3 doors - One contains a brand new car, the other two contain a goat. Choose.

B.A._Baracus

Was watching Brooklyn Nine Nine (really good show I think) and they talked about what's known as "The Monty Hall Problem" (It's been mentioned in movies such as 21 too) It has since become a good example of probability sparking debate of is the choice "50/50" or "2/3" (you'll understand as you read on)

So you are on a game show and have three doors to select from. 2 of the doors will have a goat (a dummy prize) and the other will have a brand new car. But of course you don't know what's behind each.
After you select one of the doors the host (Monty Hall, american tv host) would open up another door to reveal another goat. Monty knows what's behind each door. He then says "Do you want to swap your door?" - here is the dilmemma, do you switch or stay? is it 50/50 (or 50%) at this point or is it 66% (of winning the car) since you made your choice before Monty revealed one of the doors.


^ just an visual example

They say you should switch every time. AS you now have a 66% chance of winning. But what would you do? switch or stay?
As for me, maths says switch. But I only get to play this game once. If I played it 100 times I would switch everytime. But that's the dilemma for me Play the probability game or trust my gut.

vandriver

I want a goat.

blinding

With Oscar Pistorius I would be extremely worried for the Goats and the Car .

blinding

Have I time to put on my Giddy Goat Perfume .

vandriver

vandriver wrote: »

I want a goat.

Same here. I have a car. I don't have a goat.

But what to do to nail down that goat...

The_Valeyard

Ive played Goat Simulator



I know what they can do.


Give me the Goat.

Avatar MIA

I've heard of this before.

And I still don't understand the logic behind switching, and why it goes from 50/50 to specifically 66% (not 65 or 67, but 66%) chance of success, are we to assume the presenter is disposed to us winning the car?!?

Princess Consuela Bananahammock

It's not a 66% chance since Monty opened the second door. It;s a 50/50 and, like deal or no deal, a complete waste of a good hour's entertainment.

Fr_Dougal

Gimme the car.

Are Am Eye

The back of the goat at door 3 is behind door 2.
It looks to me like those two goats can move around back there.
Is there partitions?
The whole thing is rigged I think. You wouldn't even fit a car.

WoollyRedHat

Have the proper procedures been followed and have the goats consented to appearing in the show?

Avatar MIA

Avatar MIA wrote: »

are we to assume the presenter is disposed to us winning the car?!?

Essentially yes. When the host opens one of the other doors - after your decision - he has to open a non-winning door.

So whether you pick the winning door or not - the host _must_ open a losing door.

That is the crux of why you should always switch - and why switching gives you a 66.66666666666666666666666666666667% chance of success.

Ficheall

Avatar MIA wrote: »

I've heard of this before.

And I still don't understand the logic behind switching, and why it goes from 50/50 to specifically 66% (not 65 or 67, but 66%) chance of success, are we to assume the presenter is disposed to us winning the car?!?

66% ~= 2/3.

Avatar MIA

Are Am Eye wrote: »

The back of the goat at door 3 is behind door 2.
It looks to me like those two goats can move around back there.
Is there partitions?
The whole thing is rigged I think. You wouldn't even fit a car.

Fr_Dougal wrote: »

Gimme the car.

Here you go...



The car is free, but you need to send me €500 for postage...

Outlaw Pete

We discussed it a few years back in the mathematicsame forum too:

http://www.boards.ie/vbulletin/showthread.php?p=70063175

Tigger

Deleted User wrote: »

Essentially yes. When the host opens one of the other doors - after your decision - he has to open a non-winning door.

So whether you pick the winning door or not - the host _must_ open a losing door.

That is the crux of why you should always switch - and why switching gives you a 66.66666666666666666666666666666667% chance of success.

i dont think thats it

McMurphy

vandriver wrote: »

I want a goat.

Just don't get a Kevin.

https://www.youtube.com/watch?v=yuwprXAaSv0

dmc17

I suppose on the first go you have ~66% chance of picking a goat, so chances are you've got a goat. This is why you'd switch on the second go unless you fancy curried goat for the next week?

Cortina_MK_IV

I'm against this animal testing.

Avatar MIA

dmc17 wrote: »

I suppose on the first go you have ~66% chance of picking a goat, so chances are you've got a goat. This is why you'd switch on the second go unless you fancy curried goat for the next week?

^^^ doesn't clarify - I feel like I should be wearing a dunces hat.

I can't watch the above 21 clip. I'm in company - I'd rude enough to be on a PC, but not sufficient rude enough to put on the sound. Will look at it later.

Tigger

Tigger wrote: »

i dont think thats it

It really is yes.

The host has to remove all the wrong doors except one basically. The one being either the one you picked - or the one remaining that you did not pick.

Picture it with 1000 doors. You pick one. The host has to remove 998 other wrong doors leaving your one - and one other.

This is why you switch

Capt'n Midnight

It's not that difficult.


Pick the door that doesn't smell of goat.

Ficheall

Here:

mikeymouse

Avatar MIA wrote: »

I've heard of this before.

And I still don't understand the logic behind switching, and why it goes from 50/50 to specifically 66% (not 65 or 67, but 66%) chance of success, are we to assume the presenter is disposed to us winning the car?!?

It's 66.66...., or two turds if you like!!
I remember in the pre Google era a discussion about this went on for ages on some forum.

harry Bailey esq

It depends on what you need. Wanna get somewhere you need to be without relying on public transport? It's got to be the car. If your eldest daughter happens to be getting married to the son of a wealthy merchant however,the two goats will be more than adequate,and will increase your status with the in-laws no end.
Personally I'd take the car and sell it to buy a herd of goats,set up a fake marriage network and get some driving lessons from the profits.

shaunr68

Ficheall wrote: »

Here:

Surely here case 3 has been eliminated because we have just been shown door 3 which contains a goat.

Therefore at this point the option to switch consists of two possible rewards, one a goat and the other a car.

Ficheall

It's showing you all of the initial possible layouts. Your selection is door 1 (because it doesn't make any difference), then you can see what happens if you switch or don't switch after being shown a goat from behind door 2 or 3. Since all initial layouts are equally likely, switching is better 2/3 of the time.

shaunr68

Ficheall wrote: »

It's showing you all of the initial possible layouts. Your selection is door 1 (because it doesn't make any difference), then you can see what happens if you switch or don't switch after being shown a goat from behind door 2 or 3. Since all initial layouts are equally likely, switching is better 2/3 of the time.

I think I understand

So let's say, again because it makes no difference, that the host shows you door 3 and that contains a goat.

We now know that case 3 cannot be true, and therefore at this point there are two possible outcomes with 2 possible rewards

Of course this works the same way if he shows you door 2 which discounts case 2

jamesbere

I don't want either. I want the door, would come in very handy

shaunr68

In not very mathematical terms, I'd say that the teaser only works on the premise that there are three possible outcomes and the probability is being calculated based on the situation at the beginning of the game show. However at the point the contestant is asked to choose, one of those outcomes has now been discounted and this of course changes the odds.

corner of hells

jamesbere wrote: »

I don't want either. I want the door, would come in very handy

I'd like a door too , my shed door is bollixed.