is it better to switch?

Started by: fitzy | Replies: 25 | Views: 1,141

fitzy
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Jan 30, 2009 4:59 PM #348586
okay, i discovered something a few days ago, it took me ages to get my head around it, and i found it quite interesting. it's called the monty hall problem, as i found out a couple of days ago :)

if you are, for example, on a game show and the game show host shows you 3 doors. behind one is a brand new car, behind the other 2 there is nothing. The game show host knows where the car is and which ones have nothing in them. he says 'pick a door' and (for examples sake) you choose door 1. He then goes over to door 3 and shows you that its empty, there's nothing in it. this now leaves 2 doors, the host then says to you 'do you want to swap door number 1 for door number 2?' (i.e. instead of picking door one he will show you door 2 and whatever is in it will be yours). Now, most people would say no, due to the fact that if you swap and you had the right door in the first place...it's more devastating. and as it's a 50/50 chance of getting it right you might as well stick with your door.

but this is incorrect. You, statistically should ALWAYS swap, as sticking with your box only gives you a 1/3 chance of being right whilst swapping gives you a 2/3 chance of being right. it's mind boggling as to why this is true, but after trying to work it out with my friend for about 10 minutes we figured out why. basically, if you have 3 boxes, on your first go, you always have a 2/3 chance of being wrong, after he takes box 3 away, your stat doesnt change, you chose out of 3 boxes, you still have a 2/3 chance of being wrong. as the car had a 2/3 chance of being in one of the other 2 boxes, therefore after he takes box 3 away, that 2/3 chance of being in one of the other 2 boxes is pretty much transferred to that one box. so swapping is always right.

in simpler terms, the only way you'll get it wrong by swapping is if you pick the RIGHT door the first time you choose, if you choose ANY of the other 2 doors you will ALWAYS swap to the winning door.

i saw this during the film '21' btw, and after it i just thought 'wtf that's not right it's 50/50' then i discovered it isnt :D

i just thought it was interesting and despite my best efforts i can't convince some people in school that i'm right. i'm just wondering if people here understand why...

if you dont understand me/ don't believe me, watch this http://uk.youtube.com/watch?v=mhlc7peGlGg

if you still dont believe me i'd like to hear your thoughts :D

and by the way this isnt in debate cuz i'm right :P
Vacuum
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Jan 30, 2009 5:03 PM #348593
...What?



Lol joke.



Sounds interesting! Too bad I have no way to try it out, though.
Automaton
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Jan 30, 2009 5:05 PM #348597
No no no. If the door thats opened has nothing in it, there is a 50/50 chance that the car could be in either of the doors. Your logic is stupid.
fitzy
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Jan 30, 2009 5:07 PM #348600
actually...its right, believe it or not, seriously. watch this http://uk.youtube.com/watch?v=mhlc7peGlGg
Automaton
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Jan 30, 2009 5:15 PM #348604
I've seen it and it makes no difference. It's very convincing, but that could work both ways. He's basically saying if you pick a goat the first time, there's more of a probability that you will pick a goat. The whole idea of this seems wrong to me. Probability in this sense doesn't make any difference. I hate it when peoeple use probability in this way. The only way to look at it is that there's a 50/50 chance when one door has been opened. Forget the 2/3 chance at the beginning, because that really makes no difference.

[edit]
think of it like this: the first time there is a 2/3 chance you will pick a goat. Once the door is opened there is a 50/50 chance you'll pick a goat. Just imagine that there was never a third box, becuas that is, in effect the reality of the situation. Your logic is all wrong.
Narcotic Jew

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Jan 30, 2009 5:16 PM #348605
no one ****ing cares
fitzy
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Jan 30, 2009 5:24 PM #348614
Quote from Narcotic Jew
no one ****ing cares


you dont care...so don't post.


Quote from Fluxinator
I've seen it and it makes no difference. It's very convincing, but that could work both ways. He's basically saying if you pick a goat the first time, there's more of a probability that you will pick a goat. The whole idea of this seems wrong to me. Probability in this sense doesn't make any difference. I hate it when peoeple use probability in this way. The only way to look at it is that there's a 50/50 chance when one door has been opened. Forget the 2/3 chance at the beginning, because that really makes no difference.

[edit]
think of it like this: the first time there is a 2/3 chance you will pick a goat. Once the door is opened there is a 50/50 chance you'll pick a goat. Just imagine that there was never a third box, becuas that is, in effect the reality of the situation. Your logic is all wrong.


you can't just take the first choice out of the equation. let me try this way.

i have 100 doors and i hide £1000 behind one. i ask you to pick a door. i then open 98 empty doors, skipping over your door, and one other door. one of these 2 doors contains the money. i offer you a swap...do you still think i'ts 50/50? cuz it's not. you chose out of 100 doors, you can't just dismiss that and say that there is now only a 1/2 chance your wrong, cuz it didnt matter which door you picked, i was always gonna leave you with the money, your door and offer you a swap. if the money was in box 1, if you picked any box from 2-100 i would leave you with your box and the money box. after offering a swap, you should take it as there was a 99% chance you were wrong...so there is still that 99% chance you were wrong.

btw i accidently changed from saying door to box half way through :P
Narcotic Jew

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Jan 30, 2009 5:28 PM #348619
hey, dude, no one cares.
Automaton
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Jan 30, 2009 5:31 PM #348623
Ahhhhh... I get it.
fitzy
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Jan 30, 2009 5:34 PM #348625
awesome, i got you from this:
Quote from Fluxinator
No no no. If the door thats opened has nothing in it, there is a 50/50 chance that the car could be in either of the doors. Your logic is stupid.
(although it was a bit more mean before you edited it :P)

to this

Quote from Fluxinator
Ahhhhh... I get it.


in like 4 posts :D
Kaas
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Jan 30, 2009 5:38 PM #348630
Isn't this a standard math subject?

Just like deciding which way is the best to play tic tac toe (there are steps so you'll never lose...).

/care...
Automaton
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Jan 30, 2009 5:38 PM #348631
lol yeah. I never back down from my views unless I know I'm wrong, so well done :)
fitzy
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Jan 30, 2009 5:40 PM #348633
Quote from Kaas
Isn't this a standard math subject?

Just like deciding which way is the best to play tic tac toe (there are steps so you'll never lose...).

/care...


not everyone thinks in as logical way as you my friend :) also...tic tac toe annoys me cuz you HAVE to make a mistake in order to lose, there is no way in which both players played well but one played better. if you lost you made a big error. i pretty much always draw...but that's veering off quite a bit :P

and ty flux :P
Kaas
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Jan 30, 2009 5:42 PM #348635
Quote from fitzy
not everyone thinks in as logical way as you my friend :) also...tic tac toe annoys me cuz you HAVE to make a mistake in order to lose, there is no way in which both players played well but one played better. if you lost you made a big error. i pretty much always draw...but that's veering off quite a bit :P

and ty flux :P


That why I never play it unless I know my opponent is a dimwit :')
Omega
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Jan 30, 2009 7:35 PM #348692
There was a thread about it a while ago, and you're supposed to switch to increase your chance of winning the prize.

It's called the Monty Hall problem.