.

(I haven't played it yet.)

Oh and Mike, Mr. Tierney doesn't ask people not to tell him he's wrong. He asked his readers not to "shoot first and ask questions later" ... which, obviously, some readers will still do because they will go with their gut reaction and let their fingers take over.

[nickeye]

At the start of the problem, you have a 2 in 3 chance (66%) of picking a goat.
Monty Hall opens one of the doors you didn't pick and shows you a goat, reducing the number of doors you've got remaining to 2 and your odds of picking a goat over a car to 1 in 2 (50%), whereas, if you stick with your original choice, your odds are not the same because you only have a 1 in 3 chance (33%) of being right. Switching doors when you're given the option improves your odds to 1 in 2 if you were wrong to begin with.


Actually, the odds if you switch are even better than 50%: it's 2 in 3. You're right about the 1 in 3 if you stick with your original choice, but it's gotta add up to 100%.

[Thebazile78]

Actually, the odds if you switch are even better than 50%: it's 2 in 3. You're right about the 1 in 3 if you stick with your original choice, but it's gotta add up to 100%.

I knew I was doing something wrong by not checking my math before breakfast.

... you know what? I got so focused on the goats that I forgot about the car. So I started with the 2 in 3 shot of picking a goat in your first choice (approx. 66% odds of picking a goat with 33% odds of picking the car) ... then moved to the reduced # of doors (1 in 2 chance (50%) of picking a car if you switch doors) without re-calibrating the probability.

Next time I will check my math before I post.

[Mike Teacher]

The column (because it's part of John Tierney's "Findings" weekly column, which is often followed up with more information ... and lots of flaming... at his "TierneyLab" blog) in the Times from yesterday (4/8/08) is talking about the relationship betweent he "Monty Hall Problem" and the study of cognitive dissonance in experiments since 1956.

Within the column, there's a link to play the game ... you can play as many times as you like and have a concrete representation of how your odds change when you switch doors.

=

Yes, this is the part I was keeping out of the thread. On purpose.

[knocking head into wall]

[Thebazile78]

The column (because it's part of John Tierney's "Findings" weekly column, which is often followed up with more information ... and lots of flaming... at his "TierneyLab" blog) in the Times from yesterday (4/8/08) is talking about the relationship betweent he "Monty Hall Problem" and the study of cognitive dissonance in experiments since 1956.

Within the column, there's a link to play the game ... you can play as many times as you like and have a concrete representation of how your odds change when you switch doors.

=

Yes, this is the part I was keeping out of the thread. On purpose.

[knocking head into wall]

Until you run into someone who also reads Tuesday's Science Times.

I really think that playing the game will help the people who aren't totally sold on the idea that switching doors is the best strategy have a concrete representation of what we're using maths and probability to explicate. (So does Mr. Tierney.) Not everyone grasps probability all that well, possibly because it's not taught as thoroughly as it ought to be.

As an added bonus, it'll remove the stench of referencing Marilyn Vos Savant. She should just stay in her ivory tower.

[Mike Teacher]

wow wrong thread

[jauble]

Im going for the

http://cash4gamers.com/images/MysteryBox.gif

mystery box

A goat is just a goat, but in the mystery box there could be anything. Even a goat.

http://farm1.static.flickr.com/169/439431533_87eb736c43_o.jpg

[Mike Teacher]

A goat is just a goat, but in the mystery box there could be anything. Even a goat.



Schroedinger's Cat is alive and well in that box.

Schroedinger's Cat is dead and rotting in that box.

[mikeyboy]

Thanks for the heads up, Mike. I thought this was really interesting. I called my dad up to pose it to him and discuss it. It also made me think of my father-in-law who passed away earlier this year, because he would have loved this.

[King Hippos Bandaid]

A goat is just a goat, but in the mystery box there could be anything. Even a goat.

http://farm1.static.flickr.com/169/439431533_87eb736c43_o.jpg
wasn't it a boat

[Furtherman]

What if it was known that the person was going to pick Door #1. He tells a friend and the friend tells Monty.

So Monty puts a car behind Door #1.

The contestant picks Door #1, and is shown the goat behind Door #3.

So according to the odds, he should switch to Door #2.

Does this throw probability out the window?

[nickeye]

What if it was known that the person was going to pick Door #1. He tells a friend and the friend tells Monty.

So Monty puts a car behind Door #1.

The contestant picks Door #1, and is shown the goat behind Door #3.

So according to the odds, he should switch to Door #2.

Does this throw probability out the window?

I'm not sure that one's a question of probability. If the car is behind Door #1, there's 100% chance that it's behind Door #1.

[nickeye]

When the Monty Hall discussion is exhausted....

Suppose that explodassitis is a somewhat rare disease which strikes about one in one thousand people. The test for explodassitis is kinda accurate: its false positive rate is 5% (only 5% of non-explodassitic people test positive) and it never gives a false negative (if you have explodassitis, you'll always test positive).

Your doctor tells you that your random blood test has come back positive for explodassitis. How likely is it that your ass will explode?

[jauble]

wasn't it a boat

I hope that was typed with sarcasm...

[Thebazile78]

Schroedinger's Cat is alive and well in that box.

Schroedinger's Cat is dead and rotting in that box.

:clap::clap::clap::clap::clap:

[DolaMight]

I think everybody is missing the bigger question. What's wrong with a nice goat?

http://cache.viewimages.com/xc/3376629.jpg?v=1&c=ViewImages&k=2&d=89B856506CE546541C6BD6A5FCE4F921A55A1E4F32AD3138

[Mike Teacher]

:clap::clap::clap::clap::clap:

Thank you bazile; I cant tell if you like my thread or hate it, and me.

Not that I give a shit, but you're smart, and that's good.

:sniffle:

Be my friend!!!! Pleassssssssssssssssssseeeeeeeeeeeee.

I got nowhere else to go!!!

[Thebazile78]

Thank you bazile; I cant tell if you like my thread or hate it, and me.

Not that I give a shit, but you're smart, and that's good.

:sniffle:

Be my friend!!!! Pleassssssssssssssssssseeeeeeeeeeeee.

I got nowhere else to go!!!

Don't worry, I like you just fine; it's just fun to play "stump the teacher" ... I've been practicing. Plus, it keeps me on my toes because, Lord knows my job doesn't.

I am pretty sure that we've actually met in person ... at the "Winter Carnival Party" I was there with my brother, who you may know as "Sheepy," and my husband, who you may know as "Matty Fridays" or "Tenbats " ... we chatted a bit and I totally forgot to introduce myself. But it was so much fun speaking with you and I am really enjoying threads like these ... please don't stop posting them because I'm socially inept.

[Mike Teacher]

Coolness no worries.

You familiar with The Prisoner's Dilemma?

That will send your brain into overdrive. No way I can even begin to go into the math model here; William Poundstone has an Excellent book on the subject.

from Wiki; their 'classic' version of the problem:

THE PRISONER'S DILLEMMA:

Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence.

If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make.

So this dilemma poses the question: How should the prisoners act?

[Furtherman]

How should the prisoners act?

You won't get nothin' from me. I ain't sayin' nuthin.

[JPMNICK]

Coolness no worries.

You familiar with The Prisoner's Dilemma?

That will send your brain into overdrive. No way I can even begin to go into the math model here; William Poundstone has an Excellent book on the subject.

from Wiki; their 'classic' version of the problem:

THE PRISONER'S DILLEMMA:

Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence.

If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make.

So this dilemma poses the question: How should the prisoners act?

one of my friends got busted for selling coke, and i tried to talk to him about this. I showed him the math and explained the other people he was arrested with and what the best course of action is. he didn't listen, but I guess he was not all that smart if he was selling coke and got caught

[Gvac]

THE PRISONER'S DILLEMMA:

Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence.

If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make.

So this dilemma poses the question: How should the prisoners act?

What if both plead guilty?

That was the only option not offered.

[SinA]

shoulda picked door #3.
you can't fuck a car.

[PapaBear]

Marilyn Vos Savant is a know-it-all twat and Parade magazine makes Us Magazine look like the Utne Reader.
I totally agree. I used to read her column until one where she addressed the subject of people who don't dress like "normal people". I can't remember if she called them "immature" or they had "mental problems", but whatever it was, she came off like a total bitch. And I DO dress like "normal people".

[drjoek]

Door Number Three


By: Jimmy Buffett, Steve Goodman
1974
Oh I took a wrong turn, it was the right turn
My turn to have me a ball
Boys at the shop told me just where to stop
If I wanted to play for it all
I didn't know I'd find her on daytime TV
My whole world lies waiting behind door number three

I chose my apparel, I wore a beer barrel
And they rolled me to the very first row
I held a big sign that said, "Kiss me I'm a baker
And Monty I sure need the dough"
Then I grabbed that sucker by the throat until he called on me
'Cause my whole world lies waiting behind door number three

And I don't want what Jay's got on his table
Or the box Carol Merrill points to on the floor
No I'll hold out just as long as I am able
Or until I can unlock that lucky door
Well, she's no big deal to most folk
But she's everything to me
'Cause my whole world lies waiting behind door number three

Oh Monty, Monty, Monty, I am walkin' down your hall
Got beat, lost my seat, but I'm not a man to crawl
Though I didn't get rich, you son of a bitch
I'll be back just wait and see
'Cause my whole world lies waiting behind door number three
Yes my whole world lies waiting behind door number three

[underdog]

Schroedinger's Cat is alive and well in that box.

Schroedinger's Cat is dead and rotting in that box.

I've been sitting here staring at this trying to remember what ESD said about Schroedinger when this was brought up on the air and I can't remember. But I do know that I'll forever laugh whenever I read about Schroedinger's Cat, just because of that red headed dummy.

[Mike Teacher]

You flip a coin in the air and it lands on a table as you slam your hand over it.

Now, you sit there with your hand over the coin, not knowing if it is heads or tails.

Q: What are the odds of the coin being Heads?

Then you look at the coin. Now, again:

Q: What are the odds of the coin being heads?

and the big Q: If the odds change between before and after you look, why?

[Tall_James]

If your Aunt had balls would she then be your Uncle?

The mind wobbles.

[Tall_James]

By the same token, if your Grandmother had wheels would she then be a wagon?

[Mike Teacher]

Why does it hurt when I pee?

[BoondockSaint]

Why does it hurt when I pee?


You chose the wrong box.