History Main / GamblersFallacy

5th May '18 10:40:25 AM LadyJafaria
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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.)
4th Mar '18 4:39:22 PM nombretomado
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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]].

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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]].
16th Jan '18 8:21:03 PM Caps-luna
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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]]
7th Dec '17 5:04:09 PM Jgamer
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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.]]
20th Nov '17 10:59:42 AM garthvader
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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.

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.
13th Sep '17 6:30:24 AM VVK
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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.
6th Aug '17 9:37:47 AM MaxWest2
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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.
11th Feb '17 7:57:03 PM mlsmithca
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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 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.
14th Sep '16 9:40:41 PM Premonition45
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** In "Margical History Tour", the retelling of Henry VIII's life shows Henry (Homer) meeting Anne Boleyn (Lindsay Naegle), who touts her track record of bearing sons. So, they marry, but she produces a daughter, And Henry has her beheaded for it.
14th Aug '16 7:08:20 PM MsChibi
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* On ''Series/MyNameIsEarl'', Earl mentions a NoodleIncident wherein he lost a series of Rock-Paper-Scissors games to a monkey. The monkey threw "Rock" several times, and just when Earl decided to throw "Paper," the monkey threw "Scissors."
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http://tvtropes.org/pmwiki/article_history.php?article=Main.GamblersFallacy