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Let's discuss the Monty Hall problem (probabilities, odds)
Posted on 8/12/17 at 2:01 am
Posted on 8/12/17 at 2:01 am
Since there appears to be a plethora of mathematical geniuses in the card thread, I thought I'd see what the OT has to say about this little gem: The Monty Hall Problem (the goat of problems 
)
:quality(90)/https://curiosity-data.s3.amazonaws.com/images/memes/image/ddab06da-261a-4e7b-a67a-42a278a20d93.png)
What saith the OT?
What are your odds of guessing the right door?
How about after Monty shows you the goat?
) What saith the OT?
What are your odds of guessing the right door?
How about after Monty shows you the goat?
28
Posted on 8/12/17 at 2:02 am to SlapahoeTribe
The answer is yes for reasons I have never completely understood
Posted on 8/12/17 at 2:03 am to SlapahoeTribe
The catch is that it is presumed the host knows what is behind each door.
This does not hold true in a blind selection.
This does not hold true in a blind selection.
Posted on 8/12/17 at 2:03 am to SlapahoeTribe
Hearts can't desire anything as they have no conscience. I'm switching to door 3 and making sure I'm getting something out of this.
Posted on 8/12/17 at 2:11 am to SlapahoeTribe
Easy. Door #2
Posted on 8/12/17 at 2:13 am to SlapahoeTribe
I'm just happy I'm gonna at least win a goat.
Posted on 8/12/17 at 2:23 am to SlapahoeTribe
Ok
There are 3 doors and 2 goats... you have a 2/3 chance from the beginning of being wrong... when he opens one door revealing a goat, he is essentially telling you what door the car is behind in 2/3 of the game... and it isn't the one you picked, and clearly isn't the goat... by showing you the goat, he adds value to the last door, boosting your chances of you switch
You now have a 2/3 advantage if you switch, and only a 1/3 chance of you stay
Another way to see it:
The player has a 1/3 chance of being right the first time, and the other two doors combined have a 2/3 chance... when he shows you the goat, those odds remain, except the full 2/3 odds shift from two doors to the one remaining door you didn't pick and a goat wasn't shown
There are 3 doors and 2 goats... you have a 2/3 chance from the beginning of being wrong... when he opens one door revealing a goat, he is essentially telling you what door the car is behind in 2/3 of the game... and it isn't the one you picked, and clearly isn't the goat... by showing you the goat, he adds value to the last door, boosting your chances of you switch
You now have a 2/3 advantage if you switch, and only a 1/3 chance of you stay
Another way to see it:
The player has a 1/3 chance of being right the first time, and the other two doors combined have a 2/3 chance... when he shows you the goat, those odds remain, except the full 2/3 odds shift from two doors to the one remaining door you didn't pick and a goat wasn't shown
Posted on 8/12/17 at 2:34 am to SlapahoeTribe
It's situations like these I start accusing people of witchcraft
Posted on 8/12/17 at 2:38 am to SlapahoeTribe
Lets change the scenario to help you understand...what if there were 100 doors instead of three? You pick a door. Then the host reveals 98 goats behind 98 of the doors you didn't select.
Then he asks you if you want to swap to the remaining unknown door... Now is it more clear that you should indeed swap?
Then he asks you if you want to swap to the remaining unknown door... Now is it more clear that you should indeed swap?
Posted on 8/12/17 at 4:19 am to SlapahoeTribe
Arrogant corndog nailed the explanation
I initially did not get it back when I first saw it either but once you see it you can't unsee it, seems obvious
I initially did not get it back when I first saw it either but once you see it you can't unsee it, seems obvious
Posted on 8/12/17 at 4:23 am to SlapahoeTribe
i used to not get this but once i realized it had everything to do with "game show host" knowing where the car was and that he was always going to show you a goat is when i got it
you have a 1/3 chance at choosing the car when you initially pick say door 1. the game show host is going to open door three knowing that a goat is behind there. so now, you know that there is actually only one remaining goat for the three doors. so now your odds of choosing the car have gone up to 2/3 if you change your choice to door 2
you have a 1/3 chance at choosing the car when you initially pick say door 1. the game show host is going to open door three knowing that a goat is behind there. so now, you know that there is actually only one remaining goat for the three doors. so now your odds of choosing the car have gone up to 2/3 if you change your choice to door 2
This post was edited on 8/12/17 at 4:24 am
Posted on 8/12/17 at 5:31 am to SlapahoeTribe
The OP leaves out a very important thing - it does not mention whether the host knows which door has the goat. It only says the host shows you a goat.
If the host can be counted on to always show a goat, then you should switch. If the host is just as blind as you are, then it doesn't matter whether you switch.
The real question is how many pages this thread will have.
If the host can be counted on to always show a goat, then you should switch. If the host is just as blind as you are, then it doesn't matter whether you switch.
The real question is how many pages this thread will have.
Posted on 8/12/17 at 5:59 am to SlapahoeTribe
An interesting anecdote I remember reading about the Monty Hall Problem:
In 1990, Marilyn Vos Savant had a column in Parade magazine where people wrote her for advice and often gave her brain twisters to solve for fun. Someone asked her about the Monty Hall Problem and she responded that you should switch doors. Her answer got a lot of derision from math professors who wrote in claiming she was wrong and that there is no advantage to switching. She saved those letters from all those PhD's and has since put them on her website. LINK In any case, Marilyn was right, switching is the optimal strategy.
In case you're wondering, Vos Savant has no expertise in anything other than having an astronomically high IQ (she was tested at an IQ of 228 at age 10 which put her in the Guinness Book of World Records as having the highest known recorded IQ). However, it is well known that childhood scores that use "mental age" are not accurate when the child becomes an adult. Nonetheless, her adult IQ is still estimated to be easily one-in-a-million (over 180). For comparison, Mensa is 1 in 50 (or about 130).
Her Wiki Page
In 1990, Marilyn Vos Savant had a column in Parade magazine where people wrote her for advice and often gave her brain twisters to solve for fun. Someone asked her about the Monty Hall Problem and she responded that you should switch doors. Her answer got a lot of derision from math professors who wrote in claiming she was wrong and that there is no advantage to switching. She saved those letters from all those PhD's and has since put them on her website. LINK In any case, Marilyn was right, switching is the optimal strategy.
In case you're wondering, Vos Savant has no expertise in anything other than having an astronomically high IQ (she was tested at an IQ of 228 at age 10 which put her in the Guinness Book of World Records as having the highest known recorded IQ). However, it is well known that childhood scores that use "mental age" are not accurate when the child becomes an adult. Nonetheless, her adult IQ is still estimated to be easily one-in-a-million (over 180). For comparison, Mensa is 1 in 50 (or about 130).
Her Wiki Page
This post was edited on 8/12/17 at 6:21 am
Posted on 8/12/17 at 6:05 am to SlapahoeTribe
Is one of the goats fricking Carol Merril...?
This post was edited on 8/12/17 at 6:07 am
Posted on 8/12/17 at 6:39 am to SlapahoeTribe
Always switch. Doubles your odds.
Posted on 8/12/17 at 8:53 am to SlapahoeTribe
A goat IS what my heart desires.
No shite, my wife and I squabble over getting a pet goat quite often. Actually, I heard I need two of them to keep each other company.
No shite, my wife and I squabble over getting a pet goat quite often. Actually, I heard I need two of them to keep each other company.
Posted on 8/12/17 at 8:58 am to SlapahoeTribe
I'm going home with the greatest of all time prizes
Posted on 8/12/17 at 9:09 am to SlapahoeTribe
Seems pretty easy to understand, not sure why people have such a hard time with it.
Posted on 8/12/17 at 9:47 am to SlapahoeTribe
there was a classic OT thread about this years ago
Posted on 8/12/17 at 11:23 am to SlapahoeTribe
just go watch 21 they explain it there.
but it has to do with what i call relative probability.
ETA: Think of it this way - you pick your door for the prize. Then if someone said "i'll let you choose either to keep your door or to choose both of the other doors" which would you choose?
This is essentially what the host is doing by removing the incorrect door. While the new choice is essentially 50 / 50 - given what you know about the way the game is set up it is really 33% your door and 66% the other door since the other door has also taken on the probability of the door which the host has already revealed.
That is probably the best i can do without writing out a proof. Probability Theory and Discrete Mathematics is really fascinating - one of the courses i kept my textbook for.
but it has to do with what i call relative probability.
ETA: Think of it this way - you pick your door for the prize. Then if someone said "i'll let you choose either to keep your door or to choose both of the other doors" which would you choose?
This is essentially what the host is doing by removing the incorrect door. While the new choice is essentially 50 / 50 - given what you know about the way the game is set up it is really 33% your door and 66% the other door since the other door has also taken on the probability of the door which the host has already revealed.
That is probably the best i can do without writing out a proof. Probability Theory and Discrete Mathematics is really fascinating - one of the courses i kept my textbook for.
This post was edited on 8/12/17 at 11:29 am
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