History Main / MontyHallProblem

* 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, but Cochran did end up being {{right for the wrong reasons}} -- the unseen item ''really was'' better.

* ''Series/BrooklynNineNine'' plays this for comedy by having Captain Holt and his husband Kevin arguing over it; Holt still believes that switching is pointless and the odds are 50/50, so he ends up furiously arguing with Kevin, who's presenting the correct (2/3) answer. Santiago thinks the best way of getting them to make up is to try and get Holt to understand the answer, while Diaz, armed with the knowledge that Holt's been working the night shift a lot recently and hasn't had much free time, [[RefugeInAudacity tells Holt to his face]] that he's just pent-up and "You two just need to bone."

Named after the [[Creator/MontyHall longtime host]] of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marilyn Vos Savant got a pre-internet version of this: a lot of people (including a lot of math professors) wrote in saying she was wrong and it didn't matter if you switched or not. [[https://en.wikipedia.org/wiki/Monty_Hall_problem#Simple_solutions It turned out she was correct after all, as demonstrated by this table.]]

* ''Series/LetsMakeADeal'' is the TropeNamer for the most common formulation of the problem, as mentioned above.
* Mentioned but averted in ''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.

* 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.
* 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.

[[folder:Web Comics]]
* [[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.

'''Shaggy:''' Just call it a [[{{Irony}} dumb]] hunch.\\
'''Weird:''' Well, let's see just how [[{{Foreshadowing}} dumb]] your hunch really was!

* One of the riddles Him poses to WesternAnimation/ThePowerpuffGirls in "Him Diddle Riddle" is to determine which of two Ms. Keanes (she's their kindergarten teacher) hung by their feet over a tank of sharks is the real one. Blossom asks them who would say is the real Ms. Keane. The first says she would say she was the real one and the other says the other would say she was the real one. Blossom deduces who the real Ms. Keane is--she actually picks the wrong one but she had such a good poker face and was so believable that Him gave it to her.

[[/folder]]
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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."''
-->--'''Monty Hall''', July 1991

How it worked out on the show is irrelevant, especially since Monty Hall himself in [[https://www.youtube.com/watch?v=c1BSkquWkDo this interview]] denies that he ''ever'' actually did this deal. That said, see the Real Life folder for how he tested it out in 1991 and showed that while the Monty Hall Problem applies to many things, it didn't apply to Monty Hall.

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 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 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.

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

[[folder:Films - Live-Action]]
* ''Film/TwentyOne'', where they manage to completely [[WritersCannotDoMath screw up the answer to the problem]]: the teacher presenting the problem ''specifically states'' that Monty (who knows what's behind each door) may be using "reverse psychology" in an attempt to trick him. The student says this doesn't matter - but it does, because if it is indeed a trick and Monty only offers the switch when the correct door is picked, then the odds of switching getting you the car becomes 0%, not 66.6%.
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[[folder:Literature]]
* ''Literature/TheCuriousIncidentOfTheDogInTheNightTime''
* Explained six different ways (including a list of everything that might happen) in Ian Stewart's ''Literature/TheMagicalMaze''.
[[/folder]]

* ''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.)

* Marilyn Vos Savant, author of ''Parade'' magazine's "Ask Marilyn", infamously claimed that the correct answer was to switch. (She addressed the ambiguities in a follow-up column.)

Named after the [[Creator/MontyHall longtime host]] of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marilyn Vos Savant got a pre-internet version of this: a lot of people (including a lot of math professors) wrote in saying she was wrong and it didn't matter if you switched or not. [[https://en.wikipedia.org/wiki/Monty_Hall_problem#Simple_solutions It turned out was correct after all, as demonstrated by this table.]]

Named after the [[Creator/MontyHall longtime host]] of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marilyn Vos Savant got a pre-internet version of this: a lot of people (including a lot of math professors) wrote in saying she was wrong and it didn't matter if you switched or not. [[https://en.wikipedia.org/wiki/Monty_Hall_problem#Simple_solutions|It turned out was correct after all, as demonstrated by this table.]]

Named after the [[Creator/MontyHall longtime host]] of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marilyn Vos Savant got a pre-internet version of this: a lot of people (including a lot of math professors) wrote in pointing out she was wrong and it didn't matter if you switched or not.

Named after the [[Creator/MontyHall longtime host]] of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marilyn Vos Savant (which gave the right answer) got a pre-internet version of this: a lot of people (and not just [[{{Troll}} trolls]] and idiots, but math professors as well) wrote in insisting [[IRejectYourReality she was wrong and it didn't matter if you switched or not.]]

* 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.)

* ''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.

Named after the longtime host of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marilyn Vos Savant (which gave the right answer) got a pre-internet version of this: a lot of people (and not just [[{{Troll}} trolls]] and idiots, but math professors as well) wrote in insisting [[IRejectYourReality she was wrong and it didn't matter if you switched or not.]]

* 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.

Named after the longtime host of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marylin Vos Savant (which gave the right answer) got a pre-internet version of this: a lot of people (and not just [[{{Troll}} trolls]] and idiots, but math professors as well) wrote in insisting [[IRejectYourReality she was wrong and it didn't matter if you switched or not.]]

* 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.)

Named after the longtime host of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marylin Vos Savant (which gave the right answer) got a pre-internet version of this: a lot of people (and not just [[{{Troll}} trolls]] and idiots, but math professors as well)wrote in insisting [[IRejectYourReality she was wrong and it didn't matter if you switched or not.]]

* ''Series/LetsMakeADeal'' is the TropeMaker and TropeNamer for the most common formulation of the problem, as mentioned above.
* Subverted in ''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.

* In the first episode of ''WesternAnimation/The13GhostsOfScoobyDoo'', ThoseTwoBadGuys trick Scooby and Shaggy into opening the Chest of Demons this way. Posing as a game show (In an ancient castle in the Himalayas, no less!) Weird offers the two the following prizes; the [[CoolPlane Mystery Flying Machine]], a deluxe dog house, or they can take whatever's in the box. It didn't end well.

* Some people have proposed variants of the problem to explain why the answer is right. One has 1 million doors instead of 3, the person pick 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.

* Some people have proposed variants of the problem to explain why the answer is right. One has 1 million doors instead of 3, the person pick 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.

Named after the longtime host of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marylin Vos Savant (which gave the right answer) got a pre-internet version of this: a lot of people (and not just [[{{Troll}} trolls]] and idiots, but math professors as well) [[IRejectYourReality who were "sure" she was wrong and it didn't matter if you switched or not.]]

Named after the longtime host of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft. Even the initial article in 1990 by Marylin Vos Savant (which gave the right answer) got a pre-internet version of this: a lot of people (and not just [[Troll trolls]] and idiots, but math professors as well) [[IRejectYourReality who were "sure" she was wrong and it didn't matter if you switched or not.]]

Named after the longtime host of ''Let's Make a Deal''. It causes a surprising amount of InternetBackdraft.

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 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).