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* In ''Film/SpeedZone'', Alec demonstrates this perfectly while trying to convince Vic to let him bet on the race:
-->'''Alec:''' Give me your hand. Now, how long have I been placing bets with Big Wally?\\
'''Vic:''' Eight years.\\
'''Alec:''' Eight years. ''(writes it on Vic's hand)'' Now, how many months are in a year?\\
'''Vic:''' ''(jerking his hand away)'' What is this?\\
'''Alec:''' ''(taking his hand again)'' How many months?\\
'''Vic:''' Twelve.\\
'''Alec:''' Right! ''(writes on Vic's hand)'' Twelve times eight is ni, ni, ninety...\\
'''Vic:''' Six.\\
'''Alec:''' Right! Now, the odds on the Jag are a hundred to one. One hundred minus ninety-six is...sounds like Dinah Shore, shut the door, f-f-f-\\
'''Vic:''' Four.\\
'''Alec:''' Right! Now you can see their odds are a hundred to one. My odds are four. Vic, I can win even if that car blows all four tires and an engine!


* The [[LetsPlay/AchievementHunter Achievement Hunters]] had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his unexpected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to under stand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.

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* The [[LetsPlay/AchievementHunter Achievement Hunters]] Creator/AchievementHunter has had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his unexpected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to under stand understand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.

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* If the game has memory, this usually doesn't apply (as stated in the description). Ironically, slot machines, once the poster boy of this fallacy, usually do have quite a bit of memory these days. Most actually do have slightly better odds the more they have been played, and many will basically force a (small) payout every so often. This is for two reasons. The first is that small fairly consistent payouts can keep a player playing, and the second is so those ads about their chances aren't false advertising.


[[AC:Web Orginal]]
* The [[LetsPlay/AchievementHunter Achievement Hunters]] had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his expected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to under stand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.

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* The [[LetsPlay/AchievementHunter Achievement Hunters]] had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his expected unexpected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to under stand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.

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[[AC:Web Orginal]]
* The [[LetsPlay/AchievementHunter Achievement Hunters]] had a long drawn out ''multiple video'' discussion on this. It started with Geoff asking Gavin an inane would you rather question that involved calling the outcome of three coin flips. They asked Ryan for the odds only to be confused by his expected complicated explanation. A video later it came down to Ryan correctly pointing out the fallacy and Gavin not getting it (though Gavin's... unique... phraseology was a contributing factor, at points he seemed to under stand the fallacy but couldn't really say it or understand how Ryan was saying it). Humorously they decided to end it by actually doing to experiment... only for all the coins to land heads up, blowing Gavin's mind.


Note that Gambler's Fallacy applies only to systems that both ''have no memory'', and ''are explicitly known to be fair''. Drawing cards without replacement (read, deck now has "memory") does alter the probabilities of the next cards drawn, and if you do not explicitly know that the event being tested is fair, you can use things like n-heads-in-a-row to draw conclusions of bias in the system (see Non-examples and Theater sections below).

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Note that Gambler's Fallacy applies only to systems that both ''have no memory'', and ''are explicitly known to be fair''. Drawing cards without replacement (read, deck now has "memory") does alter the probabilities of the next cards drawn, and if you do not explicitly know that the event being tested is fair, you can use things like n-heads-in-a-row to draw conclusions of bias in the system (see Non-examples and Theater Theatre sections below).


** However this fallacy doesn't apply to older purely mechanical slots. In theory these also use a random number generator, but the analog system can potentially wear down. This leads to a case where certain individual machines favor certain combinations above others because they are more likely to stop in certain places. This is why, despite their iconic nature, no sane casinos still use the old three reel slot machines. [[note]]That and classic three reel slots have an exponentially lower number of states than a modern digital slots since digital slots have more reels and each reel has more characters on it.[[/note]]

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** However this fallacy doesn't apply to older purely mechanical slots. In theory these also use a random number generator, but the analog system can potentially wear down. This leads to a case where certain individual machines favor certain combinations above others because they are more likely to stop in certain places. This is why, despite their iconic nature, no sane casinos still use the old three reel slot machines. [[note]]That [[note]]That, and classic three reel slots have an exponentially lower number of states than a modern digital slots slots, since digital slots have more reels and each reel has more characters on it.[[/note]]

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** They're also across the street from the Alchemists' Guild, which in itself illustrates this. The Alchemists' Guild can't [[StuffBlowingUp blow up]] ''again'', can it? (...Yes, it can.)


* {{Stephen King}}'s characters reason like this a couple of times, although one of the times [[AuthorAvatar the character is himself]].

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* {{Stephen King}}'s Creator/StephenKing's characters reason like this a couple of times, although one of the times [[AuthorAvatar the character is himself]].

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** However this fallacy doesn't apply to older purely mechanical slots. In theory these also use a random number generator, but the analog system can potentially wear down. This leads to a case where certain individual machines favor certain combinations above others because they are more likely to stop in certain places. This is why, despite their iconic nature, no sane casinos still use the old three reel slot machines. [[note]]That and classic three reel slots have an exponentially lower number of states than a modern digital slots since digital slots have more reels and each reel has more characters on it.[[/note]]

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[[AC: Anime & Manga]]
* In the second Revival Round of ''Manga/LiarGame'', Nao falls into this, thinking that after her opponent had won a one-in-four chance gamble three times in a row, that it would be incredibly improbable for her to win a 4th time, meaning that she should bet all-in. [[spoiler: It's actually pretense for a trap. Nao had been fooling her opponent into think that she had a tell so that she can trick her into a massive loss. Nao was probably well aware of the actual odds but needed justification for her seemingly stupid bet.]]


Believing that dice/coins have memory, or that independent events will occur in "streaks". If a coin has just landed on heads four times in a row, surely it's much more likely to get tails this time, to even things out... or alternatively, heads is on a roll and will appear next time, too. See also RandomNumberGod and ArtisticLicenceStatistics. In fact, if you toss a previously untested coin and (say) heads come up, there's a larger chance to get heads on a second roll, because the coin might be biased, although not very much larger, unless the coin is so warped that the imperfection is clearly visible.

Psychologically, this fallacy tends to come from the fact that the odds to replicate a pattern ''do'' go up cumulatively. The probability of rolling 20 on a d20 twice is 1/400, the same as any expected sequence of two numbers. The probability of rolling the first is 1/20, and the probability of rolling the second is also 1/20. The fallacy occurs when someone assumes that once they've rolled two 20s in a row, it's less likely than usual (< 1/20) that they'll get another 20. In reality, once they've rolled two 20s in a row, it's just as likely as ever (1/20) that they'll roll a 20 again. This also, most notably, works the other way around - if they've lost many bets in a row, they aren't any more likely to win the next bet. Psychologically, what you're doing is inventing patterns that fit with the events you observe despite not really being there at all, combined with a big scoop of entitlement.

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Believing that dice/coins have memory, or that independent events will occur in "streaks". If a coin has just landed on heads four times in a row, surely it's much more likely to get tails this time, to even things out... or alternatively, heads is on a roll and will appear next time, too. See also RandomNumberGod and ArtisticLicenceStatistics. In fact, if you toss a previously untested coin and (say) heads come up, there's a larger chance to get heads on a second roll, because the coin might be biased, although not very much larger, unless the coin is so warped that the imperfection is clearly visible.

ArtisticLicenceStatistics.

Psychologically, this fallacy tends to come from the fact that the odds to replicate a pattern ''do'' go up cumulatively. The probability of rolling 20 on a d20 twice is 1/400, the same as any expected sequence of two numbers. The probability of rolling the first is 1/20, and the probability of rolling the second is also 1/20. The fallacy occurs when someone assumes that once they've rolled two 20s in a row, it's less likely than usual (< 1/20) that they'll get another 20. In reality, once they've rolled two 20s in a row, it's just as likely as ever (1/20) that they'll roll a 20 again. This also, most notably, works the other way around - if they've lost many bets in a row, they aren't any more likely to win the next bet. Psychologically, what you're doing is inventing desirable patterns that fit with the events you observe despite the patterns not really being there at all, combined with a big scoop of entitlement.
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To explain the above in another way, flip a coin 10 times, and the chances that heads was flipped 4 times or more is 82.81%. Flip it 1000 times, and the chances heads was flipped 400 times or more is 99.99999999%. But even if it was less than 400, the next flip will still be 50/50. This is also the reason why playing a high number of low-stakes games in Casinos increases the chances of the house making money; the house advantage only affects who wins a small percentage of the time, but this advantage "evens out" over the long haul. Unless you're a good card counter, taking advantage of free stuff, or just enjoy playing, you're more likely to be successful with a small number of high-stakes events.

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To explain the above in another way, flip a coin 10 times, and the chances that heads was flipped 4 times or more is 82.81%. Flip it 1000 times, and the chances heads was flipped 400 times or more is 99.99999999%. But even if it was less than 400, the next flip will still be 50/50.50/50: long-term odds predict the general trend of many results, not what will happen in a specific instance. This is also the reason why playing a high number of low-stakes games in Casinos increases the chances of the house making money; the house advantage only affects who wins a small percentage of the time, but this advantage "evens out" over the long haul. Unless you're a good card counter, taking advantage of free stuff, or just enjoy playing, you're more likely to be successful with a small number of high-stakes events.



* If it has not been established that the trials are fair, then a significant deviation from the expected results could count as evidence that they are biased somehow. If a die rolls a 6 at least 10 times in a row, simple statistics say that the die is extremely likely to be weighted, which means that, [[IKnowYouKnowIKnow your adversary trying to manipulate you notwithstanding]], you'd better bet on another 6.

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* If it has not been established that the trials are fair, then a significant deviation from the expected results could count as evidence that they are biased somehow. If a die rolls a 6 at least 10 times in a row, simple statistics say that the die is extremely likely to be weighted, which means that, [[IKnowYouKnowIKnow your adversary trying to manipulate you notwithstanding]], you'd better bet on another 6. This is also how sniper rifles were selected until fairly recently: while all rifles from a production line should theoretically shoot the same, in practice variations in assembly produced weapons that were consistently more accurate than the norm. Rather than it being assumed this was some incredibly consistent coincidence, militaries put scopes on these rifles and gave them to men with particularly impressive moustaches.



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* {{Stephen King}}'s characters reason like this a couple of times, although one of the times [[AuthorAvatar the character is himself]].
** In ''Literature/TheLangoliers'', the characters are faced with the mystery of how most people on their airplane have vanished while they slept. They are only saved because one of the passengers still present can fly the plane, which is, of course, an unlikely coincidence. At the point where they still assume that the same has happened to other planes in the air, one of them reasons that the odds anyone else has survived it like them are minuscule because it happening a second time have now become as unlikely as it happening twice since it already happened once. (As opposed to: it's unlikely to happen twice, but if the unlikely already happened once, that doesn't affect future odds.)
** In ''Literature/SongOfSusannah'', King fictionalizes his own nearly fatal car accident. Before it happens, his AuthorAvatar is shown musing that since a similar accident happened in the area recently, the odds of something like that happening to him have dropped to almost zero. He doesn't say why, but he certainly doesn't say it's because people will be really careful now.



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* Job seekers invoke this when sending out resumes or applications to employers and job postings. They may believe that the more they apply, at least one will have to hire them sooner or later. Hiring though can be reliant on many factors such as the overall economy, the job outlook in an industry or occupation, the number of applicants, one's credentials and so on.
* The above example also applies to creative professionals such as the writer who constantly submits to publishing houses, the musician who sends out demo recordings to many record labels, etc. They may believe that sooner or later, at least one will have to accept out of the many submissions. Again, being accepted, signed on, published, etc. often depends on many factors such as the market, the quality of the applicant's submission, and so on.


Psychologically, this fallacy tends to come from the fact that the odds to replicate a pattern ''do'' go up cumulatively. The odds of rolling 20 on a d20 twice is 1/400, the same as any expected sequence of two numbers. The odds of rolling the first is 1/20, and the odds of rolling the second is also 1/20. The fallacy occurs when someone assumes that once they've rolled two 20s in a row, it's less likely than usual (< 1/20) that they'll get another 20. In reality, once they've rolled two 20s in a row, it's just as likely as ever (1/20) that they'll roll a 20 again. This also, most notably, works the other way around - if they've lost many bets in a row, they aren't any more likely to win the next bet. Psychologically, what you're doing is inventing patterns that fit with the events you observe despite not really being there at all, combined with a big scoop of entitlement.

A similar misinterpretation is that if an event has the odds of 1-in-n, then you are guaranteed a success if you make n attempts. As an exaggerated example, the probability of a "heads" on an unbiased coin is 1/2, therefore, flipping a coin twice is guaranteed to get at least one "heads." This is not true.

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Psychologically, this fallacy tends to come from the fact that the odds to replicate a pattern ''do'' go up cumulatively. The odds probability of rolling 20 on a d20 twice is 1/400, the same as any expected sequence of two numbers. The odds probability of rolling the first is 1/20, and the odds probability of rolling the second is also 1/20. The fallacy occurs when someone assumes that once they've rolled two 20s in a row, it's less likely than usual (< 1/20) that they'll get another 20. In reality, once they've rolled two 20s in a row, it's just as likely as ever (1/20) that they'll roll a 20 again. This also, most notably, works the other way around - if they've lost many bets in a row, they aren't any more likely to win the next bet. Psychologically, what you're doing is inventing patterns that fit with the events you observe despite not really being there at all, combined with a big scoop of entitlement.

A similar misinterpretation is that if an event has the odds a probability of 1-in-n, then you are guaranteed a success if you make n attempts. As an exaggerated example, the probability of a "heads" on an unbiased coin is 1/2, therefore, flipping a coin twice is guaranteed to get at least one "heads." This is not true.

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