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Originally posted by WheelyI just showed you mathematically that the information you get from opening the door is different and therefore the probability assigned to which door is different, so of course there is a point.
There is therefore no point in discussion whether this was arrived at randomly or not.
In the original case you should switch, in the other one you are indifferent.
Don't know if this has been said before but really as i see it, the first time you chose a door with a 1/3 chance of winning. what the presenter is doing is presenting you with another situation, this time with a 1/2 chance.
in my opinion, these two events have nothing to do with one another. after the first event you didn't lose or win, you just chose one, the anouncer doesn't say if you won or lost but bumps you to event number two, where you have 50% chance of winning. so really your chances are 50% no matter if you change your option or not.
maybe the probability specialists have a diferent opinion, but me as a person who hates this science(pseudo science in my opinion) see things this way.
Originally posted by ZahlanziPseudo-science? What are you talking about? Probability theory is a branch of mathematics.
Don't know if this has been said before but really as i see it, the first time you chose a door with a 1/3 chance of winning. what the presenter is doing is presenting you with another situation, this time with a 1/2 chance.
in my opinion, these two events have nothing to do with one another. after the first event you didn't lose or win, you just chose ...[text shortened]... but me as a person who hates this science(pseudo science in my opinion) see things this way.
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Originally posted by PalynkaThere is only one case. The case in the original post. In the case in question, the presenter opened the door that contained salt. Therefore, the contestant would be more likely to be correct if he switched his choice.
I just showed you mathematically that the information you get from opening the door is different and therefore the probability assigned to which door is different, so of course there is a point.
In the original case you should switch, in the other one you are indifferent.
However, the presenter can only show a) a door with salt (in which case you are better off switching) or b) the presenter shows you the porche (in which case you have lost and it becomes irrelevant whether you switch your choice or not). Thus, in the general case, it is important to know if the presenter knows what is behind the doors or not. However, in answer to the original question, it is not.
Given, as mentioned before, that this is a well known problem, the question is always asked with the presenter knowing what is behind each door.
Originally posted by ZahlanziGo back and try it for yourself. The link ATY posted is a flash game that demonstrates the question. Play it for a while and you will see, if you always change your guess, you will win around 75% of the time.
Don't know if this has been said before but really as i see it, the first time you chose a door with a 1/3 chance of winning. what the presenter is doing is presenting you with another situation, this time with a 1/2 chance.
in my opinion, these two events have nothing to do with one another. after the first event you didn't lose or win, you just chose ...[text shortened]... but me as a person who hates this science(pseudo science in my opinion) see things this way.
To me it is fairly clear and if you start playing around with math it just makes it look more complicated than it is. The math always ignores the fact that in the case in question, you have been shown one door which contains the salt thereby adding an element of certainty in the math of probability.
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Originally posted by WheelyLOL! That's the original problem! And if you let it run, it will converge to 66,6(6)%.
Go back and try it for yourself. The link ATY posted is a flash game that demonstrates the question. Play it for a while and you will see, if you always change your guess, you will win around 75% of the time.
To me it is fairly clear and if you start playing around with math it just makes it look more complicated than it is. The math always ignores the ...[text shortened]... door which contains the salt thereby adding an element of certainty in the math of probability.
The modified problem is not that problem. I've showed here that in that problem, where ex-ante there was the possibility of him opening the door with the car, finding salt behind the door means you'll have a 50/50 chance of winning on the remaining two doors.
The math isn't subjective and does NOT ignore anything.
Originally posted by WheelyThe problem I have is not that I don't agree, but that I don't understand it.
Go back and try it for yourself. The link ATY posted is a flash game that demonstrates the question. Play it for a while and you will see, if you always change your guess, you will win around 75% of the time.
To me it is fairly clear and if you start playing around with math it just makes it look more complicated than it is. The math always ignores the ...[text shortened]... door which contains the salt thereby adding an element of certainty in the math of probability.
Although I know the odds increase by changing, I can't see how they can. I mean, either the bloody door has salt behind it or not. And suddenly knowing that there's salt behind another door, doesn't increase the chances of salt being behind my chosen door or not...
But it does.
And it can't.
But it does.
Surely it can't.
But it does.
No.
Yes.
No.
God damn.
Crap.
I need a f^cking beer, that's what I need.
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Originally posted by shavixmirMy example with the same problem with a million doors is very intuitive. Imagine the game is such that there are a million doors and you choose one. Then the announcer will then open 999.998 doors without the car and you'll have the possibility to choose to switch or not.
The problem I have is not that I don't agree, but that I don't understand it.
Although I know the odds increase by changing, I can't see how they can. I mean, either the bloody door has salt behind it or not. And suddenly knowing that there's salt behind another door, doesn't increase the chances of salt being behind my chosen door or not...
But i
No.
Yes.
No.
God damn.
Crap.
I need a f^cking beer, that's what I need.
Suppose the car is in door 505. If you chose door 1, he'll open all except 505. If you chose 2, he'll open all except 505 and so on... You only lose by switching if initially you have chosen 505!
Originally posted by shavixmirOK, 3 doors, 1 with a porche, 2 with salt.
The problem I have is not that I don't agree, but that I don't understand it.
Although I know the odds increase by changing, I can't see how they can. I mean, either the bloody door has salt behind it or not. And suddenly knowing that there's salt behind another door, doesn't increase the chances of salt being behind my chosen door or not...
But i ...[text shortened]...
No.
Yes.
No.
God damn.
Crap.
I need a f^cking beer, that's what I need.
You pick one. You probably did not pick the porche. Do you agree? Let's start with that.
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Originally posted by shavixmirLet's assume you pick a door with salt.
Yes. I agree.
Now, if you switch, there are two possibilities. Imagine the presenter does NOT open a door for you.
One possibility is that you get the Porche, one is that you keep the salt. If you switch, you have a 50% chance of Porche, assuming Salt was the first pick.
But the presenter DOES open the door for you. That means that if you switch, you will DEFINITELY win - assuming you lost in the first place, which we already agreed you probably did. Do you agree?
Summarized - if you pick salt the first time, which you probably will, and the presenter shows you a door with salt, then the last door must be the porche, because you know where the two piles of salt are (one of them you're not sure about, but you think you know where it is - behind your first pick).
When people say you "have more information" because of the door opening, the information is "Psst - don't pick this door, if you pick it, you'll lose".
If you know one way to lose, you can avoid it and make it easier to win.
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Originally posted by PalynkaExcellent example that makes it clear how the odds have changed.
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 AThousandYoungI guess that sort of makes sense.
Let's assume you pick a door with salt.
Now, if you switch, there are two possibilities. Imagine the presenter does NOT open a door for you.
One possibility is that you get the Porche, one is that you keep the salt. If you switch, you have a 50% chance of Porche, assuming Salt was the first pick.
But the presenter DOES open the door for you ...[text shortened]... u'll lose".
If you know one way to lose, you can avoid it and make it easier to win.
So, basically with a 2/3 chance of choosing salt to start with and then being shown that another door has salt behind it, you have 1/3 chance of a porche if you don't change, yet a 1/2 chance of a porche if you do change?
That's pretty bizarre.
Thank you. I think I get it now.
Originally posted by shavixmiractually it is 2/3 chance of thr Porche if you switch but by golly I think he's got it 🙂 ( and I've had loads of beers thanks)
I guess that sort of makes sense.
So, basically with a 2/3 chance of choosing salt to start with and then being shown that another door has salt behind it, you have 1/3 chance of a porche if you don't change, yet a 1/2 chance of a porche if you do change?
That's pretty bizarre.
Thank you. I think I get it now.
Thanks for helping him get this ATY !!
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Originally posted by Palynka
LOL! That's the original problem! And if you let it run, it will converge to 66,6(6)%.
The modified problem is not that problem. I've showed here that in that problem, where ex-ante there was the possibility of him opening the door with the car, finding salt behind the door means you'll have a 50/50 chance of winning on the remaining two doors.
The math isn't subjective and does NOT ignore anything.