You're given the choice of three doors: behind one door is a car, and behind the other two are goats. You pick a door, say #1. The host, who knows what's behind all the doors, opens another door, say #3, which he knows is hiding a goat. He then says to you, "Do you want to pick door #2 instead?"

Is it better to switch your choice or stick with door #1?

3/6/2011 9:38:07 PM

it is always in your interest to switch, the odds are better

3/6/2011 9:38:52 PM

OH GOD NOT MONTE HALL!

3/6/2011 9:39:53 PM

I would totally switch and be happy if I got the goat. Much easier to find a good butcher than it is to deal with the hassle of paying taxes on, insuring, and registering a new car.

3/6/2011 9:41:13 PM

This is about goats, not a flying circus

3/6/2011 9:41:26 PM

I already have a car
I do not have a goat

therefore, goat

3/6/2011 9:42:58 PM

but seriously, you don't have enough information to tell. Knowing that the host knows what's where doesn't matter. Given that the host knows, you need to know if he's trying to help you or hurt you. Odds can go either way depending on that.

3/6/2011 9:43:55 PM

goat sounds so common, let's refer to them as chevres from here on

[Edited on March 6, 2011 at 9:46 PM. Reason : ^we'll assume that he doesn't pay for the prizes and is impartial]

3/6/2011 9:44:50 PM

fine.
I'll tour the USA with my Chevres

3/6/2011 9:49:00 PM

are they fainting chevres?

3/6/2011 9:50:43 PM

yes

> uknown car

3/6/2011 9:52:47 PM

mathematically, it's ALWAYS better to switch.

When you make your initial pick, since there are 3 doors, and you randomly pick one, the door you pick has a 1 in 3 chance of winning.

When one door is opened, and there are 2 doors left, the OTHER door has a 1 in 2 chance of winning, while your original door is only 1 in 3. So you go from a 30% chance to win to a 50% chance to win.

3/6/2011 9:55:36 PM

I, too, have seen the movie 21

3/6/2011 9:57:48 PM

wrong.

3/6/2011 9:58:23 PM

A plane is standing on runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

The question: Will the plane takeoff??

3/6/2011 10:01:02 PM

This is a stupid question. You're basically faced with a second choice and can choose either way. The way the question is posed there is only an illusion that your first choice is the only one you have to make.

3/6/2011 10:01:45 PM

Quote :

"I, too, have seen the movie 21"

never heard of it

[Edited on March 6, 2011 at 10:09 PM. Reason : ^i guess you would forfeit then]

3/6/2011 10:04:37 PM

Quote :

"I, too, have seen the movie 21"

3/6/2011 10:06:41 PM

Quote :

"never heard of it"

Obviously not, or else you wouldn't have made this thread thinking that you were being clever or interesting.

3/6/2011 10:06:53 PM

sick burn, bro

3/6/2011 10:11:34 PM

So what does this have to do with the movie 21...?

3/6/2011 10:17:33 PM

love the monty hall problem

it's one of the few things that if you understand it, it instantly makes you smarter

3/6/2011 10:20:44 PM

Quote :

"When one door is opened, and there are 2 doors left, the OTHER door has a 1 in 2 chance of winning, while your original door is only 1 in 3. So you go from a 30% chance to win to a 50% chance to win"

serious response?

Quote :

"A plane is standing on runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction). The question: Will the plane takeoff?? "

the plane will go faster, then the belt, then the plane, then the belt again. pretty soon, they'll both be going 8 mph

3/6/2011 10:24:08 PM

I edited my post because I think it's a purely semantic issue, and I realized I didn't feel like getting into a big thing about it. If the host can choose the door, then fine, it works. But if it's really just randomly chosen, then there is no issue. The real reason the probability changes is just because Monty gets to choose a door to open.

[Edited on March 6, 2011 at 10:44 PM. Reason : f]

3/6/2011 10:33:57 PM

I like how you started your post with "I have always understood the math behind the problem" and then proceded to write a term paper proving otherwise.

[Edited on March 6, 2011 at 10:39 PM. Reason : Haha. Edited away the insanity. ]

3/6/2011 10:38:17 PM

It's two separate choices.

[Edited on March 6, 2011 at 10:39 PM. Reason : ]

3/6/2011 10:38:24 PM

[Edited on March 6, 2011 at 10:39 PM. Reason : everyone's doing it]

3/6/2011 10:38:35 PM

Quote :

"If the host can choose the door, then fine, it works. But if it's really just randomly chosen, then there is no issue. The real reason the probability changes is just because Monty gets to choose a door to open. "

What are you talking about randomly chosen? The only what-if scenario arises if you aren't 100% certain that the host will open a door and show you a goat. I guess if you run this scenario 1000 times and sometimes he shows you a door and sometimes he doesn't then that would change things based on the fact that he could be using your knowledge of doing the mathematically correct thing to make you change doors when you've selected the car on your first pick. But if you're just talking about a one-off scenario as described in the OP, then your odds are twice as good by switching.

3/6/2011 10:51:28 PM

Pretty sure he means the odds only improve if the host knows the door he's opening doesn't have the car

3/6/2011 10:53:41 PM

Which was the "one-off scenario as described in the OP".

Correct?

3/6/2011 10:58:12 PM