The Monty Hall Problem

[Millael]

Here's a fun and easy way to prove that this is a 2/3 chance.

1. Decide beforehand whether the player has to "stick" or "switch" for all iterations.
2. Choose a number between 1 and 3.
3. Have someone else guess this number.
4. Tell them one of the incorrect numbers that is not the number they picked.
5. Force them to decide what they chose beforehand. (Stick/switch)
6. Repeat ad nauseam, or until the pattern becomes clear.

If they choose "Stick", they'll hover around 33%
If they choose "Switch", they'll be at around 66%.

[evilbau]

Xfaustx,

On behalf of everyone here, I ask you:

Do you really believe there's an element of human error in this problem?


We're all cheering for you,

Bart

who are you? i dont get it. and good luck trying to figure this out, cuz not everything can be solved mathematically. or as simple as as it seems.

your brain sir is human error >.>

i don't want to be mean, but it is solvable mathematically (and logically)

[aurik]

I think you should go ahead and be mean, he's an idiot and probably won't pay attention unless you insult him.

[quannum]

who are you? i dont get it. and good luck trying to figure this out, cuz not everything can be solved mathematically. or as simple as as it seems.

your brain sir is human error >.>

let's search our feelings for the true answer, then we'll have a discussion circle to share our answers. everybody is a winner at the game of life and somethings should remain a mystery.

[GRT]

this is one of those problems with wording to make it more complex than it is

the simple answer is: 1/3

everything between the first line of the body of text and the result is just a means to confuse you

too bad 1/3 isn't one of the poll options

[Tricen]

The "useful information" you talk about is a wrong answer. You have 3 doors, one is revielded as wrong. You now have 2 doors. Now you KNOW how the game games, so what are your options? 1 door HAS a goat, the other door HAS a car. Now, you only have 2 choices. The game originally says there are 3 doors and 2 goats and 1 car. You have 1 goat out of the way. So now it is down to a goat and a car. Goat = 1 car = 1. 2/2 50% chance.

... do you even read anything anyone else says? You just posted pretty much the exact same thing as in your last post, and you don't do anything to refute the points other people made besides say "nuh uh, you're wrong." Aurik makes a really good point in his last few points, but you've pretty much ignored it.

EDIT: wtf, Birdhair now? Someone else try to claim it's 1/2, and maybe I can argue up to CoP Dynamis or something.

I would be using logic, not math for this. If he did pick the door with the car, then game over. If he picked the one with a goat behind it you are stuck with 2 choices. What am I thinking wrong about?

[Tajin]

who are you? i dont get it. and good luck trying to figure this out, cuz not everything can be solved mathematically. or as simple as as it seems.

your brain sir is human error >.>

let's search our feelings for the true answer, then we'll have a discussion circle to share our answers. everybody is a winner at the game of life and somethings should remain a mystery.

hahahahahaha =D> =D>

Man hugs for everyone :D

[Kaelan]

If he picked the one with a goat behind it you are stuck with 2 choices. What am I thinking wrong about?

that ----v

If you were shown 3 doors, 1 of which was open and had a goat, then yes, you're just choosing between 2 doors and you have a 50/50 chance. However, you have more information than that due to your initial selection possibly restricting the host's choice of which door to reveal. 2/3 of the time, the host doesn't have a choice which door to reveal to you, this is information you can extrapolate to mean 2/3 of the time, the door he doesn't reveal must have the prize behind it.

Took me a while to notice this too, but its right

If the door you pick is wrong(2/3 chance), he'll eliminate the other wrong one, which only leaves the right one. In this situation, if you switch, you win. This situation happens 2/3 of the time, the other 1/3 being when your first pick was the right door

[aurik]

The "useful information" you talk about is a wrong answer. You have 3 doors, one is revielded as wrong. You now have 2 doors. Now you KNOW how the game games, so what are your options? 1 door HAS a goat, the other door HAS a car. Now, you only have 2 choices. The game originally says there are 3 doors and 2 goats and 1 car. You have 1 goat out of the way. So now it is down to a goat and a car. Goat = 1 car = 1. 2/2 50% chance.

... do you even read anything anyone else says? You just posted pretty much the exact same thing as in your last post, and you don't do anything to refute the points other people made besides say "nuh uh, you're wrong." Aurik makes a really good point in his last few points, but you've pretty much ignored it.

EDIT: wtf, Birdhair now? Someone else try to claim it's 1/2, and maybe I can argue up to CoP Dynamis or something.

I would be using logic, not math for this. If he did pick the door with the car, then game over. If he picked the one with a goat behind it you are stuck with 2 choices. What am I thinking wrong about?

You're using logic to approach a math problem, that's your first mistake.

OK, follow along with me here.

Choose a door. What's the chance that the door you chose has a goat behind it?

2/3, right?

Let's say that this is the case.

Now Monty's gonna show you a door that you didn't pick that has a goat behind it. Because only one of those doors qualifies, that means that the door he DOESN'T open has the car, 100% of the time.

So, 2/3rds of the time, the door that Monty declines to open ALWAYS has the car behind it.

Let's look at the opposite case, and suppose you got lucky and picked the car-door the first time. What's the chance of that?

1/3 right?

Let's say that this is the case.

Now Monty's gonna show you a door that you didn't pick that has a goat behind it. Unfortunately, that's both of them, so he'll pick one at random and open it. Because you've already chosen the car-door, the last door must have a goat.

So, 1/3 of the time, the door that Monty declines to open NEVER has a car behind it.

Now Monty turns to you and says, "do you want to stay with the door you originally chose? Or do you want to choose the door I declined to open?"

So now you think, 2/3rds of the time that door is 100% car, and 1/3rd of the time that door is 0% car. What's the chance the door Monty declined is correct in general? 2/3 * 100% + 1/3 * 0% = 66.6%

[Seyrr]

If he did pick the door with the car, then game over. If he picked the one with a goat behind it you are stuck with 2 choices. What am I thinking wrong about?

Ah, there's a problem there. The host KNOWS where the car is, even if he isn't the one who placed it there. He will ALWAYS show you a goat. And you know that one of the two that you didn't choose has a goat behind it.

So him showing you a goat doesn't change your situation at all. Before you knew that it was 1/3 behind first choice, and 2/3 behind not-first-choice.

The host said "Hey, one of the ones you didn't choose was a goat!" But you knew that already. So nothing has changed. It's still 1/3 behind first choice, and 2/3 behind not-first-choice.

[Isiolia]

The "useful information" you talk about is a wrong answer. You have 3 doors, one is revielded as wrong. You now have 2 doors. Now you KNOW how the game games, so what are your options? 1 door HAS a goat, the other door HAS a car. Now, you only have 2 choices. The game originally says there are 3 doors and 2 goats and 1 car. You have 1 goat out of the way. So now it is down to a goat and a car. Goat = 1 car = 1. 2/2 50% chance.

You're confusing the order of things.

When you pick a door, it's a 2 out of 3 chance that the car is behind one of the other two doors. Revealing a door with a goat behind it means that if the car was behind one of those two doors, switching will get you the car 100% of the time.

If you don't swap, you have no greater chance than the 1 out of 3 you started with. There will *always* be a goat behind one of the other doors to show you.

[Tricen]

Ok so what was I saying lol?
A B C
^

I chose A and he goes:

A B C
^
Is a goat.

So now

A B C
? G ?

Which means out of the 3 choices, you have 2 unkown and a known. 3/3 but you are still ganna chose out of 2?

[Seyrr]

Except he will never do that. He always shows you a door you did not choose.

EDIT: I guess that arrow is supposed to be pointing to B. But seriously, you're ignoring what everyone said. The unknown A and unknown C are not the same. If all you look at is after he reveals B, then yes, they're the same. But before the reveal, they're not.

As long as you keep harping on that point, you'll never get it.

[Tricen]

Oooh I think I know what I am doing. You pick a door first and then he reveals one... Not he reveals one and then you pick >_>

[aurik]

yea that makes a difference.

[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

[Devek]

All the smart people agree

It is like south park.. can't do anything about the retarded 1/4th of the population so you might as well take advantage of them.

Here is an idea for the stupid people.

You guys can mail me $100.. Now I will either send you $10,000 back a week later or I won't send you anything at all.

That is a 50% chance to make a 1000% profit!

[Semitry]

Doors A B C

A has the car, B & C have goats.

The 3 case scenarios possible

1. User picks A, host shows B or C, you'll lose switching doors
2. User picks B, host shows C, you'll win switching doors
3. User picks C, host shows B, you'll win switching doors.

Since there's 3 scenarios total, with 2 winning if the user switches means the user has a 2/3 chance of winning by switching after the host shows which door has a goat.

On the flip side, if you stick with the door you chose instead of switching, your chance of winning is 1 out of 3.

I briefly read through so hopefully I didn't steal someones explaination.

[Ramor]

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.

[layoneil]

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.

it does change after he reveals the goat, but what it changes to is dependent on what you do.

it remains 1/3 if you refuse to switch.
it increases to 2/3 if you do switch.
it'll be 1/2 if 50% of the time you switch and 50% of the time you don't switch.