The Monty Hall Problem

[rehmwa]

always switch - then you win either

1/3 of the time - you win TWO GOATS - YAYYYYY!!!!

2/3 of the time - you win a CAR AND A GOAT - YAYYYYY!!!!

that's how it should be

[iacas]

Now, if Monty had simply said "you can keep your door or I will give you both of the other doors" then it would be obvious that you switch.

That's another good way for people to "get it."

[Abu3baid]

There is no intent on the part of the host.  There are always 2 unchosen doors, at least one of them has to have a goat, and he always reveals a door that has a goat.  The host's role is, essentially, mechanical. It is fairy easy to verify the correctness of the answer using monte carlo simulation.  I even did it using Excel a few years ago, to convince someone who said it just couldn't be right but who would only believe empirical evidence.. To me the easiest way to see the answer is to consider that I have a 1/3 chance of hitting the correct door the first time and a 2/3 chance of hitting the wrong door the first time.  Monty showing one of the unchosen 2 doors does not chance the probability that I got it right the first time.  And it means that the probability of the car being behind one of the 2 unchosen doors is 2/3, and revealing the one the car is NOT behind does not change that.  Now, if Monty had simply said "you can keep your door or I will give you both of the other doors" then it would be obvious that you switch.  And that is EXACTLY what he is really saying, but he confuses things, psychologically, but revealing the unchosen goat door.  That gives the contestant the illusion that he is choosing between 2 single doors whereas the real underlying reality is that he is choosing between the initial door and BOTH unchosen doors.

Yes, it absolutely made sense to me after I saw the diagram. I have a 67% chance of choosing a goat and only a 33% chance of choosing a car when we start. When he removes the other goat I switch because most likely I picked a goat the first time around.

[Chilli Dipper]

Here's another (messy) way to look at the problem.

[JonMA1]

You are faced with three closed doors and told behind one of them is a new Mercedes. Behind the other two, a couple of goats. The car is your’s if you choose the correct door. You choose #1. The host then opens door #3 and out walks a goat. You get excited because you’re still in the running. There are now only 2 doors left and there’s a new car behind one or the other.

The host asks you if you want to switch your original choice of door #1 with door #2. What do you do?

Now that door #3 has been ruled out, what are the odds that the car is behind door #1? What are the odds it is behind #2?

[westcyderydin]

It depends if you'd rather have the goat or the Mercedes.  If you want the Mercedes than switch to door #2.

[JonMA1]

It depends if you'd rather have the goat or the Mercedes.  If you want the Mercedes than switch to door #2.

C'mon @westcyderydin , just because I'm from Northern Michigan (where nothing says lovin' like marrying your cousin) doesn't mean I'd take a goat over a Mercedes. Ideally, I'd want both.

[westcyderydin]

UP or northern mitten? (1/3, 2/3)  I'm in the SW corner.

[JonMA1]

Northern Lower. Just south of Traverse City.

[westcyderydin]

I've heard its really nice up that way...never been there.  Lots of good courses around you up there?

And I love this statistical problem...or whatever you call it.  It makes sense, but doesn't make sense.

[Patch]

Forget the car, and the goat. Take Tiffany instead.  She can buy you a car, and a farm for a goat. Might want to clear it with her husband first.

[Golfingdad]

http://thesandtrap.com/t/80355/the-monty-hall-problem

[Lihu]

Which door is wide enough for the Mercedes?

[JonMA1]

http://thesandtrap.com/t/80355/the-monty-hall-problem

Sorry everyone. I should have performed search.

Move along... nothing to see here.

[JonMA1]

I've heard its really nice up that way...never been there.  Lots of good courses around you up there?

I think so. I mean, there are a lot of courses and in my opinion, some are very nice. But my standards may be low. If nothing else, there are enough of them to where I don't have to play 5 hours rounds because they're so backed up.

The area itself is beautiful. I'm not from here originally but I love the woods and there is plenty of that up here.

[nevets88]

Interesting video on the problem from Vox:

 

[No Mulligans]

On 2/23/2015 at 4:51 AM, rehmwa said:

you've never watched Let's Make a Deal clearly - game show, extending the game, titilating the audience IS the intent

 

Let's change the story - Monte has 10 doors (9 have goats, 1 has a car)  You pick a door.   Now, Monte opens up 8 of the remaining 9 doors and reveals goats.  (it doesn't matter which door you picked, there is always 8 other doors he can reveal).  Now he offers you the chance to switch to the last remaining door.

Exactly how I thought of it too, but I used 100 doors.  I often like to take things to what I call the "ridiculous extreme".  When you do the answer often becomes obvious.  As does this one.

[natureboy]

On 2/24/2015 at 1:36 PM, Chilli Dipper said:

Here's another (messy) way to look at the problem.

 

The horror....the horror...all that wasted beer.