Right. My head is about to implode... I need some help.
Say there are three doors. Behind two of the doors there are sacks of salt and behind the third door there is a Porche 911 GTI turbo 10.6 liter 1.000.000 horse power... convertable...
The door I eventually pick will yield me the prize behind it.
So, I pick a door. Before it's opened, the presenter opens a different door showing a sack of salt and asks me if I want to reconsider my choice of door.
WHY do my odds increase if I change doors?
I know they do, someone told me and tried to explain it to me... but alas, a couple of liters of beer, two joints and a lap dancer sort of foggied my mind.
Don't focus on why I was discussing odds at a lap dancing bar, stick to the question at hand...
Originally posted by shavixmir So, I pick a door. Before it's opened, the presenter opens a different door showing a sack of salt and asks me if I want to reconsider my choice of door.
WHY do my odds increase if I change doors?
They increase because you gain information. Before you picked that door, you knew nothing. Now, however, you have gained part of the knowledge that the presenter has. It's only part of his knowledge, and that in disguised form, but you gain information. That information is just enough to change the odds.
Originally posted by Shallow Blue They increase because you gain information. Before you picked that door, you knew nothing. Now, however, you have gained part of the knowledge that the presenter has. It's only part of his knowledge, and that in disguised form, but you gain information. That information is just enough to change the odds.
Richard
I hear what you're saying... but...
Even with that extra information, there's still just as much chance of the Porche being behind the door I've chosen, rather than the door I'd switch to.
Originally posted by shavixmir I hear what you're saying... but...
Even with that extra information, there's still just as much chance of the Porche being behind the door I've chosen, rather than the door I'd switch to.
But there's not. How come switching is better?
So your saying the odds are the same even with new information, the
new information does not change how many doors you could/will pick
from?
Kelly
Originally posted by KellyJay So your saying the odds are the same even with new information, the
new information does not change how many doors you could/will pick
from?
Kelly
What I'm saying (I think) is that I don't see how changing my opinion increases odds.
Originally posted by shavixmir What I'm saying (I think) is that I don't see how changing my opinion increases odds.
There are a million doors. You choose one, the gameshow host then opens 999998 doors that don't have the Porsche, leaving you just with your initial choice and another one. Would you change?
Originally posted by shavixmir WHY do my odds increase if I change doors?
They don't. If you had picked the wrong door, the game show host would have simply told you so and let you move on as a looser. The fact that he offers you the chance to change tells you you have probably made the right choice.
You didn't specify whether the game show host knows which door the prize is behind. That would affect the odds calculation quite considerably.
Originally posted by shavixmir Right. My head is about to implode... I need some help.
Say there are three doors. Behind two of the doors there are sacks of salt and behind the third door there is a Porche 911 GTI turbo 10.6 liter 1.000.000 horse power... convertable...
The door I eventually pick will yield me the prize behind it.
So, I pick a door. Before it's opened, the pre ...[text shortened]... on why I was discussing odds at a lap dancing bar, stick to the question at hand...
Thanks.
Here's a way to think of it:
After picking a door, you have a 1/3 chance of having the Porsche.
That means that there is a 2/3 chance that the presenter has the Porsche.
The presenter knows which door has the Porsche. So he shows you a door that has salt.
There is still a 2/3 chance that the presenter has the Porsche. Opening a door with salt doesn't change that.
There are no guarantees, you still have a 1 in three chance of losing but perhaps think of it like this.
There are two salt doors and one porche. The presenter guarantees to show you one salt door and you are most likely to have picked the other one in which case you changing your choice will get you the porche.
The important thing here is not to look at it as probabilities because the presenter is dealing in certainties and blowing the statistics. The whole thing hinges on the fact that you have most likely chosen a salt door and the salesman guarantees to show you the other one.
I believe your answer lies here. This is the website of the worlds most intelligent human being Marylin Vos Savant......
http://www.marilynvossavant.com/articles/gameshow.html
Your odds are 2/3s that you DIDN'T pick the porsche, meaning if you switch, then you have a 2/3 chance of winning the porsche. The host only has a 1/3 chance of being able to open either of the other doors, which means you have only a 1/3 chance of NOT winning the porsche if you switch.
Originally posted by shavixmir Right. My head is about to implode... I need some help.
Say there are three doors. Behind two of the doors there are sacks of salt and behind the third door there is a Porche 911 GTI turbo 10.6 liter 1.000.000 horse power... convertable...
The door I eventually pick will yield me the prize behind it.
So, I pick a door. Before it's opened, the pre ...[text shortened]... on why I was discussing odds at a lap dancing bar, stick to the question at hand...
Thanks.
The problem is that if you get it right (1/3 chance), then you will lose if you switch.
If you get it wrong the first time (2/3 chance) the host will then make sure you don't get it wrong the second time by showing you which is the other wrong one.
Therefore, if you switch, 2/3 chance of getting it right. If you don't, 1/3 chance of getting it right.
In all replies I read here, assumptions are made that the presenter will this or would that. In the initial question, there is no hint towards such assumptions.
In such a case, your adds are 50%, and they are independent of the presenter and of the door you then choose (out of 2).
If this is incorrect, I'd be glad to hear it and understand why.
Beyond that, I think the discussion is pointless. You can make any assumption about the intention of the presenter when opening a door, and doing so, you can modify the outcome of the problem at will.
Originally posted by CeSinge In all replies I read here, assumptions are made that the presenter will this or would that. In the initial question, there is no hint towards such assumptions.
In such a case, your adds are 50%, and they are independent of the presenter and of the door you then choose (out of 2).
If this is incorrect, I'd be glad to hear it and understand why.
Beyo ...[text shortened]... presenter when opening a door, and doing so, you can modify the outcome of the problem at will.
No, the original post mentions that the presenter will show you a door with the salt. This is crucial. The presenter knows which door is which (otherwise he couldn´t guarantee showing you a door with the salt) and therefore all this nice math we see around boils down to the following.
You are most likely to have picked a door with salt. The presenter will show you a door with salt. Therefore, the most likely situation is that you have picked a door with salt and the presenter has shown you the other one. The one remaining door is the one most likely to contain the porche.
I have actually, physically demonstrated this with computer backup tapes (of all things) and can confirm that if you pick a door, get someone to show you the other unwanted door, and then change your selection, you are more likely to achieve the goal. It is not a 50/50 chance.
Odds... can someone explain?
05 Aug '08 05:56
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