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* ''Series/LetsMakeADeal'' is the TropeNamer for the most common formulation of the problem, as mentioned above, but rarely if ever allowed it to play out verbatim. The show usually offered a lump sum of cash instead of the switch.
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* ''Series/LetsMakeADeal'' is ''Series/BrooklynNineNine'' plays this for comedy by having Captain Holt and his husband Kevin get into a running argument over it. Santiago desperately tries to resolve the TropeNamer for the most common formulation argument by trying to convince Holt of the problem, as mentioned above, but rarely if ever allowed it right answer. Diaz, on the other hand, points that they're only arguing because they haven't been spending much time together and they're both testy. She [[RefugeInAudacity tells Holt to play his face]] "You two just need to bone." Guess who's solution works.
* In ''Series/CriminologistHimuraAndMysteryWriterArisugawa'', the DeadlyGame that Moroboshi and Himura engage in is based on the Monty Hall problem. Moroboshi sets outverbatim. The show usually offered a lump sum three glasses of cash instead wine, one of which is poisoned. She'll let Himura pick one, drink one of the switch.remaining glasses that ''isn't'' poisoned, offer him the chance to switch his choice, and then drink whatever glass he hasn't chosen. Himura's solution [[spoiler:is to bypass the problem entirely: he waits until Moroboshi isn't looking, pours all the wine into one glass, then re-distributes it into the three glasses. That way both Himura and Moroboshi take a diluted amount of the poison, which knocks them both out until the ambulance arrives to save them.]]
* In ''Series/CriminologistHimuraAndMysteryWriterArisugawa'', the DeadlyGame that Moroboshi and Himura engage in is based on the Monty Hall problem. Moroboshi sets out
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* ''Series/MythBusters'' not only [[JustForFun/TropesExaminedByTheMythBusters 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.)
* ''Series/LetsMakeADeal'' is the TropeNamer for the most common formulation of the problem, as mentioned above, but rarely if ever allowed it to play out verbatim. The show usually offered a lump sum of cash instead of the switch.
* ''Series/MythBusters'' not only [[JustForFun/TropesExaminedByTheMythBusters 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.)
* Discussed in ''Series/{{Numb3rs}}'', 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.
* The old game show ''Play Your Hunch'' (1958-63) employed basic intuition into determining which of three objects was the answer to a question.
* ''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 $500 given to the contestant at the start of the game. The decision brings the problem into play where the contestant, after blindly picking three prizes, has a 75% chance of winning if the choice is made to switch.
* ''Series/MythBusters'' not only [[JustForFun/TropesExaminedByTheMythBusters tested]] the probabilities of the Monty Hall problem as stated above, but also contestant behavior when presented with the situation. (All 20 "contestants" tested stuck with their original decision rather than switching.)
* Discussed in ''Series/{{Numb3rs}}'', as most mathematical concepts are. It turned out to be an example of ChekhovsClassroom, although in this case ''teaching'' the Monty Hall Problem is what helped Charlie have a EurekaMoment.
* The old game show ''Play Your Hunch'' (1958-63) employed basic intuition into determining which of three objects was the answer to a question.
* ''Series/ThePriceIsRight'' had a pricing game called '''Barker's Marker$''' 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 $500 given to the contestant at the start of the game. The decision brings the problem into play where the contestant, after blindly picking three prizes, has a 75% chance of winning if the choice is made to switch.
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* Discussed in ''Series/{{Numb3rs}}'', as most mathematical concepts are. It turned out to be an example of ChekhovsClassroom, although in this case ''teaching'' the Monty Hall Problem is what helped Charlie have a EurekaMoment.
* ''Series/ThePriceIsRight'' had a pricing game called '''Barker's Marker$''' 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 $500 given to the contestant at the start of the game. The decision brings the problem into play where the contestant, after blindly picking three prizes, has a 75% chance of winning if the choice is made to switch.
* ''Series/BrooklynNineNine'' plays this for comedy by having Captain Holt and his husband Kevin get into a running argument over it. Santiago desperately tries to resolve the argument by trying to convince Holt of the right answer. Diaz, on the other hand, points that they're only arguing because they haven't been spending much time together and they're both testy. She [[RefugeInAudacity tells Holt to his face]] "You two just need to bone." Guess who's solution works.
* The old game show ''Play Your Hunch" (1958-63) employed basic intuition into determining which of three objects was the answer to a question.
* ''Series/ThePriceIsRight'' had a pricing game called '''Barker's Marker$''' 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 given to the contestant at the start of the game. 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.
* ''Series/BrooklynNineNine'' plays this for comedy by having Captain Holt and his husband Kevin get into a running argument over it. Santiago desperately tries to resolve the argument by trying to convince Holt of the right answer. Diaz, on the other hand, points that they're only arguing because they haven't been spending much time together and they're both testy. She [[RefugeInAudacity tells Holt to his face]] "You two just need to bone." Guess who's solution works.
* The old game show ''Play Your Hunch" (1958-63) employed basic intuition into determining which of three objects was the answer to a question.
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%%[[folder:Card Games]]
%%* ''TabletopGame/PerplexCity''
%%* ''TabletopGame/PerplexCity''
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%%*
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[[folder:Fan Works]]
* ''Fanfic/DanganronpaParadiseLost'': [[spoiler:The first execution, aptly titled "Monokuma Hall Problem", has [[SmarmyHost Takeshi]] facing the problem, complete with an offer to switch -- and behind every door is a stash of illegal drugs. He takes the middle door to get his fix, which ends with him [[PopGoesTheHuman ballooning up and gorily exploding]]]].
[[/folder]]
* ''Fanfic/DanganronpaParadiseLost'': [[spoiler:The first execution, aptly titled "Monokuma Hall Problem", has [[SmarmyHost Takeshi]] facing the problem, complete with an offer to switch -- and behind every door is a stash of illegal drugs. He takes the middle door to get his fix, which ends with him [[PopGoesTheHuman ballooning up and gorily exploding]]]].
[[/folder]]
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* In ''Conned Again, Watson!'' by Colin Bruce, a book explaining probability theory via Franchise/SherlockHolmes stories, the mathematician [[Creator/LewisCarroll Charles Dodgson]] sets up a Monty Hall Problem scenario for Watson to pass the time on a train journey. Watson insists the odds are fifty/fifty until Dodgson suggests they switch places. Once he sees how his options in revealing an empty box are constrained by which box Dodgson picked, he gets it.
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* The puzzle is presented in ''VisualNovel/UminekoWhenTheyCry'' as a way to encourage Ange to hold onto her version of what happened all those years ago.
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* The puzzle is presented using slices of cake[[note]]the servants who baked and sliced the cake obviously know where the secret prize is and, wanting Ange to get the prize, only remove non-prize containing slices when taking a piece[[/note]] in ''VisualNovel/UminekoWhenTheyCry'' as a way to encourage Ange to hold onto her version of what happened all those years ago.ago (by way of metaphor, all of the alternate theories here are slices that "can't possibly hold the prize", so instead switching is a bad idea).
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* {{Parodied|Trope}} in [[https://xkcd.com/1282/ this]] ''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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* {{Parodied|Trope}} in [[https://xkcd.com/1282/ this]] ''Webcomic/{{xkcd}}''. The Existentialist in a Beret delightedly walks off with the first goat revealed, instead of making the choice., because he doesn't consider getting a goat to be a failure state. According to the AltText, the other goat drove off in the car a few minutes later.
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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 opening any one of three doors to claim whatever is behind the chosen door. One door 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 their 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 Website/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 opening any one of three doors to claim whatever is behind the chosen door. One door 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 two doors, revealing a goat. The contestant is then offered the choice to switch to the unrevealed door or stick with their 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 Website/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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* Referenced in ''VisualNovel/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. Interestingly, the fact that it only increases your chance of getting the prize is taken into account. You can choose the "correct" choice and still get an empty locker, since it isn't 100%.
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* Referenced in ''VisualNovel/ZeroTimeDilemma'', where an entire fragment is named for this problem, including demonstrating the problem in a slightly modified form. In the relevant room, a room filling with DeadlyGas, there are 10 lockers. Only lockers, only one locker of which has a gas mask. mask in it. After you choose a selection is made, locker, the game opens 8 of the lockers open, all of them empty. Then, empty ones (not including the player is asked if they want one you picked, obviously) and asks you to stick with their original choice, or to switch to choose again from the other locker.remaining 2 lockers. The problem is discussed by the characters during this scenario. Interestingly, the fact that it only increases choosing the other locker merely ''increases'' your chance of getting winning the prize is taken into account. You can choose account, as it's entirely possible for you make the "correct" choice and still get wind up with an empty locker, since it isn't 100%.locker.
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* 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.
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* 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]], 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.
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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 opening any one of three doors to claim whatever is behind the chosen door. One door 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 their 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 Website/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 opening any one of three doors to claim whatever is behind the chosen door. One door 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 their 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 Website/TheOtherWiki [[http://en.wikipedia.org/wiki/Monty_Hall_problem for an explanation of the math]]. 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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Wiki/ namespace cleaning.
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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 opening any one of three doors to claim whatever is behind the chosen door. One door 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 their 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 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.
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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 opening any one of three doors to claim whatever is behind the chosen door. One door 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 their 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 Wiki/TheOtherWiki Website/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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adding a redlink
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* The Monty Hall problem is explained six different ways (including a list of everything that might happen) in Ian Stewart's ''Literature/TheMagicalMaze''.
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* The Monty Hall problem is explained six different ways (including a list of everything that might happen) in Ian Stewart's Creator/IanStewart's ''Literature/TheMagicalMaze''.
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%%* Explained six different ways (including a list of everything that might happen) in Ian Stewart's ''Literature/TheMagicalMaze''.
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[[folder:Films - Live-Action]]
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[[folder:Films - -- Live-Action]]
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-->--'''Creator/MontyHall''', July 1991
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[[/folder]]
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----
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-->So if you change, 2 times out of 3 you get a car. And if you stick, you only get a car 1 time out of 3.\\
And this shows that intuition can sometimes get things wrong. And intuition is what people use in life to make decisions. But logic can help you work out the right answer.\\
It also shows that Mr. Jeavons was wrong and numbers are sometimes very complicated and not very straightforward at all. And that is why I like '''The Monty Hall Problem.'''
And this shows that intuition can sometimes get things wrong. And intuition is what people use in life to make decisions. But logic can help you work out the right answer.\\
It also shows that Mr. Jeavons was wrong and numbers are sometimes very complicated and not very straightforward at all. And that is why I like '''The Monty Hall Problem.'''
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* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime'': The protagonist explains the Monty Hall problem to the reader, using a tree diagram to illustrate all the different ways it can play out and the odds of each possible outcome.
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* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime'': The protagonist explains the Monty Hall problem to the reader, using [[https://static.tvtropes.org/pmwiki/pub/images/curious_incident_monty_hall.png a tree diagram diagram]] to illustrate all the different ways it can play out and the odds of each possible outcome.
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* Referenced in ''VisualNovel/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.
to:
* Referenced in ''VisualNovel/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. Interestingly, the fact that it only increases your chance of getting the prize is taken into account. You can choose the "correct" choice and still get an empty locker, since it isn't 100%.
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* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime'': The protagonist explains the Monty Hall problem, using a tree diagram to illustrate all the different ways it can play out and the odds of each possible outcome.
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* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime'': The protagonist explains the Monty Hall problem, problem to the reader, using a tree diagram to illustrate all the different ways it can play out and the odds of each possible outcome.
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%%[[folder:Literature]]
%%* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime''
%%* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime''
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%%* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime''
* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime'': The protagonist explains the Monty Hall problem, using a tree diagram to illustrate all the different ways it can play out and the odds of each possible outcome.
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%%[[/folder]]
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** 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...
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** Monty started out with doing the problem as commonly stated, eventually proving Marilyn Vos Savant's statement that Savant switching was correct. After this, he read her original article and noticed something she wasn't considering...
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These aren't specific instances of the trope happening, but are instead commentary about it.
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* Marilyn Vos Savant, author of ''Parade'' magazine's "Ask Marilyn", infamously said that the correct answer was to switch. (She addressed the ambiguities in a follow-up column.)
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* Some people (including Vos Savant herself) have proposed variants of the problem to explain why the answer is right. One has 1 million doors instead of 3, the person picks a random door (say 472,865) and the host open all doors except, say 983,724, and ask if you want to switch [[MST3KMantra (don't worry about how he'd open 999,998 doors on his own)]]. This makes it more obvious, as is only 1 in a million at first, so obviously after he removes all but one wrong door, the one left behind after would be more likely to be right.
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* ''Series/BrooklynNineNine'' plays this for comedy by having Captain Holt and his husband Kevin get into a running argument over it. Santiago desperately tries to resolve the argument by trying to convince Holt of the right answer.
Diaz, on the other hand, points that they're only arguing because they haven't been spending much time together and they're both testy. She [[RefugeInAudacity tells Holt to his face]] "You two just need to bone." Guess who's solution works.
Diaz, on the other hand, points that they're only arguing because they haven't been spending much time together and they're both testy. She [[RefugeInAudacity tells Holt to his face]] "You two just need to bone." Guess who's solution works.
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* ''Series/BrooklynNineNine'' plays this for comedy by having Captain Holt and his husband Kevin get into a running argument over it. Santiago desperately tries to resolve the argument by trying to convince Holt of the right answer. \n Diaz, on the other hand, points that they're only arguing because they haven't been spending much time together and they're both testy. She [[RefugeInAudacity tells Holt to his face]] "You two just need to bone." Guess who's solution works.
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* {{Parodied|Trope}} 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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* {{Parodied|Trope}} in [[https://xkcd.com/1282/ this]] ''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.
