Editing 1282: Monty Hall
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==Explanation== | ==Explanation== | ||
− | This comic is a reference to the US game show | + | This comic is a reference to the {{w|Monty Hall Problem}}, a probability puzzle based on the US game show '{{w|Let's Make a Deal}}' and named after its original host, {{w|Monty Hall}}. The premise of the show was that Hall would offer "deals" to contestants pulled from the audience in which they could win cash and prizes. Some deals involved games/tasks the contestant had to perform, while others simply involved the contestant making choices between a series of doors or boxes. In such games of choice, there were often several prizes and typically at least one "zonk", the show's name for an undesirable "gag" prize, which on the original Monty Hall version of the show were frequently animals such as goats. |
− | In the | + | In the classic version of the Monty Problem, a contestant is offered a choice of three doors. Behind two of the doors are goats, and behind one of them is a car. First, the contestant chooses a door, which remains closed. The host then opens one of the two remaining doors and reveals a goat. The contestant is then offered a final choice of whether to switch his choice to the remaining closed door, or keep the door they originally chose. The problem involves an analysis of the the probability of the contestant choosing the car given certain circumstances. |
− | The problem assumes that a contestant would want to win a car, and would be disappointed to win a goat, which most contestants would have no ability to house, and no use for. The comic shows that [[Beret Guy]], upon the host revealing that door B has a goat behind it, chooses to take the goat to keep as a pet, which makes them both very happy | + | The problem assumes that a contestant would want to win a car, and would be disappointed to win a goat (a zonk), which most contestants would have no ability to house, and no use for. The comic shows that [[Beret Guy]], upon the host revealing that door B has a goat behind it, chooses to take the goat to keep as a pet, which makes them both very happy. |
− | The title text references the car and the | + | The title text references the car and the remaining goat, untouched behind the remaining doors. |
===The Monty Hall Problem=== | ===The Monty Hall Problem=== | ||
− | :'' | + | :''for an in-depth analysis of the Monty Hall Problem, see {{w|Monty Hall Problem|its article at Wikipedia}}'' |
− | The apparent "paradox" of the Monty Hall Problem is that many people's initial reaction once the host opens a door to reveal a goat, is that there are two remaining doors, one with a car and one with a goat; and therefore there is an equal probability the car is behind each door. Many people therefore believe that switching makes no difference to the odds of winning a car. | + | The apparent "paradox" of the Monty Hall Problem is that many people's initial reaction once the host opens a door to reveal a goat, is that there are two remaining doors, one with a car and one with a goat; and therefore there is an equal probability the car is behind each door. Many people therefore believe that switching makes no difference to the odds of winning a car. |
− | + | However, assuming that the host has knowledge of which doors contain goats, and that his choice of which door to open is always an unchosen door containing a goat, it is actually twice as likely that the contestant will win the car if they switch than if they keep their original choice. This is because the contestant initially had a one-in-three chance of choosing the car (and a two-in-three chance of choosing a goat). Switching always wins the car in those two-thirds of cases where the contestant initially chose a goat. The probability of winning by switching is therefore the same as the probability that the contestant initially chose a goat. | |
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− | However, assuming that the host has knowledge of which doors contain goats, and that | ||
The switch essentially gives the contestant ''both'' remaining doors instead of just the ''one'' door originally chosen. Because the host ''always'' has at least one goat available, the fact that the host reveals a goat does not provide the contestant any new information about their initially chosen door. The initial door still has a two-in-three chance of being a goat, and switching still has a two-in-three chance of winning. Opening a goat-door simply shifts all of the probability of the remaining two doors being a car to the remaining unchosen door. | The switch essentially gives the contestant ''both'' remaining doors instead of just the ''one'' door originally chosen. Because the host ''always'' has at least one goat available, the fact that the host reveals a goat does not provide the contestant any new information about their initially chosen door. The initial door still has a two-in-three chance of being a goat, and switching still has a two-in-three chance of winning. Opening a goat-door simply shifts all of the probability of the remaining two doors being a car to the remaining unchosen door. | ||
− | + | There has been great debate about the precise wording of the problem, and what assumptions or rules might apply. Variants of the problem have the host open one of the two remaining doors at random, which could result in the car being revealed, and the game ending. In that scenario, if a goat is revealed, there is in fact an equal probability of winning by switching or keeping the initial door. | |
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− | There has been great debate about the precise wording of the problem, and what assumptions or rules might apply. | ||
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==Transcript== | ==Transcript== | ||
− | :[A | + | :[A game show presenter is standing in front of three doors, the left door labeled "A", the right door labeled "C", and the middle door presumably labeled "B". The "B" door is open. Beret Guy is walking away with a goat.] |
− | :Beret Guy: ... | + | :Beret Guy: ...And my yard has so much grass, and I'll teach you tricks, and... |
− | : | + | :[There is an affectionate heart coming out of the goat's head, as if it likes this idea.] |
==Trivia== | ==Trivia== | ||
− | *The Monty Hall problem is strikingly similar to the {{w|Two envelope problem|Two Envelope Paradox}}, one of [http://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/ several notoriously provocative thought experiments] (some of which are "banned" on the xkcd forums). Admittedly, the Monty Hall problem has only one clear solution. Because of this, it is much less likely to spark the kinds of arguments like "the goddamn airplane on the goddamn treadmill" or the " | + | *The Monty Hall problem is strikingly similar to the {{w|Two envelope problem|Two Envelope Paradox}}, one of [http://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/ several notoriously provocative thought experiments] (some of which are "banned" on the xkcd forums). Admittedly, the Monty Hall problem has only one clear solution. Because of this, it is much less likely to spark the kinds of arguments like "the goddamn airplane on the goddamn treadmill" or the "Feynman sprinkler" incite. |
{{comic discussion}} | {{comic discussion}} | ||
[[Category:Comics featuring Beret Guy]] | [[Category:Comics featuring Beret Guy]] |