The Monty Hall Problem

[BarthelloSylph]

i like the flaming of me but after 4 pages no one can still agree on a number. kinda funny, youre right you cant beat the stupid outta people.

what did those scholars come to the conclusion of that the guy in the video said was misleading?

1/3 chance in the beginning and 1/2 in the end. flame on

The reason that we are flaming you, xfaustx, for being wrong is this:

You not only were wrong - which is OK, because there are smart people and there are dumb people, not everyone can be smart, so God made you dumb - but you decided to inform us (thanks by the way, I'm so glad you did, it was a huge breakthrough) that we were ignoring the incredibly important element of human error in our 100% math/probability question. It was so insightful I choke on my water and nearly shat my pants.

There is no human error in the actual solving of this equation. The only human error on this thread has been identified, it's called xfaustx. The correct answer is 2/3s. Get over the fact you are dumb and can't understand - it'll help you a lot in life.

[Xfaustx]

i like the flaming of me but after 4 pages no one can still agree on a number. kinda funny, youre right you cant beat the stupid outta people.

what did those scholars come to the conclusion of that the guy in the video said was misleading?

1/3 chance in the beginning and 1/2 in the end. flame on

The reason that we are flaming you, xfaustx, for being wrong is this:

You not only were wrong - which is OK, because there are smart people and there are dumb people, not everyone can be smart, so God made you dumb - but you decided to inform us (thanks by the way, I'm so glad you did, it was a huge breakthrough) that we were ignoring the incredibly important element of human error in our 100% math/probability question. It was so insightful I choke on my water and nearly shat my pants.

There is no human error in the actual solving of this equation. The only human error on this thread has been identified, it's called xfaustx. The correct answer is 2/3s. Get over the fact you are dumb and can't understand - it'll help you a lot in life.

lol god made me dumb for opposing your wrong answer? thats funny. fine lets remove human error from it. you are elminating door C from the equation once he shows you it. you can NO LONGER choose that option. thats called process of elmination. you know what that is right? in math you can eliminate variables from problems. ok so once C is removed youre left with A and B. now you can choose one of them. thats 1/2 which is also called 50%. just because i like to argue different sides of things does not make me an idiot. and because you cannot see where im coming from. you see black and white sir. i do not. youre like a nazi, anyone who thinks differently is wrong and should be flamed.

so go ahead and flame but youre still an idiot. i just like to throw out more options into the field for critical thinking purposes. i was debating the outcome % at 1st which was my error cuz the question was not specified clearly enough. they we redebating pure probability. alot more then myself were confused at the original question. enjoy your day ma'am. next time get your panties outta the knot that theyre so aught up in.

[Byrd]

lol god made me dumb for opposing your wrong answer?

He might be an ass, but he's still right. I'm not going to call you an idiot, but you're still wrong.

There's a very good dissertation on the subject at http://en.wikipedia.org/wiki/The_monty_hall_problem

This isn't an opinion matter, Democrat/Republican, Asian chicks/white chicks, Pac-10/SEC football, etc. It's a simple mathemtical issue, with a right and a wrong answer. I encouage you to read the Wiki, watch the videos on YouTube, and finally, do the test yourself with a friend to figure out the answer.

you are elminating door C from the equation once he shows you it. you can NO LONGER choose that option. thats called process of elmination. you know what that is right? in math you can eliminate variables from problems. ok so once C is removed youre left with A and B. now you can choose one of them. thats 1/2 which is also called 50%.

You're eliminating Option C based on a decision you made beforehand. If Monty Haul showed you three doors and opened one to reveal a goat without any input from you, that would be 50%. As it is, you're basically gambling on whether you were right or wrong when you first made your initial decision. You had a 33% chance of being right the first time. That never changes.

[Daydreamer]

This is why I hate this problem, and to all of you who voted for 2/3 (yes I realize I really poorly worded the poll, but at least you can figure it out) go die D: At least my 1/2 is winning, means I got 5$

I still think it's 1/2, and not 1/3 by any means... the initial chance of a car is in fact 1/3 but that changes after he reveals a goat, there's no way your chance post facto is going to remain 1/3.

I get what you're saying about the 1/2, but you are forgetting that you have to consider the entire problem as a whole, not just after he reveals the goat. Seriously just watch that video, it explains the whole thing.

Just do what everyone else said and make it 100 doors. After eliminating 98 of them do you still think there chance yours is behind the original door is 1/2? Yes, if you are originally given only 2 doors to choose it IS 1/2, but because you chose the door when there were 100 doors the probability of your door being correct is 1/100 not 1/2. It's the same thing 3 doors starting. If you don't swap your probability of being correct is 1/3 not 1/2 because there are 3 doors to start with.

[Xfaustx]

lol god made me dumb for opposing your wrong answer?

He might be an ass, but he's still right. I'm not going to call you an idiot, but you're still wrong.

There's a very good dissertation on the subject at http://en.wikipedia.org/wiki/The_monty_hall_problem

This isn't an opinion matter, Democrat/Republican, Asian chicks/white chicks, Pac-10/SEC football, etc. It's a simple mathemtical issue, with a right and a wrong answer. I encouage you to read the Wiki, watch the videos on YouTube, and finally, do the test yourself with a friend to figure out the answer.

you are elminating door C from the equation once he shows you it. you can NO LONGER choose that option. thats called process of elmination. you know what that is right? in math you can eliminate variables from problems. ok so once C is removed youre left with A and B. now you can choose one of them. thats 1/2 which is also called 50%.

You're eliminating Option C based on a decision you made beforehand. If Monty Haul showed you three doors and opened one to reveal a goat without any input from you, that would be 50%. As it is, you're basically gambling on whether you were right or wrong when you first made your initial decision. You had a 33% chance of being right the first time. That never changes.

technically you never chose the door he showed though, nor can you choose it in the end, you can never choose the door that he opens, so why would it be part of the problem? thats kinda where this thing gets me. the math makes sense for the 2/3 but not the reasoning (to me at least). the reasoning for 1/2 makes sense and so does the math. if there is a variable in math, that you can do nothing with, how does that work with probability? theres gotta be some huge math book with all the damn rules in it. lol

[Jeryhn]

I find it strangely funny when certain people call others idiots and Nazis (gogo Godwin's Law?) yet refuse to use proper punctuation when trying to explain "critical thinking purposes".

[Xfaustx]

I find it strangely funny when certain people call others idiots and Nazis (gogo Godwin's Law?) yet refuse to use proper punctuation when trying to explain "critical thinking purposes".

my punctuation was fine other than on my abbreviations sir. anywho, back to my above post. i just think the 3rd door is information that does not need to be included into the problem. while it is there in the start, it has no use in the end. the only way i can think to get this point across is this. say youre trying to get miles per hour, you have these variables... how long it took to get to A, the distance from A to B, and you also have some random crap thrown in like Altitude... while altitude is there in the beginning it does not help the problem in any way and is eliminated. i know this is not a probability question, but the questions are similar.

[ubermonkey]

technically you never chose the door he showed though, nor can you choose it in the end, you can never choose the door that he opens, so why would it be part of the problem?

Because you could have chosen it. Monty only eliminates a door after you have picked one.

[Jeryhn]

say youre trying to get miles per hour, you have these variables... how long it took to get to A, the distance from A to B, and you also have some random crap thrown in like Altitude... while altitude is there in the beginning it does not help the problem in any way and is eliminated. i know this is not a probability question, but the questions are similar.

Only in the real world, altitude would actually matter.

[Xfaustx]

say youre trying to get miles per hour, you have these variables... how long it took to get to A, the distance from A to B, and you also have some random crap thrown in like Altitude... while altitude is there in the beginning it does not help the problem in any way and is eliminated. i know this is not a probability question, but the questions are similar.

Only in the real world, altitude would actually matter.

lol <.< you get what im saying though? i just dont wanna dismiss 1/2 as a possible answer without people thinking everything through thoroughly. ill change altitude to say "how many STD's Anna Nicole Smith has"


*edit* had

[ubermonkey]

my punctuation was fine other than on my abbreviations sir. anywho, back to my above post. i just think the 3rd door is information that does not need to be included into the problem. while it is there in the start, it has no use in the end. the only way i can think to get this point across is this. say youre trying to get miles per hour, you have these variables... how long it took to get to A, the distance from A to B, and you also have some random crap thrown in like Altitude... while altitude is there in the beginning it does not help the problem in any way and is eliminated. i know this is not a probability question, but the questions are similar.

The 3rd door is required because it forms part of the initial conditions of the supposition.

[ubermonkey]

lol <.< you get what im saying though? i just dont wanna dismiss 1/2 as a possible answer without people thinking everything through thoroughly.

They have.

It's called a proof.

They have been aptly demonstrated throughout the thread.

The fact that you don't understand them correctly does not make them any less rigourous, or indeed any less correct.

[Xfaustx]

lets get one extremely bored person to test this out 5,000 times. and come back with hard results to back up the conclusion. i call not it

[ubermonkey]

lets get one extremely bored person to test this out 5,000 times. and come back with hard results to back up the conclusion. i call not it

Why? We can rigorously prove mathematically which is right.

[Daydreamer]

Faust think of it this way. There are 3 doors at the beginning. You choose one, and don't swap. Do you really think your chance of it being correct is 1/2 when there were 3 doors to start with? I'll say it again, just make it 100 doors. Pick one. At the end do the other 98 doors not matter like you are saying because we are now down to just two doors? Yes, they matter a lot, if you don't swap your chances of being right are a tiny 1%, because there are 100 doors to start with!

[Xfaustx]

lets get one extremely bored person to test this out 5,000 times. and come back with hard results to back up the conclusion. i call not it

Why? We can rigorously prove mathematically which is right.

its the scientific method sir. all good lil mathmeticians do such.

[Byrd]

technically you never chose the door he showed though, nor can you choose it in the end, you can never choose the door that he opens, so why would it be part of the problem? thats kinda where this thing gets me. the math makes sense for the 2/3 but not the reasoning (to me at least). the reasoning for 1/2 makes sense and so does the math. if there is a variable in math, that you can do nothing with, how does that work with probability? theres gotta be some huge math book with all the damn rules in it. lol

That's pretty common with this problem, in that it's counterintuitive in a lot of ways. What you need to take into account is that your choice of two doors is not pure random chance, but you already have information about the doors.

I think maybe it's best illustrated if we walk through the possible "paths" the game can take. There are three doors, and you can pick either door 1, 2 or 3, and the prize can be either behind door 1, 2, or 3. This leaves nine possibilites.

Contestant picks door 1, the prize is behind door 1: Monty can show either door 2 or door 3, you LOSE by switching, WIN by staying.

Contestant picks door 1, the prize is behind door 2: Monty has to show door 3, you WIN by switching, LOSE by staying.

Contestant picks door 1, the prize is behind door 3: Monty has to show door 2, you WIN by switching, LOSE by staying.

Contestant picks door 2, the prize is behind door 1: Monty has to show door 3, you WIN by switching, LOSE by staying.

Contestant picks door 2, the prize is behind door 2: Monty can show either door 1 or door 3, you LOSE by switching, WIN by staying.

Contestant picks door 2, the prize is behind door 3: Monty has to show door 1, you WIN by switching, LOSE by staying.

Contestant picks door 3, the prize is behind door 1: Monty has to show door 2, you WIN by switching, LOSE by staying.

Contestant picks door 3, the prize is behind door 2: Monty has to show door 1, you WIN by switching, LOSE by staying.

Contestant picks door 3, the prize is behind door 3: Monty can show either door 1 or door 2, you LOSE by switching, WIN by staying.

Out of 9 possible variations, 6 of the times you win by switching, only 3 times do you win by staying with your original pikck.

What you are doing if you pick an incorrect door to start with is forcing Monty to open a particular door. So, 2/3 of the time, he has to show you a particular door. This is valuable, valuable information. At the beginning, you had a 1/3 chance to pick the right door. Your odds of having initially picked the right door never, ever change because that decision was made on random chance. The remaining two doors have a 2/3 chance of having the car behind one of them. Once he shows you a goat, you know with 100% certainty which of those two doors is worth selecting. But that the odds of you being wrong in the first place is still 2/3.

[ubermonkey]

its the scientific method sir. all good lil mathmeticians do such.

Actually, no, mathematical proofs do not require empirical evidence, they require rigorous logic and need to be founded on sound axioms.

Or can you explain how one would obtain empirical evidence of a flop transition of an n-dimensional object, or indeed any n-dimensional topological proof*. I didn't think so.

Edit: *I really didn't just make these up on the spot, they're an actual branch of topology.

[BarthelloSylph]

technically you never chose the door he showed though, nor can you choose it in the end, you can never choose the door that he opens, so why would it be part of the problem? thats kinda where this thing gets me. the math makes sense for the 2/3 but not the reasoning (to me at least). the reasoning for 1/2 makes sense and so does the math. if there is a variable in math, that you can do nothing with, how does that work with probability? theres gotta be some huge math book with all the damn rules in it. lol

That's pretty common with this problem, in that it's counterintuitive in a lot of ways. What you need to take into account is that your choice of two doors is not pure random chance, but you already have information about the doors.

I think maybe it's best illustrated if we walk through the possible "paths" the game can take. There are three doors, and you can pick either door 1, 2 or 3, and the prize can be either behind door 1, 2, or 3. This leaves nine possibilites.

Contestant picks door 1, the prize is behind door 1: Monty can show either door 2 or door 3, you LOSE by switching, WIN by staying.

Contestant picks door 1, the prize is behind door 2: Monty has to show door 3, you WIN by switching, LOSE by staying.

Contestant picks door 1, the prize is behind door 3: Monty has to show door 2, you WIN by switching, LOSE by staying.

Contestant picks door 2, the prize is behind door 1: Monty has to show door 3, you WIN by switching, LOSE by staying.

Contestant picks door 2, the prize is behind door 2: Monty can show either door 1 or door 3, you LOSE by switching, WIN by staying.

Contestant picks door 2, the prize is behind door 3: Monty has to show door 1, you WIN by switching, LOSE by staying.

Contestant picks door 3, the prize is behind door 1: Monty has to show door 2, you WIN by switching, LOSE by staying.

Contestant picks door 3, the prize is behind door 2: Monty has to show door 1, you WIN by switching, LOSE by staying.

Contestant picks door 3, the prize is behind door 3: Monty can show either door 1 or door 2, you LOSE by switching, WIN by staying.

Out of 9 possible variations, 6 of the times you win by switching, only 3 times do you win by staying with your original pikck.

What you are doing if you pick an incorrect door to start with is forcing Monty to open a particular door. So, 2/3 of the time, he has to show you a particular door. This is valuable, valuable information. At the beginning, you had a 1/3 chance to pick the right door. Your odds of having initially picked the right door never, ever change because that decision was made on random chance. The remaining two doors have a 2/3 chance of having the car behind one of them. Once he shows you a goat, you know with 100% certainty which of those two doors is worth selecting. But that the odds of you being wrong in the first place is still 2/3.

xfaustx, there's your proof. The person switched and won 6 of 9 times. Is that enough?

Obviously I was trying to be a dick, but look at yourself man. This is math - there is a right answer. We're trying to show it to you. You obviously don't get it, which is OK. Stop telling us that we are thinking it through. YOU AREN'T GIVING THIS ENOUGH THOUGHT AND YOU TELL *US* TO THINK ABOUT IT MORE? Ok that makes sense. If you aren't going to spend any time thinking about this, why keep replying? And why keep calling us wrong?

[Isiolia]

lol god made me dumb for opposing your wrong answer?

He might be an ass, but he's still right. I'm not going to call you an idiot, but you're still wrong.

There's a very good dissertation on the subject at http://en.wikipedia.org/wiki/The_monty_hall_problem

This isn't an opinion matter, Democrat/Republican, Asian chicks/white chicks, Pac-10/SEC football, etc. It's a simple mathemtical issue, with a right and a wrong answer. I encouage you to read the Wiki, watch the videos on YouTube, and finally, do the test yourself with a friend to figure out the answer.

you are elminating door C from the equation once he shows you it. you can NO LONGER choose that option. thats called process of elmination. you know what that is right? in math you can eliminate variables from problems. ok so once C is removed youre left with A and B. now you can choose one of them. thats 1/2 which is also called 50%.

You're eliminating Option C based on a decision you made beforehand. If Monty Haul showed you three doors and opened one to reveal a goat without any input from you, that would be 50%. As it is, you're basically gambling on whether you were right or wrong when you first made your initial decision. You had a 33% chance of being right the first time. That never changes.

technically you never chose the door he showed though, nor can you choose it in the end, you can never choose the door that he opens, so why would it be part of the problem? thats kinda where this thing gets me. the math makes sense for the 2/3 but not the reasoning (to me at least). the reasoning for 1/2 makes sense and so does the math. if there is a variable in math, that you can do nothing with, how does that work with probability? theres gotta be some huge math book with all the damn rules in it. lol

Remove the opening of the goat door. It's just a distraction. As there are two goats, there will never be a situation where Monty Hall won't have a goat to show you.

Consider it this way. You pick a door. That's a one in three chance. You are now offered the option to open both other doors -or- stick with your original door.

That's the real end result of switching. While you as the player can only open one door, if the car is behind one of the other two doors (which, odds are, it is), the wrong door is eliminated for you so you won't pick it. You essentially open two doors for the price of one.