History Main / MontyHallProblem

17th Mar '16 3:14:43 PM StFan
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A classic mathematical problem involving probabilites. 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.

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A classic mathematical problem involving probabilites.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.






!!Examples of this in works:

[[AC:{{Card Games}}]]
* ''PerplexCity''

[[AC:{{Film}}]]
* ''[[Film/TwentyOne 21]]'', 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.

[[AC:{{Literature}}]]
* ''[[Literature/TheCuriousIncidentOfTheDogInTheNightTime The Curious Incident of the Dog in the Night-Time]]''
* Explained six different ways (including a list of everything that might happen) in Ian Stewart's ''TheMagicalMaze''.

[[AC:{{Live-Action TV}}]]

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!!Examples of this in works:

[[AC:{{Card Games}}]]
!!Examples:

[[foldercontrol]]

[[folder:Card Games]]
* ''PerplexCity''

[[AC:{{Film}}]]
''TabletopGame/PerplexCity''
[[/folder]]

[[folder:Films -- Live-Action]]
* ''[[Film/TwentyOne 21]]'', ''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.

[[AC:{{Literature}}]]
goat.
[[/folder]]

[[folder:Literature]]
* ''[[Literature/TheCuriousIncidentOfTheDogInTheNightTime The Curious Incident of the Dog in the Night-Time]]''
''Literature/TheCuriousIncidentOfTheDogInTheNightTime''
* Explained six different ways (including a list of everything that might happen) in Ian Stewart's ''TheMagicalMaze''.

[[AC:{{Live-Action TV}}]]
''Literature/TheMagicalMaze''.
[[/folder]]

[[folder:Live-Action TV]]




[[AC:{{Video Games}}]]

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\n[[AC:{{Video Games}}]][[/folder]]

[[folder:Video Games]]




[[AC:{{Webcomics}}]]

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\n[[AC:{{Webcomics}}]][[/folder]]

[[folder:Web Comics]]




[[AC:{{Western Animation}}]]

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\n[[AC:{{Western Animation}}]][[/folder]]

[[folder:Western Animation]]



-->'''Weird:''' So, you took the box. Why?
-->'''Shaggy:''' Just call it a [[{{Irony}} dumb]] hunch.
-->'''Weird:''' Well, let's see just how [[{{Foreshadowing}} dumb]] your hunch really was!

[[AC:{{Real Life}}]]

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-->'''Weird:''' So, you took the box. Why?
-->'''Shaggy:'''
Why?\\
'''Shaggy:'''
Just call it a [[{{Irony}} dumb]] hunch.
-->'''Weird:'''
hunch.\\
'''Weird:'''
Well, let's see just how [[{{Foreshadowing}} dumb]] your hunch really was!

[[AC:{{Real Life}}]]
was!
[[/folder]]

[[folder:Real Life]]


Added DiffLines:

[[/folder]]
18th Jan '16 6:45:04 PM LadyJafaria
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* Discussed in ''Series/{{Numbers}}'', as most mathematical concepts are. It turned out to be an example of ChekhovsClassroom, although in this case ''teaching'' the Monty Hall Problem is what helped Charlie have a EurekaMoment.
29th Oct '15 6:29:11 AM Morgenthaler
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* Subverted in ''DealOrNoDeal''. While a contestant who reached the final case was offered the opportunity to switch it out with his/her case, Howie Mandel went out of his way to explain that this was ''not'' a Monty Hall situation: The show offered the switch to everyone who got that far, and he had no knowledge of which case contained which dollar amount.
* ''{{Numb3rs}}''

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* Subverted in ''DealOrNoDeal''.''Series/DealOrNoDeal''. While a contestant who reached the final case was offered the opportunity to switch it out with his/her case, Howie Mandel went out of his way to explain that this was ''not'' a Monty Hall situation: The show offered the switch to everyone who got that far, and he had no knowledge of which case contained which dollar amount.
* ''{{Numb3rs}}''%%* ''Series/{{Numb3rs}}''



* ''Series/JamesMaysManLab'' did a RussianRoulette version of this with beer cans called, wait for it, "[[TheDeerHunter The Beer Hunter]]." The rules were simple: there would be three cans, two of which were shaken up. James would pick one can, but always change his mind after Tom took away a "dangerous" can, and Simmy would be left with the one that James originally picked. They would then hold the cans next to their face and open the cans together. They did this for one hundred rounds; along with getting hypothermia and minor carbon dioxide poisoning, James also proved this version true by winning 40:60.

to:

* ''Series/JamesMaysManLab'' did a RussianRoulette version of this with beer cans called, wait for it, "[[TheDeerHunter "[[Film/TheDeerHunter The Beer Hunter]]." The rules were simple: there would be three cans, two of which were shaken up. James would pick one can, but always change his mind after Tom took away a "dangerous" can, and Simmy would be left with the one that James originally picked. They would then hold the cans next to their face and open the cans together. They did this for one hundred rounds; along with getting hypothermia and minor carbon dioxide poisoning, James also proved this version true by winning 40:60.
13th Jul '15 6:54:54 PM Llygodenfawr
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* Implemented in in ''Videogame/SandcastleBuilder'', and can be played multiple times. Rather than a car, the prize for picking the correct door is gaining 50% of your sandcastle balance. You lose all your sandcastles if you choose incorrectly, but receive a goat as a consolation, as this is largely a reference to the ''Webcomic/{{xkcd}}' [[ParodiedTrope parody]]. Unlike that comic, if a goat is revealed behind a door you didn't pick (which does not always occur, in order to make it harder to figure out whether or not to take a switch when offered), you can't choose to keep it: if you want a goat you have to find the other goat. In order to sow confusion, this game feature is named 'Monty Haul Problem'.

to:

* Implemented in in ''Videogame/SandcastleBuilder'', and can be played multiple times. Rather than a car, the prize for picking the correct door is gaining 50% of your sandcastle balance. You lose all your sandcastles if you choose incorrectly, but receive a goat as a consolation, as this is largely a reference to the ''Webcomic/{{xkcd}}' ''Webcomic/{{xkcd}}'' [[ParodiedTrope parody]]. Unlike that comic, if a goat is revealed behind a door you didn't pick (which does not always occur, in order to make it harder to figure out whether or not to take a switch when offered), you can't choose to keep it: if you want a goat you have to find the other goat. In order to sow confusion, this game feature is named 'Monty Haul Problem'.
17th Aug '14 10:04:47 AM gallium
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* ''[[Film/TwentyOne 21]]''

to:

* ''[[Film/TwentyOne 21]]''
21]]'', 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.
23rd May '14 2:59:47 PM sunnie31
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* Incorrectly invoked in ''Series/{{Survivor}}: Caramoan''. When Reynold is given a choice between the slice of pizza he has already won or an unseen item, Cochran tells him that this is the Monty Hall Problem and Reynold should pick the unseen item. This is not the Monty Hall problem at all, although Cochran did end up being right for the wrong reasons because the unseen item WAS better.
5th Feb '14 3:00:30 PM Antigone3
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* ''MythBusters'' not only tested the probabilities of the Monty Hall problem as stated above, but also contestant behavior when presented with the situation. (All 20 "contestants" tested stuck with their original decision rather than switching.)

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* ''MythBusters'' ''Series/MythBusters'' not only tested the probabilities of the Monty Hall problem as stated above, but also contestant behavior when presented with the situation. (All 20 "contestants" tested stuck with their original decision rather than switching.)
4th Dec '13 3:51:29 PM EternalDensity
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* Implemented in in ''Videogames/SandcastleBuilder'', and can be played multiple times. Rather than a car, the prize for picking the correct door is gaining 50% of your sandcastle balance. You lose all your sandcastles if you choose incorrectly, but receive a goat as a consolation, as this is largely a reference to the ''Webcomic/{{xkcd}}' [[ParodiedTrope parody]]. Unlike that comic, if a goat is revealed behind a door you didn't pick (which does not always occur, in order to make it harder to figure out whether or not to take a switch when offered), you can't choose to keep it: if you want a goat you have to find the other goat. In order to sow confusion, this game feature is named 'Monty Haul Problem'.

to:

* Implemented in in ''Videogames/SandcastleBuilder'', ''Videogame/SandcastleBuilder'', and can be played multiple times. Rather than a car, the prize for picking the correct door is gaining 50% of your sandcastle balance. You lose all your sandcastles if you choose incorrectly, but receive a goat as a consolation, as this is largely a reference to the ''Webcomic/{{xkcd}}' [[ParodiedTrope parody]]. Unlike that comic, if a goat is revealed behind a door you didn't pick (which does not always occur, in order to make it harder to figure out whether or not to take a switch when offered), you can't choose to keep it: if you want a goat you have to find the other goat. In order to sow confusion, this game feature is named 'Monty Haul Problem'.
4th Dec '13 3:49:42 PM EternalDensity
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Added DiffLines:

[[AC:{{Video Games}}]]
* Implemented in in ''Videogames/SandcastleBuilder'', and can be played multiple times. Rather than a car, the prize for picking the correct door is gaining 50% of your sandcastle balance. You lose all your sandcastles if you choose incorrectly, but receive a goat as a consolation, as this is largely a reference to the ''Webcomic/{{xkcd}}' [[ParodiedTrope parody]]. Unlike that comic, if a goat is revealed behind a door you didn't pick (which does not always occur, in order to make it harder to figure out whether or not to take a switch when offered), you can't choose to keep it: if you want a goat you have to find the other goat. In order to sow confusion, this game feature is named 'Monty Haul Problem'.
25th Oct '13 8:57:27 AM ReplacementSquark
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* ''Series/JamesMaysManLab'' did a RussianRoulette version of this with beer cans called, wait for it, "[[TheDeerHunter The Beer Hunter]]." The rules were simple: there would be three cans, two of which were shaken up. James would pick one can, but always change his mind after Tom took away a "dangerous" can, and Simmy would be left with the one that James originally picked. They would then hold the cans next to their face and open the cans together. They did this for one hundred rounds; along with getting hypothermia and minor carbon dioxide poisoning, James also proved this version true by winning 40:60.

to:

* ''Series/JamesMaysManLab'' did a RussianRoulette version of this with beer cans called, wait for it, "[[TheDeerHunter The Beer Hunter]]." The rules were simple: there would be three cans, two of which were shaken up. James would pick one can, but always change his mind after Tom took away a "dangerous" can, and Simmy would be left with the one that James originally picked. They would then hold the cans next to their face and open the cans together. They did this for one hundred rounds; along with getting hypothermia and minor carbon dioxide poisoning, James also proved this version true by winning 40:60.
40:60.

[[AC:{{Webcomics}}]]
* [[ParodiedTrope Parodied]] in ''Webcomic/{{xkcd}}''. The Existentialist in a Beret delightedly walks off with the first goat revealed, instead of making the choice. According to the AltText, the other goat drove off in the car a few minutes later.
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