History Main / MontyHallProblem

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 doesn't apply to Monty Hall.

* ''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%.

** 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".

-->-- '''Monty Hall''', July 1991

* ''Series/Brooklyn99'' 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."

-->''"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.''\\

-->[-''"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-]

* ''Film/TwentyOne'', where they manage to completely [[WritersCannotDoMath screw up the answer to the problem]].
** Specifically, 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 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%.

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 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.

* Referenced in ''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.

* 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.

* The cat in the ''WesternAnimation/LooneyTunes'' cartoon "Early To Bet" is in crutches by the end of the film after enduring punishments from losing at gin rummy to a bulldog. When the bulldog finally calls the game off, not wanting the cat to suffer any further, trhe Gambling Bug (which caused the cat to play gin rummy with the dog in the first place) offers to play the cat for high card. The cat draws a three. "Not so good, cat. Watch." The Gambling bug's draw: a two. The cat dishes out his own punishment to the Gambling Bug--a rolled up copy of the Post ("No, no! Not the Post!")

** Specifically, 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 if it is indeed a trick and Monty only offers the switch when the correct door is picked, then switching gives a 100% chance of receiving a goat.

* ''Film/TwentyOne'', where they manage to completely [[WritersCannotDoMath 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.

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.

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).

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.

''"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."''

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.

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).

[[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.)

----

* ''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.

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.

* 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.

%%* ''Series/{{Numb3rs}}''

* 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'.

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.

!!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}}]]

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

[[AC:{{Webcomics}}]]

[[AC:{{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}}]]

* 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}}''

* ''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.