History Main / MontyHallProblem

2nd Jul '17 12:16:02 PM nombretomado
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A classic mathematical problem involving probabilities. The basic form is based on one of the games on the GameShow ''Series/LetsMakeADeal''. The contestant is offered the choice of three doors. One has a car behind it, the two others hide [[{{Zonk}} goats]]. The contestant chooses a door. The host (who knows what is behind each door) then opens one of the two other doors, revealing a goat. The contestant is then offered the choice to switch to the unrevealed door or stick with his original decision. The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. This is because there was a 2 in 3 chance that you chose a goat originally, and switching will always get you the opposite of what you initially picked. The host isn't providing any new information, since he can ''always'' open a door with a goat. See TheOtherWiki [[http://en.wikipedia.org/wiki/Monty_Hall_problem for an explanation of the math]]. Note that this number is true only if the host is ''required'' to reveal a goat and then offer the contestant the choice to switch. See ''[[http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=all The New York Times]]'' for what happens when the host is not.

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A classic mathematical problem involving probabilities. The basic form is based on one of the games on the GameShow ''Series/LetsMakeADeal''. The contestant is offered the choice of three doors. One has a car behind it, the two others hide [[{{Zonk}} goats]]. The contestant chooses a door. The host (who knows what is behind each door) then opens one of the two other doors, revealing a goat. The contestant is then offered the choice to switch to the unrevealed door or stick with his original decision. The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. This is because there was a 2 in 3 chance that you chose a goat originally, and switching will always get you the opposite of what you initially picked. The host isn't providing any new information, since he can ''always'' open a door with a goat. See TheOtherWiki Wiki/TheOtherWiki [[http://en.wikipedia.org/wiki/Monty_Hall_problem for an explanation of the math]]. Note that this number is true only if the host is ''required'' to reveal a goat and then offer the contestant the choice to switch. See ''[[http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=all The New York Times]]'' for what happens when the host is not.
10th May '17 12:53:09 AM XenMon2
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This problem is often presented with a flaw where the question does not include the notion that the host will always reveal a goat, as opposed to revealing either of the unpicked doors at random. In the latter case, your odds do not improve one way or the other, even if the car remains unrevealed. [[Film/TwentyOne Especially egregious examples]] may not include the notion that the host will always give the player the opportunity to switch, allowing for the possibility that the host only allows you to switch if you pick the car (in which case switching gets you a 100% chance of getting a goat).

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This problem is often presented with a flaw where the question does not include the notion that the host will always reveal a goat, as opposed to revealing either of the unpicked doors at random. In the latter case, your odds do not improve one way or the other, even if the car remains unrevealed. [[Film/TwentyOne Especially egregious examples]] may not include the notion that the host will always give the player the opportunity to switch, switch at all, allowing for the possibility that the host only allows you to switch if you pick the car (in which case switching gets you a 100% chance of getting a goat).
9th May '17 11:23:10 PM XenMon2
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This problem is often presented with a flaw where the question does not include the notion that the host will always reveal a goat, as opposed to revealing either of the unpicked doors at random. In the latter case, your odds do not improve one way or the other, even if the car remains unrevealed.

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This problem is often presented with a flaw where the question does not include the notion that the host will always reveal a goat, as opposed to revealing either of the unpicked doors at random. In the latter case, your odds do not improve one way or the other, even if the car remains unrevealed.
unrevealed. [[Film/TwentyOne Especially egregious examples]] may not include the notion that the host will always give the player the opportunity to switch, allowing for the possibility that the host only allows you to switch if you pick the car (in which case switching gets you a 100% chance of getting a goat).
5th May '17 10:37:28 PM WarioBarker
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''"If the host is required to open a door all the time and offer you a switch, then you should take the switch, But if he has the choice whether to allow a switch or not, beware. Caveat emptor. It all depends on his mood.''

''My only advice is, if you can get me to offer you $5,000 not to open the door, take the money and go home."''

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''"If -->[-''"If the host is required to open a door all the time and offer you a switch, then you should take the switch, But if he has the choice whether to allow a switch or not, beware. Caveat emptor. It all depends on his mood.''

''My
''-]

-->[-''My
only advice is, if you can get me to offer you $5,000 not to open the door, take the money and go home."''"''-]
--->[-'''Monty Hall''', July 1991-]
5th May '17 10:31:44 PM WarioBarker
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How it worked out on the show is irrelevant, especially since Monty Hall himself in [[http://www.youtube.com/watch?v=c1BSkquWkDo this interview]] denies that he ''ever'' actually did this deal...but see the Real Life folder for how he tested it out in 1991 and added his own twist. The Monty Hall Problem applies to many things, but not Monty Hall.

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How it worked out on the show is irrelevant, especially since Monty Hall himself in [[http://www.youtube.com/watch?v=c1BSkquWkDo this interview]] denies that he ''ever'' actually did this deal...but deal. That said, see the Real Life folder for how he tested it out in 1991 and added his own twist. The showed that while the Monty Hall Problem applies to many things, but not it doesn't apply to Monty Hall.
5th May '17 10:29:24 PM WarioBarker
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How it worked out on the show is irrelevant, especially since Monty Hall himself is alleged to have said that he usually offered the switch only if the contestant had picked correctly in the first place (and in an interview [[http://www.youtube.com/watch?v=c1BSkquWkDo here]] denies that he ''ever'' actually did this).

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\nHow it worked out on the show is irrelevant, especially since Monty Hall himself is alleged to have said that he usually offered the switch only if the contestant had picked correctly in the first place (and in an interview [[http://www.youtube.com/watch?v=c1BSkquWkDo here]] this interview]] denies that he ''ever'' actually did this).
this deal...but see the Real Life folder for how he tested it out in 1991 and added his own twist. The Monty Hall Problem applies to many things, but not Monty Hall.






[[folder:Films -- Live-Action]]

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[[folder:Films -- - Live-Action]]



* Marilyn Vos Savant, author of ''Parade'' magazine's Ask Marilyn, is one of the proud few who got it completely right. (She addressed the ambiguities in a follow-up column.)

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* Marilyn Vos vos Savant, author of ''Parade'' magazine's Ask Marilyn, "Ask Marilyn", is one of the proud few who got it completely right. (She addressed the ambiguities in a follow-up column.))
* In July 1991, [[http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html Monty himself was asked to help settle the debate once and for all]], with the tests done in his home with a set of keys representing the car and a couple of cheap snacks representing the goats.
** Monty started out with doing the problem as commonly stated, eventually proving that Savant was correct. After this, he read her original article and noticed something she wasn't considering...
** The next set of tests saw Monty in full-on hosting mode, which pretty much meant all bets were off: he'd sometimes open the chosen door immediately, or offer various amounts of cash to call off the deal in lieu of a switch. As Monty noted, "there's the psychological factor to consider".



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''"If the host is required to open a door all the time and offer you a switch, then you should take the switch, But if he has the choice whether to allow a switch or not, beware. Caveat emptor. It all depends on his mood.''

''My only advice is, if you can get me to offer you $5,000 not to open the door, take the money and go home."''
27th Mar '17 6:56:05 PM KoopaKid17
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* ''Film/TwentyOne'', where they manage to completely screw up the answer to the problem. The student says that it doesn't matter if Monty only offers the switch when you pick the correct door, when in fact, if Monty only offers the switch when you pick the correct door, switching gives you a 100% chance of receiving a goat.

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* ''Film/TwentyOne'', where they manage to completely [[WritersCannotDoMath screw up the answer to the problem.problem]]. The student says that it doesn't matter if Monty only offers the switch when you pick the correct door, when in fact, if Monty only offers the switch when you pick the correct door, switching gives you a 100% chance of receiving a goat.
27th Mar '17 6:47:29 PM KoopaKid17
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* ''Series/ThePriceIsRight'' had a pricing game called '''Barker's Marker$''' which imposed a four-way Monty Hall problem. The game board had four prices, three of which matched prizes on display. The contestant marked three prices and, after two were revealed, had the option of switching the last marker to the other price at a cost of $500. The decision brings the problem into play where the contestant, after blindly picking three prizes, has a 75% chance of winning if the choice is made to switch.
26th Jan '17 10:26:17 PM AgentSalt
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A classic mathematical problem involving probabilities. The basic form is based on one of the games on the GameShow ''Series/LetsMakeADeal''. The contestant is offered the choice of three doors. One has a car behind it, the two others hide [[{{Zonk}} goats]]. The contestant chooses a door. The host (who knows what is behind each door) then opens one of the two other doors, revealing a goat. The contestant is then offered the choice to switch to the unrevealed door or stick with his original decision. The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. This is because there was a 2 in 3 chance that you chose a goat originally, and the host isn't providing any new information since he can ''always'' open a door with a goat. See TheOtherWiki [[http://en.wikipedia.org/wiki/Monty_Hall_problem for an explanation of the math]]. Note that this number is true only if the host is ''required'' to reveal a goat and then offer the contestant the choice to switch. See ''[[http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=all The New York Times]]'' for what happens when the host is not.

to:

A classic mathematical problem involving probabilities. The basic form is based on one of the games on the GameShow ''Series/LetsMakeADeal''. The contestant is offered the choice of three doors. One has a car behind it, the two others hide [[{{Zonk}} goats]]. The contestant chooses a door. The host (who knows what is behind each door) then opens one of the two other doors, revealing a goat. The contestant is then offered the choice to switch to the unrevealed door or stick with his original decision. The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. This is because there was a 2 in 3 chance that you chose a goat originally, and switching will always get you the opposite of what you initially picked. The host isn't providing any new information information, since he can ''always'' open a door with a goat. See TheOtherWiki [[http://en.wikipedia.org/wiki/Monty_Hall_problem for an explanation of the math]]. Note that this number is true only if the host is ''required'' to reveal a goat and then offer the contestant the choice to switch. See ''[[http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=all The New York Times]]'' for what happens when the host is not.


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30th Jun '16 6:27:43 AM SiennaCiShan
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* Referenced in ''VideoGame/ZeroEscapeZeroTimeDilemma'', where an entire fragment is named for this problem, including demonstrating the problem in a slightly modified form. In the relevant room, there are 10 lockers. Only one locker has a gas mask. After a selection is made, 8 of the lockers open, all of them empty. Then, the player is asked if they want to stick with their original choice, or to switch to the other locker. The problem is discussed by the characters during this scenario.

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* Referenced in ''VideoGame/ZeroEscapeZeroTimeDilemma'', ''VideoGame/ZeroTimeDilemma'', where an entire fragment is named for this problem, including demonstrating the problem in a slightly modified form. In the relevant room, there are 10 lockers. Only one locker has a gas mask. After a selection is made, 8 of the lockers open, all of them empty. Then, the player is asked if they want to stick with their original choice, or to switch to the other locker. The problem is discussed by the characters during this scenario.
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