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#1
http://en.wikipedia.org/wiki/Monty_Hall_Problem

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Vos Savant's response was that the contestant should always switch to the other door. If the car is initially equally likely to be behind each door, a player who picks Door 1 and doesn't switch has a 1 in 3 chance of winning the car while a player who picks Door 1 and does switch has a 2 in 3 chance. The host has removed an incorrect option from the unchosen doors, so contestants who switch double their chances of winning the car.


Discuss your thoughts.
#2
Did you get this from the list of misconceptions posted in the other thread too? I was just reading this and I was just about to post a thead on it, too.

Freaky...
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#3
Quote by Kensai
Did you get this from the list of misconceptions posted in the other thread too? I was just reading this and I was just about to post a thead on it, too.

Freaky...

Yes! I'm not sure i agree with it, after the goat has been shown behind a door then there is only a 50/50 chance left, i am tired though but this thing is upsetting me.
#4
It's like this:

Door1/Door2/Door3/resultbyswitch/resultbystaying
Car Goat Goat Goat Car
Goat Car Goat Car Goat
Goat Goat Car Car Goat
If you pick door 1, and he opens door 3, switching will give you a goat.
If you pick door 1, and he opens door 3, switching will give you a car
If you pick door 1, and he opens door 2, switching will give you a car.

Suggesting that the host knows where the car is, and he always opens a door with a goat, you will get a car two out of three times, if you switch.
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#5
Surely once one door has been opened and it's not the car, there's a 50/50 option for it to be through either of the other two?
#6
Ahhhh this question again. I've heard many high up mathematicians getting the answer to this wrong. I can't remember what the correct answer is for sure, but I think switching doors every time gets you the best chance, like the article says.
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#7
ROFL.

I thought they taught this in high school.

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#8
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#9
Monty hall? didn't some kid get jumped by UG for posting about Dark side of the rainbow a few hours ago?
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#10
Quote by Zoot Allures
Yes! I'm not sure i agree with it, after the goat has been shown behind a door then there is only a 50/50 chance left, i am tired though but this thing is upsetting me.

It doesn't matter if you agree or not...


If you want to look up more surprising maths things, http://en.wikipedia.org/wiki/Birthday_problem
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#11
Quote by Zoot Allures
Discuss your thoughts.


There are no thoughts to discuss. It is a proven mathematical fact that changing doors improves your chances of winning.
Give it a try yourself and see:
http://math.ucsd.edu/~anistat/chi-an/MonteHallParadox.html
Last edited by Shaharz at Oct 22, 2011,
#12
Quote by Zoot Allures
Yes! I'm not sure i agree with it, after the goat has been shown behind a door then there is only a 50/50 chance left, i am tired though but this thing is upsetting me.

Yeah, I've had the same 'wtf, that makes no sense!' reaction too. It makes more sense if you think about it as an ongoing strategy rather than as a one-off.
If you didn't get a chance to change doors, that would be the same situation as if you always stayed with the same choice. You pick one door and have a 1/3 chance.
If you ALWAYS change, you get whatever is left in the final two. 1/3 of the time your first choice will have been a car and you'll swap to a goat. The other 2/3 of the time you'll pick a goat first and swap to a car.
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#13
Mathematical fact: switching doors is your best option. This have been proven many times, to the point of exhaustion.
#14
Quote by Zoot Allures
Yes! I'm not sure i agree with it, after the goat has been shown behind a door then there is only a 50/50 chance left, i am tired though but this thing is upsetting me.


That's really freaky. I was just about to post it as well.

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It doesn't matter if you agree or not...


If you want to look up more surprising maths things, http://en.wikipedia.org/wiki/Birthday_problem

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#15
That ^

I just don't even.. what?
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#16
This Monty Hall problem is bullshit.

You've got a 1 in 3 chance of getting the car when you pick the door.
Once one option has been removed there's a 50/50 chance of the car being behind either door.

No matter what switching happens if you step back and rechoose from the start it's a 1 in 2 chance. It's just a trick with the statistics that make one door more desirable.
#17
wait a minute, so if this is true i have a 2 in 3 chance of winning a goat? me gusta!
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#18
Quote by SG_dave
This Monty Hall problem is bullshit.

You've got a 1 in 3 chance of getting the car when you pick the door.
Once one option has been removed there's a 50/50 chance of the car being behind either door.

No matter what switching happens if you step back and rechoose from the start it's a 1 in 2 chance. It's just a trick with the statistics that make one door more desirable.

That's most peoples initial thoughts, but no. Read the wiki article.

Think of it as you have a 2/3 chance of picking a goat, meaning there's a 2/3 chance the car will be in one of the other doors. Since the host always reveals the goat, if you swap every time you'll have a 2/3 chance of getting the car.
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#19
Who says the host always reveals the goat, though?

What if he doesn't?
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#20
Quote by Sleaze Disease
Who says the host always reveals the goat, though?

What if he doesn't?


why would he reveal the car though? that would make the game much less exciting.
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#21
i remember doing this in 2nd year in uni
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#22
But what if I wanted to win the goat instead of the car? Vos whatever doesn't explain that now does he? I might need a goat. Goats are kewl too, and sort of useful around the yard.
I wonder if anybody who actually won one got one? Like, did they demand their goat since they won it instead of the car? Would the show actually produce one for them? Like special UPS goat delivery? See, it's these things that are important to ask. Why? Don't ask me.
#23
Quote by theogonia777
why would he reveal the car though? that would make the game much less exciting.

Nah, if a game show is genuinely exciting, things like that wouldn't matter.

If all it took to make it exciting was the host revealing the goat, then the show is probably pretty bad to begin with.
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#24
Quote by Sleaze Disease
Nah, if a game show is genuinely exciting, things like that wouldn't matter.

If all it took to make it exciting was the host revealing the goat, then the show is probably pretty bad to begin with.


think of it this way: if they revealed the car first, it's a lose-lose situation after that, and then there's really no point in picking a door, if they're both a goat. you know there's not a car. so at that point there's no longer a reason to continue. also, in all my years of watching gameshows on TV, i've never seen the car or similar prize revealed first even once.
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#25
I understand it, I guess I just don't get why someone thought it was necessary to come up with this 'theory' in the first place.

People can't just watch a tv show without bringing math and science into it?
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#26
Quote by Venice King
It doesn't matter if you agree or not...


If you want to look up more surprising maths things, http://en.wikipedia.org/wiki/Birthday_problem


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#27
Oh God, I remember this from The Curious Incident of The Dog In The Night-Time. I still don't really understand it years on but I know that you're better to switch doors.
#28
Ugh every single math teacher I've had for the last 5 years has spent a class talking about it and I still don't get it so I probably never will.
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#29
Quote by Sleaze Disease
I understand it, I guess I just don't get why someone thought it was necessary to come up with this 'theory' in the first place.

People can't just watch a tv show without bringing math and science into it?

Obviously you wanna win 2/3 times instead of 1/3 times right?

I remember my teacher used this example to introduce conditional probability in 11th grade. For most people it messes with their mind but it's actually pretty simple.
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#31
I've found this problem exceeds in bringing about assholes who take it upon themselves to sneer and act like complete cunts at any confusion about it. You're not impressing anybody and probability will not guarantee you the prize car if you decide to switch to a door that has a goat. I know, I know... it's about numbers, not actually winning the game. I got it, it makes sense.


Take your probability and ram it up your ass you hoity-toity fuck.
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COWBOY: Sir, no, sir!
SGT. HARTMAN: Are you a peter-puffer!?
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#32
My mind is so full of f*ck

EDIT: Does this work better when there are more than 3 choices?
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#34
So... if I prefer goats to cars, I don't switch? Got it. That goat will be mine.


What kind of game show gives goats away anyway?
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#35
Quote by catempire
Yeah, I've had the same 'wtf, that makes no sense!' reaction too. It makes more sense if you think about it as an ongoing strategy rather than as a one-off.
If you didn't get a chance to change doors, that would be the same situation as if you always stayed with the same choice. You pick one door and have a 1/3 chance.
If you ALWAYS change, you get whatever is left in the final two. 1/3 of the time your first choice will have been a car and you'll swap to a goat. The other 2/3 of the time you'll pick a goat first and swap to a car.

Does it only come into effect after more than 1 game has been played then? :S
#37
Quote by Trowzaa
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Not how it works, brah.
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#39
Quote by Zaphikh
I've found this problem exceeds in bringing about assholes who take it upon themselves to sneer and act like complete cunts at any confusion about it. You're not impressing anybody and probability will not guarantee you the prize car if you decide to switch to a door that has a goat. I know, I know... it's about numbers, not actually winning the game. I got it, it makes sense.


Take your probability and ram it up your ass you hoity-toity fuck.




This is pretty cool. I've not heard about it before.
#40
Always switch.

At first, you have a 1 in 3 chance of picking the prize. Once he eliminates one of the bad options, the other door has a 50-50 chance of being correct one. But the one you chose has a 1 in 3 chance, because you chose it out of 3 possibilities.
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