History Main / GamblersFallacy

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."
2nd Aug '16 5:59:17 PM Premonition45
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Compare SunkCostFallacy.
24th Jun '16 11:45:50 AM HiddenWindshield
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* Generally speaking, many video games have a mechanic that tweaks the RNG, so that long strings of excessively bad (or good) luck are less likely than they would be in a memoryless system. This is partly because players expect this, and partly such strings are friggin annoying to deal with in games that aren't centered around being CrazyPrepared to deal with them.

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* Generally speaking, many video games have a mechanic that tweaks the RNG, so that long strings of excessively bad (or good) luck are less likely than they would be in a memoryless system. This is partly because players expect this, and partly because such strings are [[TropesAreNotBad really friggin annoying to deal with with]] (at least, in games that aren't centered around being CrazyPrepared to deal with them.them).
13th Jun '16 2:02:41 AM PaulA
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* The narrator in Creator/EdgarAllanPoe's "The Mystery of Marie Roget" mistakenly believes that this fallacy is right, although finds it hard to convince someone.
-->Nothing, for example, is more difficult than to convince the merely general reader that the fact of sixes having been thrown twice in succession by a player at dice, is sufficient cause for betting the largest odds that sixes will not be thrown in the third attempt. A suggestion to this effect is usually rejected by the intellect at once. It does not appear that the two throws which have been completed, and which lie now absolutely in the Past, can have influence upon the throw which exists only in the Future. The chance for throwing sixes seems to be precisely as it was at any ordinary time—that is to say, subject only to the influence of the various other throws which may be made by the dice. And this is a reflection which appears so exceedingly obvious that attempts to controvert it are received more frequently with a derisive smile than with anything like respectful attention.

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* The narrator in Creator/EdgarAllanPoe's "The Mystery of Marie Roget" "Literature/TheMysteryOfMarieRoget" mistakenly believes that this fallacy is right, although finds it hard to convince someone.
-->Nothing, for example, is more difficult than to convince the merely general reader that the fact of sixes having been thrown twice in succession by a player at dice, is sufficient cause for betting the largest odds that sixes will not be thrown in the third attempt. A suggestion to this effect is usually rejected by the intellect at once. It does not appear that the two throws which have been completed, and which lie now absolutely in the Past, can have influence upon the throw which exists only in the Future. The chance for throwing sixes seems to be precisely as it was at any ordinary time—that time--that is to say, subject only to the influence of the various other throws which may be made by the dice. And this is a reflection which appears so exceedingly obvious that attempts to controvert it are received more frequently with a derisive smile than with anything like respectful attention.
10th Apr '16 2:16:40 PM Josef5678
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* Similar to the roulette example above, gamblers apply this logic to slot machines, which is pointed out in the book ''[[http://www.amazon.com/Smart-Slot-Strategies-mathematical-strategies/dp/1453609261/ref=sr_1_1?ie=UTF8&qid=1351266797&sr=8-1&keywords=smart+slot+strategies Smart Slot Strategies]]''. The author points out how gamblers will ignore the fact that a machine is controlled by a random number generator and will assume a machine is "hot" or "cold" based on how it's performing. It's further explained that many players believe they can tell how a machine is programmed by playing the machine around 20 times, despite the random number generator having millions of possibilities. A sample size of 20 plays is far too small to determine any trend in a population that size. With that said, individual machines really can be set with different payout tables. Still, 20 plays is too small for trends.

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* Similar to the roulette example above, gamblers Gamblers apply this logic to slot machines, which is pointed out in the book ''[[http://www.amazon.com/Smart-Slot-Strategies-mathematical-strategies/dp/1453609261/ref=sr_1_1?ie=UTF8&qid=1351266797&sr=8-1&keywords=smart+slot+strategies Smart Slot Strategies]]''. The author points out how gamblers will ignore the fact that a machine is controlled by a random number generator and will assume a machine is "hot" or "cold" based on how it's performing. It's further explained that many players believe they can tell how a machine is programmed by playing the machine around 20 times, despite the random number generator having millions of possibilities. A sample size of 20 plays is far too small to determine any trend in a population that size. With that said, individual machines really can be set with different payout tables. Still, 20 plays is too small for trends.
7th Apr '16 6:22:18 PM Nakuyabi
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* During each of the World Wars, a variant of this appeared as the Shell Hole Fallacy: when enemy artillery were randomly blazing away at the field, some troops (and some commanders!) believed that jumping into a crater a bursting shell had just made would increase their chances of survival, since the odds of a place being hit ''twice'' during any giving shelling were relatively low. While the artillery gunners weren't ''entirely'' unbiased (since they were trying to distribute their shots so as to hit as many parts of the field as possible in hopes of maximizing the number of targets hit), they really didn't have much control over any of the randomizing factors, so the actual odds that any given shell would strike where one had already struck were pretty much the same as the odds of that place being struck the first time. In any event, jumping into those craters did not perceptibly improve the soldiers' survival rate.
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