Epic Perfect World

Monty Hall Problem

Hello EPW, today I would like to introduce you a problem - the Monty Hall Problem. It is a famous problem, so some of you might have heard about it. It was originated from a game show and named after the host, Monty Hall. Here's the problem (copied from Wikipedia):

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, 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?

One thing to emphasize: The host will always open a door which has a goat, and of course he knows what's behind every door.

Comment below whether or not you should switch.

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It's good to see some debates going on this post, and I enjoyed reading them. However, there are a few CORRECT ways to see this problem and here's a less mathematical one:

Let's label the door with 1,2,3 ; c = car, g = goat
There are only 3 possible scenarios for this problem, each with an equal chance of 1/3 of happening:
scenario 1: 1c 2g 3g
scenario 2: 1g 2c 3g
scenario 3: 1g 2g 3c

Suppose you choose door 1 and you don't know what's behind it, then the host opens another door, says door 3 and reveals there's a goat behind it. The host asks you whether or not you want to switch to door 2, which is still unknown.

Based on the total 3 possible scenarios, the scenario described above is matched with scenario 1 and scenario 2, and we know one thing for sure, that is scenario 3 did not happen since door 3 doesn't have a car. Putting it in simple words, you just made a decision such that scenario 3 will never happen, by choosing door 1 at the beginning, and the chance for it is 2/3 (2 out of the 3 scenarios match it).

Now, don't forget among scenario 1 and scenario 2, only scenario 1 has door 1 with a car, so the chance for it after eliminating door 3 is 1/2. BUT, you cannot just eliminate door 3 from air, you need to be in that 2/3 chance which we just explained above, in order to eliminate door 3 from your option. So, finally 2/3*1/2=1/3 = chance of door 1 having a car in the above scenario; that means after the host reveals door 3 which has no car, the chance of having a car behind door 1 still doesn't chance, it is still 1/3...And this leads us to a conclusion that the remaining door 2 has 2/3 chance of having a car, since the remaining 2/3 chance has to go somewhere...and door 2 is the only remaining door after door 3 is opened.

Again, feel free to comment with your thoughts.
Last Edit: June 20, 2014, 04:24 pm by IDuKnow

Offline Nea

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This, is technically a math paradox, since every room has 33.33% chance.Once he tells u to change, he gives u a chance, if u change the door u increase ur chance of geting the great prize
The answer is 'you should change'.
There was a show on discovery some years ago, i remember this.
This, is technically a math paradox, since every room has 33.33% chance.Once he tells u to change, he gives u a chance, if u change the door u increase ur chance of geting the great prize
The answer is 'you should change'.
There was a show on discovery some years ago, i remember this.
Yes, the correct answer is switching to another door. There are tons of information and explanation on the internet about this problem. But what is your take on the problem? How do you reason it?

Offline DignityPK

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Hello EPW, today I would like to introduce you a problem - the Monty Hall Problem. It is a famous problem, so some of you might have heard about it. It was originated from a game show and named after the host, Monty Hall. Here's the problem (copied from Wikipedia):

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, 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?

One thing to emphasize: The host will always open a door which has a goat, and of course he knows what's behind every door.

Comment below whether or not you should switch.

Hello, unknown, here I present you the problem of your question. The question implies that people that are supposed to guess the door are smart enough to think through a math formula which is false because smart people wouldn't be doing that, they would already have a car and they wouldn't be required to guess some random doors thus making this question under a question whether you would rather spend more of your time thinking about what door would be right to guess or get off your ass and earn yourself a car?

Offline Nea

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It's just psyhology and math all together
If u remove 33,3% leaves u with 66,6% chance that one of those 2 left is the good one, if he tells u to change, he just tests u, and most people choose to stay, but if u change it, u purely do what he wasn't expecting, do what he says.Most people don't wanna do what some1 tells them to do, so he tells u that, to make u feel more confident about ur door.In the end, if u change, u just get a higher chance of geting the prize, i can't explain it as i really believe since my english isn't good enough for me to say all i'd like to.In general, i'd change because humans tend to do what they are not told to. If he tells u to switch, he just tries to make u stay at the same door as u are.
Hope that what i've said made any sense, if not, sorry.

Offline DignityPK

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It's just psyhology and math all together
If u remove 33,3% leaves u with 66,6% chance that one of those 2 left is the good one, if he tells u to change, he just tests u, and most people choose to stay, but if u change it, u purely do what he wasn't expecting, do what he says.Most people don't wanna do what some1 tells them to do, so he tells u that, to make u feel more confident about ur door.In the end, if u change, u just get a higher chance of geting the prize, i can't explain it as i really believe since my english isn't good enough for me to say all i'd like to.In general, i'd change because humans tend to do what they are not told to. If he tells u to switch, he just tries to make u stay at the same door as u are.
Hope that what i've said made any sense, if not, sorry.

What if he exactly knew that you would follow him because you think your smart and thus pointed you to the wrong door? Don't try to argue on this question :)

Offline Nea

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What if he exactly knew that you would follow him because you think your smart and thus pointed you to the wrong door? Don't try to argue on this question :)
That's why it's called paradox, w.e u choose, there is a turning back.
These are the things u can't really predict, there are just ways of making ur chances A BIT higher, not being sure of a win. It's like gambling with less risks.

Offline DignityPK

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That's why it's called paradox, w.e u choose, there is a turning back.
These are the things u can't really predict, there are just ways of making ur chances A BIT higher, not being sure of a win. It's like gambling with less risks.

If you're a good psychologist you should still be able to up your chances to 66 2/3% of making the right choice.
Except these kind of shows don't allow psychologist to play there.

Offline Harry

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1/3 - Probability of getting car.

1/2 - Probability of getting car after first door is opened.

1/2 - Probability if you change.

Offline Nea

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If you're a good psychologist you should still be able to up your chances to 66 2/3% of making the right choice.
Except these kind of shows don't allow psychologist to play there.
Only chance of winning that game is to use this paradox in ur advantage and read the body language of the guy that presents the show, asking some sh1t that would make him give away, un-wanted info.
Like, the way he moves, if he's moving his hands, if his lips are shaking and so on, it requires some practice, but only to make ur chances higher, not get a 100% win.

Offline DignityPK

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Only chance of winning that game is to use this paradox in ur advantage and read the body language of the guy that presents the show, asking some sh1t that would make him give away, un-wanted info.
Like, the way he moves, if he's moving his hands, if his lips are shaking and so on, it requires some practice, but only to make ur chances higher, not get a 100% win.

Assuming you can ask him questions, ask him where is the right door and where is the wrong door - then let him talk the whole show and count how many times he says the name of each door - the one that has been mentioned the most is probably the one with the car.

bvanharjr

It's actually THIS forumla after the first door's opened.

1/3 You get a car
2/3 You get ditto.

YES. THE THIRD DOOR DOES MATTER STILL. Even after it's opened.

It doesn't change. Ever.

Offline ᴰᴱᴬᴰ†

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u open the door

hop on the goat

and run away

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Offline 엔젤ღ

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u open the door

hop on the goat

and run away
^this the best solution

goat can be like donkey too

LOOOOOOOOOOOOL
AngeliqMyst - Sage Mystic

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Offline Harry

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Surely if 'The host will always open a door which has a goat'

Then you can just ask: "Are you willing to open this door?"

If he says yes, then tell him to open it - if he doesn't, it's a car - if he does, tell him to stop and open the other.