Two Plus Two Poker Forums 3 door game show question
 Register FAQ Search Today's Posts Mark Forums Read Video Directory TwoPlusTwo.com

 Notices 2013 Two Plus Two Party at South Point BET RAISE FOLD screening at 3PM in lounge next to poker room. July 6th Party registration at 5PM. Food served at 6PM

 Probability Discussions of probability theory

 06-05-2012, 09:32 PM #1 Pooh-Bah     Join Date: Mar 2008 Location: snapples Posts: 4,203 3 door game show question saw this on myth busters i dont understand any chance someone can explain it please. there are 3 doors you select a door (dont get to open it yet) the host opens another door it is empty then he gives you option to STAY with your initial choice (still not opened) or choose the other door remaining. they said you should always change but i dont understand because theres only 2 doors left staying and changing is the same odds right? they said if you chance doors your odds become 2/3 from 1/3 thought i would ask the math wizards of 2+2 (: was season 5 i think
 06-05-2012, 10:11 PM #2 Pooh-Bah     Join Date: Mar 2008 Location: snapples Posts: 4,203 Re: 3 door game show question its called the monty hall paradox am a retard for thinking its all bs? because saying switching or staying door at the end is just another way of saying left or right door and the probability is equal the initial choice is irrelavant because he exposed a door so now we just have option of 1 or 2 which is the same right?
 06-05-2012, 10:18 PM #3 Carpal \'Tunnel     Join Date: Jun 2005 Location: Psychology Department Posts: 7,450 Re: 3 door game show question This 5 minute video is the best explanation I have seen for those who do not understand why switching is correct. http://www.youtube.com/watch?v=mhlc7peGlGg The key is (and you have left it out of your problem) that the host KNOWS which doors has the prize and which one's do not. If the door the host decides to open NEVER contains a prize (b/c he intentionally does not choose that one), then switching is best. Another way people like to think about is to imagine 100 doors with 99 goats and 1 prize. You pick one door. Then the host proceeds to open 98 doors each containing a goat. Do you want to switch now? For what it is worth, the example is useful, but I think not as helpful initially as the nice youtube video.
 06-05-2012, 10:21 PM #4 Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 15,085 Re: 3 door game show question Look at wikipedia or google it, it's been discussed to death. Yes, you should switch. Short answer as to why: the host has introduced an extra piece of information, because he knows where the prize is. He will NOT open the door that has the prize, he will only pick a non-winning door. It's easy to work out for yourself - enumerate all the possibilities. That is, number the doors 1 2 and 3. There are 3 places the prize could be, and 3 possible places the winner could be. Make a table, like C=1 P=1 (chose 1, prize is 1) C=1 P=2 (chose 1, prize is 1) for each entry in the table, "open" one of the doors that is NOT a winner and NOT chosen by the player. Could how often you win by switching, and how often you win by staying. If you do this it should be very clear.
 06-05-2012, 10:51 PM #5 Pooh-Bah     Join Date: Mar 2008 Location: snapples Posts: 4,203 Re: 3 door game show question thnx sorry for repost was just curious
06-05-2012, 11:02 PM   #6
Carpal \'Tunnel

Join Date: Jun 2005
Location: Psychology Department
Posts: 7,450
Re: 3 door game show question

Quote:
 Originally Posted by metski thnx sorry for repost was just curious
The repost doesn't really bother me. What would bother me is if you now did not understand why switching it better.

 06-05-2012, 11:56 PM #7 Carpal \'Tunnel     Join Date: Sep 2002 Posts: 8,953 Re: 3 door game show question If you did this a million times and always just ignore what the host shows you, staying with your original choice, then obviously your choice will be right 1/3 of the time, and wrong 2/3 of the time. So if you switch every time, you will be right 2/3 of the time and wrong 1/3 of the time.
06-06-2012, 04:15 AM   #8
veteran

Join Date: Mar 2009
Location: In the wires
Posts: 2,335
Re: 3 door game show question

Quote:
 Originally Posted by Sherman The key is (and you have left it out of your problem) that the host KNOWS which doors has the prize and which one's do not. If the door the host decides to open NEVER contains a prize (b/c he intentionally does not choose that one), then switching is best.
And there is one other condition that is sometimes left out but must be included to be rigorous. The host must ALWAYS eliminate a door, without exception. He can't choose when to do it. And as you point out, he obviously can never eliminate the prize door, which is the real key.

 06-06-2012, 11:27 AM #9 Carpal \'Tunnel     Join Date: Feb 2006 Location: Austin, TX Posts: 15,085 Re: 3 door game show question In case I sounded crotchety in my reply, I'm not bothered by the repost. But there's really not too much to say about it that hasn't already been said. I first saw the problem in 1992 when I got my first access to the internet as a whole (on usenet). So it's been out there for a minimum of 20 years, and I suspect much much longer than that.
06-06-2012, 04:15 PM   #10
Pooh-Bah

Join Date: Jul 2005
Location: Phoenix
Posts: 4,677
Re: 3 door game show question

Quote:
 Originally Posted by BruceZ If you did this a million times and always just ignore what the host shows you, staying with your original choice, then obviously your choice will be right 1/3 of the time, and wrong 2/3 of the time. So if you switch every time, you will be right 2/3 of the time and wrong 1/3 of the time.

06-06-2012, 05:01 PM   #11
Carpal \'Tunnel

Join Date: Jun 2005
Location: Psychology Department
Posts: 7,450
Re: 3 door game show question

Quote:
 Originally Posted by BruceZ If you did this a million times and always just ignore what the host shows you, staying with your original choice, then obviously your choice will be right 1/3 of the time, and wrong 2/3 of the time. So if you switch every time, you will be right 2/3 of the time and wrong 1/3 of the time.
This actually isn't that helpful because it misses the common mistake that people make, namely assuming that it doesn't matter if they switch or not (i.e. each one is 1/3 and therefore after the goat has been revealed the odds are now 50:50).

If it was obvious from the problem that "staying = 1/3, therefore switching must be 2/3" it wouldn't be such a famous problem.

06-06-2012, 05:33 PM   #12
Carpal \'Tunnel

Join Date: Sep 2002
Posts: 8,953
Re: 3 door game show question

Quote:
 Originally Posted by Sherman This actually isn't that helpful because it misses the common mistake that people make, namely assuming that it doesn't matter if they switch or not (i.e. each one is 1/3 and therefore after the goat has been revealed the odds are now 50:50). If it was obvious from the problem that "staying = 1/3, therefore switching must be 2/3" it wouldn't be such a famous problem.
Nonsense, of course it's obvious. You'd have to be awfully stupid to not know that your initial choice will be right 1/3 of the time. Most people think that the probabilities have to be 1/2, and they don't see any paradox. My answer shows them that the probabilities clearly have to be 1/3 and 2/3. Then they can think about why their assumption must be wrong.

Last edited by BruceZ; 06-06-2012 at 05:59 PM.

06-06-2012, 06:02 PM   #13
veteran

Join Date: Mar 2009
Location: In the wires
Posts: 2,335
Re: 3 door game show question

Quote:
 Originally Posted by BruceZ Nonsense, of course it's obvious. You'd have to be awfully stupid to not know that your initial choice will be right 1/3 of the time. Most people think that the probabilities have to be 1/2, and they don't see any paradox. My answer shows them that the probabilities clearly have to be 1/3 and 2/3. Then they can think about why their assumption must be wrong.
The majority of people who have never heard of the problem do not reach this conclusion easily, and most people are not awfully stupid. It is a terrific explanation once you understand the problem or have thought it through. But the thought process to get there is more complicated than just "doh 1/3 chance per door herpderp"

06-06-2012, 06:38 PM   #14
Carpal \'Tunnel

Join Date: Sep 2002
Posts: 8,953
Re: 3 door game show question

Quote:
 Originally Posted by NewOldGuy The majority of people who have never heard of the problem do not reach this conclusion easily, and most people are not awfully stupid.
I agree with the first half of that and never said otherwise. In fact I stated as much when I said that most people never get past the initial assumption that the doors have the same probability. My explanation gets them to realize that there is even another answer worth considering, and that explanation is compelling even to those with virtually no probability background. The accusation was that the explanation doesn't follow obviously from knowledge of how the game is played, and of course it does.

Quote:
 It is a terrific explanation once you understand the problem or have thought it through. But the thought process to get there is more complicated than just "doh 1/3 chance per door herpderp"
Well if someone doesn't even know that when they pick 1 door out of 3 that the probability of being right is 1/3, then I doubt that any explanation can help them because it would mean that they have no conception of what probability even means. Then if they're too dumb to understand that it must be behind the other door 2/3 of the time, then perhaps a game of "got your nose" would be more appropriate for them.

 06-06-2012, 07:29 PM #15 Carpal \'Tunnel     Join Date: Sep 2002 Posts: 8,953 Re: 3 door game show question This old problem of mine has some similarity to the Monty Hall problem, though it's (I think) more subtle and it's a poker combinatorics problem. David Sklansky answered it correctly, so don't read his if you want to figure it out yourself.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are Off Refbacks are Off Forum Rules

All times are GMT -4. The time now is 08:53 AM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top