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which door? and why?
02GF74 - 6/12/09 at 08:36 PM



You are on a game show. The prize is behind one of three doors.

You have to pick one door.

Then one of the remaining two doors (that the prize is not behind) is opened.

Then, you are given the choice of changing from your original door to the other closed door.

Do you change? If so why?

(don't spill the beans if you know the answer).

iank - 6/12/09 at 09:09 PM

Yes you should always change as it doubles your chance of winning.

I won't provide a spoiler as requested.

David Jenkins - 6/12/09 at 09:09 PM

Known as the Monty Hall Problem - if anyone wants to cheat and Google the answer!

cd.thomson - 6/12/09 at 09:36 PM

I got taught the maths behind this on a hadrians wall visit.

My dad still refuses to believe me

dmac - 7/12/09 at 08:47 PM

If you pick a door at random there is a two thirds chance that you are wrong, once you know which of the doors you didn't pick is empty you should change to the other one as there is still a two thirds chance that the prize is behind this door and a one third chance that it is behind the door you originally picked.

Duncan

JoelP - 7/12/09 at 09:09 PM

quote:
Originally posted by dmac
If you pick a door at random there is a two thirds chance that you are wrong, once you know which of the doors you didn't pick is empty you should change to the other one as there is still a two thirds chance that the prize is behind this door and a one third chance that it is behind the door you originally picked.

Duncan


i may be wrong but im pretty sure that counts as a spoiler!

dmac - 7/12/09 at 09:20 PM

Sorry,

he asked the question, and I thought the idea of the forum was to answer questions, asking people not to give the right answer is just silly.

Duncan

02GF74 - 8/12/09 at 07:56 AM

quote:
Originally posted by dmac
If you pick a door at random there is a two thirds chance that you are wrong, once you know which of the doors you didn't pick is empty you should change to the other one as there is still a two thirds chance that the prize is behind this door and a one third chance that it is behind the door you originally picked.

Duncan


that is not actually correct - your logic states that the original door you picked is still 50/50 so there is not point changing it as the chances are the same for both unclosed doors.


this explains it, if I have the right linky.

scootz - 8/12/09 at 12:20 PM

I thought I got 'it', then I thought some more and I didn't get 'it' anymore!

Logic is telling me that if you eliminate a wrong door and are asked if you want to change, then it's a 'new' game, so new odds apply... you have a choice of two... has to then be a 50/50 split.

PS - I know the maths says otherwise, but it's the same principle as someone telling me the Earth is round - I mean, come on!

MikeRJ - 8/12/09 at 04:03 PM

quote:
Originally posted by 02GF74
quote:
Originally posted by dmac
If you pick a door at random there is a two thirds chance that you are wrong, once you know which of the doors you didn't pick is empty you should change to the other one as there is still a two thirds chance that the prize is behind this door and a one third chance that it is behind the door you originally picked.

Duncan


that is not actually correct - your logic states that the original door you picked is still 50/50 so there is not point changing it as the chances are the same for both unclosed doors.


His logic is correct. The first door picked has a 1/3 chance of being correct. By opening one of the other doors after the player has chosen, it gives the player no extra information about what is behind his original door, so the probability of it being correct remains at 1/3, and there is a 2/3 chance the remaining door is correct.

If one door was opened prior to the first choice being made, it would be a simple 50/50 chance, and swapping would not gain you anything.

Peteff - 8/12/09 at 05:02 PM

I would open the green door because Shakin' Stevens said so.

iank - 8/12/09 at 05:04 PM

Wikipedia has the full maths/logic behind it (you can solve it a couple of ways).

http://en.wikipedia.org/wiki/Monty_Hall_problem

However it is so counter intuitive that PhD's and Nobel prize winners have been known to get it wrong.

I find the first diagram explains it best to my mind.

Basically you have a 1/3 chance of picking the prize with your first guess, and will lose if you swap.
If you pick either goat (2/3 chance) then the quizmaster is forced to take the other goat out and swapping always wins.

MikeRJ - 9/12/09 at 01:37 AM

quote:
Originally posted by iank
and swapping always wins.


Swapping simply improves the odds of picking the right door, it doesn't guarantee a win.

Liam - 9/12/09 at 01:54 PM

quote:
Originally posted by scootz
Logic is telling me that if you eliminate a wrong door and are asked if you want to change, then it's a 'new' game, so new odds apply... you have a choice of two... has to then be a 50/50 split.


But it isn't a 'new' game, or in mathsy-speak, the two events are not mutually exclusive. The initial choice and the non-random actions of the host (he has to eliminate a wrong door/goat/whatever) give information that feeds into the second choice.

In a nutshell, you were only 1/3 likely to have chosen the prize first time round, so when the game is reduced to only one other door, there must be a 2/3 chance the prize is behind that one, so of course you swap.

Liam

[Edited on 9/12/09 by Liam]

iank - 9/12/09 at 04:31 PM

quote:
Originally posted by MikeRJ
quote:
Originally posted by iank
and swapping always wins.


Swapping simply improves the odds of picking the right door, it doesn't guarantee a win.


No you've quoted me out of context, if you've picked a losing door then the other losing door is removed from the game (forced by the rules). So if you swap in this case you are guaranteed a win.

What this means is if you swap the only way to lose is to pick the prize with your first guess - which was the first case I gave.

MikeRJ - 9/12/09 at 05:30 PM

quote:
Originally posted by iank
quote:
Originally posted by MikeRJ
quote:
Originally posted by iank
and swapping always wins.


Swapping simply improves the odds of picking the right door, it doesn't guarantee a win.


No you've quoted me out of context, if you've picked a losing door then the other losing door is removed from the game (forced by the rules). So if you swap in this case you are guaranteed a win.

What this means is if you swap the only way to lose is to pick the prize with your first guess - which was the first case I gave.


Sorry about that, I see what you are saying now.

MautoK - 9/12/09 at 09:07 PM

My take on it is this:

Three doors; one hides a car, two hide goats.
You specify one door not to be opened in the next stage.

The host opens one of the other two doors to reveal a goat.
There are now two doors; one has the car and the other has the second goat - therefore 50/50.

It doesn't matter what the first choice was - the scenario has altered half way through the process.
John.

02GF74 - 9/12/09 at 09:14 PM

quote:
Originally posted by MautoK
There are now two doors; one has the car and the other has the second goat - therefore 50/50.



no. it is not 50/50.

if you were not to change, you would win less cars than if you did change,

the youtube link expllains it all.

Liam - 9/12/09 at 11:34 PM

quote:
Originally posted by MautoK
There are now two doors; one has the car and the other has the second goat - therefore 50/50.

It doesn't matter what the first choice was - the scenario has altered half way through the process.
John.


Well OK, your place or mine, I'm not fussed. We'll set up some boxes, take turns being the host and sticking a tenner in a box. We'll play the game a thousand times or so, I'll keep what I win, and you keep what you win. What do you say? Yeah ha, easy money. For me.

Liam