History Main / MontyHallProblem

* 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'.

* ''[[Film/TwentyOne 21]]''

* ''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.)

* 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'.

* ''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.

* In the first episode of ''The Thirteen Ghosts of ScoobyDoo'', 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.

* In the first episode of ''The Thirteen Ghosts of ScoobyDoo'', ThoseTwoBadGuys trick Scooby and Shaggy into opening the Chest of Demons this way. Posing as a game show (In an ancient castle in the Himilayas, 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.

* ''Series/JamesMaysManLab'' did a RussianRoulette version of this with beer cans called, wait for it, [[TheDeerHunter The Beer Hunter]]. Rules where simple three cans, two of which where shaken up, James would pick one can but always change his mind while 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 for 100 rounds, they ended up getting hypothermia, but James won 40:60.

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

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.

* ''[[TheCuriousIncidentOfTheDogInTheNightTime The Curious Incident of the Dog in the Night-Time]]''

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 that case, your odds do not improve one way or the other (if the car even remains unrevealed).

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. [[hottip:*: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.]]

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

* Subverted in ''DealOrNoDeal.'' While a contestant who reached the final case was offered the opportunity to switch it out with his/her case, Howie 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.

* 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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A classic mathematical problem involving probabilites. The basic form is based on one of the games on the GameShow ''[=~Let's Make a Deal~=]''. 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. [[hottip:*: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.]]

A classic mathematical problem involving probabilites. The basic form is based on one of the games on the GameShow ''[=~Let's Make a Deal~=]''. 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. [[hottip:*: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. 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.]]

* Marilyn Vos Savant, author of Parade Magazine's Ask Marilyn, is one of the [[{{pride}} pro]][[InsufferableGenius ud]] few who got it completely right. (She addressed the ambiguities in a follow-up column.)

A classic mathematical problem involving probabilites. The basic form is based on one of the games on the GameShow ''[=~Let's Make a Deal~=]''. 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. [[hottip:*:The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. 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.]]

A classic mathematical problem involving probabilites. The basic form is based on one of the games on the GameShow ''[=~Let's Make a Deal~=]''. 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. [[hottip:*:The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door, because there was a 2 in 3 chance that the door you picked had a goat behind it. 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.]]

A classic mathematical problem involving probabilites. The basic form is based on one of the games on the GameShow ''[=~Let's Make a Deal~=]''. 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. [[hottip:*:The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. 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.]]

A classic mathematical problem involving probabilites. The basic form is based on one of the games on the GameShow ''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 other two doors, revealing a goat. The contestant is then offered the choice to switch to the unrevealed door or stick with his original decision. [[hottip:*:The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. 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 that case, your odds do not improve one way or another (if the car even remains unrevealed).

How it worked out on the show is irrelevant, especially since Monty Hall himself is alleged to have said that he usually only offered the switch if the contestant had picked correctly in the first place.

This trope makes an appearance in:
* ''{{Numb3rs}}''

*Explained six different ways (including a list of everything that might happen) in Ian Stewart's ''TheMagicalMaze''.
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* Parade Magazine's Ask Marilyn is one of the [[{{pride}} pro]][[InsufferableGenius ud]] few who got it completely right. (She adressed the ambiguities in a follow up column.)

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A classic mathematical problem involving probabilites. The basic form is based on one of the games on the GameShow ''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 other two doors, revealing a goat. The contestant is then offered the choice to switch to the unrevealed door or stick with his original decision. [[hottip:*:The correct answer is to switch, as the probability is 66.7% that the car will be behind the other door. 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.]]