Editing Gambler's fallacy (section)

==Psychology==

===Origins===
The gambler's fallacy arises out of a belief in a [[Hasty generalization|law of small numbers]], leading to the erroneous belief that small samples must be representative of the larger population. According to the fallacy, streaks must eventually even out in order to be representative.<ref name=TverskyKahneman1971>{{cite journal |last=Tversky |first=Amos |author2=Daniel Kahneman |year=1971 |title=Belief in the law of small numbers |journal=Psychological Bulletin |volume=76 |issue=2 |pages=105–110 |doi=10.1037/h0031322|url=http://www.nurs.or.jp/~lionfan/small_e.pdf |archive-url=https://web.archive.org/web/20170706083653/http://www.nurs.or.jp/%7Elionfan/small_e.pdf |archive-date=2017-07-06 |url-status=live |citeseerx=10.1.1.592.3838 }}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] first proposed that the gambler's fallacy is a [[cognitive bias]] produced by a [[heuristics in judgement and decision making|psychological heuristic]] called the [[representativeness heuristic]], which states that people evaluate the probability of a certain event by assessing how similar it is to events they have experienced before, and how similar the events surrounding those two processes are.<ref name=TverskyKahneman1974>{{cite journal |last=Tversky |first=Amos |author2=Daniel Kahneman |year=1974 |volume=185 |title=Judgment under uncertainty: Heuristics and biases |journal=Science |pages=1124–1131 |doi=10.1126/science.185.4157.1124 |pmid=17835457 |issue=4157 |bibcode=1974Sci...185.1124T |s2cid=143452957 |url=http://www.dtic.mil/docs/citations/AD0767426 |access-date=2017-06-19 |archive-date=2018-06-01 |archive-url=https://web.archive.org/web/20180601235707/http://www.dtic.mil/docs/citations/AD0767426 |url-status=dead }}</ref><ref name=TverskyKahneman1971/> According to this view, "after observing a long run of red on the roulette wheel, for example, most people erroneously believe that black will result in a more representative sequence than the occurrence of an additional red",<ref name=TverskyKahneman1974 /> so people expect that a short run of random outcomes should share properties of a longer run, specifically in that deviations from average should balance out. When people are asked to make up a random-looking sequence of coin tosses, they tend to make sequences where the proportion of heads to tails stays closer to 0.5 in any short segment than would be predicted by chance, a phenomenon known as [[insensitivity to sample size]].<ref>{{cite journal |last=Tune |first=G. S. |title=Response preferences: A review of some relevant literature |journal=Psychological Bulletin |year= 1964 |volume=61 |pages=286–302 |doi=10.1037/h0048618 |pmid=14140335 |issue=4}}</ref> Kahneman and Tversky interpret this to mean that people believe short sequences of random events should be representative of longer ones.<ref name=TverskyKahneman1971 /> The representativeness heuristic is also cited behind the related phenomenon of the [[clustering illusion]], according to which people see streaks of random events as being non-random when such streaks are actually much more likely to occur in small samples than people expect.<ref>{{cite book |first=Thomas |last=Gilovich |author-link=Thomas Gilovich |title=How we know what isn't so |url=https://archive.org/details/howweknowwhatisn00gilorich |url-access=registration |year=1991 |publisher=The Free Press |location=New York |isbn=978-0-02-911706-4 |pages=[https://archive.org/details/howweknowwhatisn00gilorich/page/16 16–19]}}</ref>

The gambler's fallacy can also be attributed to the mistaken belief that gambling, or even chance itself, is a fair process that can correct itself in the event of streaks, known as the [[just-world fallacy]].<ref name="Rogers1998">{{cite journal|last1=Rogers|first1=Paul|title=The cognitive psychology of lottery gambling: A theoretical review|journal=Journal of Gambling Studies|volume=14|issue=2|year=1998|pages=111–134|issn=1050-5350|doi=10.1023/A:1023042708217|pmid=12766438|s2cid=21141130}}</ref> Other researchers believe that belief in the fallacy may be the result of a mistaken belief in an [[internal locus of control]]. When a person believes that gambling outcomes are the result of their own skill, they may be more susceptible to the gambler's fallacy because they reject the idea that chance could overcome skill or talent.<ref name=SundaliCroson2006 />

===Variations===
Some researchers believe that it is possible to define two types of gambler's fallacy: type&nbsp;one and type&nbsp;two. Type&nbsp;one is the classic gambler's fallacy, where individuals believe that a particular outcome is due after a long streak of another outcome. Type&nbsp;two gambler's fallacy, as defined by Gideon Keren and Charles Lewis, occurs when a gambler underestimates how many observations are needed to detect a favorable outcome, such as watching a roulette wheel for a length of time and then betting on the numbers that appear most often. For events with a high degree of randomness, detecting a bias that will lead to a favorable outcome takes an impractically large amount of time and is very difficult, if not impossible, to do.<ref name="KerenLewis1994">{{cite journal|last1=Keren|first1=Gideon|last2=Lewis|first2=Charles|title=The Two Fallacies of Gamblers: Type I and Type II|journal=Organizational Behavior and Human Decision Processes|volume=60|issue=1|year=1994|pages=75–89|issn=0749-5978|doi=10.1006/obhd.1994.1075}}</ref> The two types differ in that type&nbsp;one wrongly assumes that gambling conditions are fair and perfect, while type&nbsp;two assumes that the conditions are biased, and that this bias can be detected after a certain amount of time.

Another variety, known as the retrospective gambler's fallacy, occurs when individuals judge that a seemingly rare event must come from a longer sequence than a more common event does. The belief that an imaginary sequence of die rolls is more than three times as long when a set of three sixes is observed as opposed to when there are only two sixes. This effect can be observed in isolated instances, or even sequentially. Another example would involve hearing that a teenager has [[unprotected sex]] and becomes pregnant on a given night, and concluding that she has been engaging in unprotected sex for longer than if we hear she had unprotected sex but did not become pregnant, when the probability of becoming pregnant as a result of each intercourse is independent of the amount of prior intercourse.<ref>{{cite journal | last1 = Oppenheimer | first1 = D. M. | last2 = Monin | first2 = B. | year = 2009 | title = The retrospective gambler's fallacy: Unlikely events, constructing the past, and multiple universes | journal = Judgment and Decision Making | volume = 4 | issue = 5 | pages = 326–334 | doi = 10.1017/S1930297500001170 | s2cid = 18859806 | doi-access = free }}</ref>

===Relationship to hot-hand fallacy===
Another psychological perspective states that gambler's fallacy can be seen as the counterpart to basketball's [[hot-hand fallacy]], in which people tend to predict the same outcome as the previous event - known as positive recency - resulting in a belief that a high scorer will continue to score. In the gambler's fallacy, people predict the opposite outcome of the previous event - negative recency - believing that since the roulette wheel has landed on black on the previous six occasions, it is due to land on red the next. Ayton and Fischer have theorized that people display positive recency for the hot-hand fallacy because the fallacy deals with human performance, and that people do not believe that an inanimate object can become "hot."<ref>{{cite journal | last1 = Ayton | first1 = P. | last2 = Fischer | first2 = I. | year = 2004 | title = The hot-hand fallacy and the gambler's fallacy: Two faces of subjective randomness? | journal = Memory and Cognition | volume = 32 | issue = 8| pages = 1369–1378 | doi=10.3758/bf03206327| pmid = 15900930 | doi-access = free }}</ref> Human performance is not perceived as random, and people are more likely to continue streaks when they believe that the process generating the results is nonrandom.<ref name="Burns2004">{{cite journal|last1=Burns|first1=Bruce D.|last2=Corpus|first2=Bryan|title=Randomness and inductions from streaks: "Gambler's fallacy" versus "hot hand"|journal=Psychonomic Bulletin & Review|volume=11|issue=1|year=2004|pages=179–184|issn=1069-9384|doi=10.3758/BF03206480|pmid=15117006|doi-access=free}}</ref> When a person exhibits the gambler's fallacy, they are more likely to exhibit the hot-hand fallacy as well, suggesting that one construct is responsible for the two fallacies.<ref name=SundaliCroson2006>{{cite journal | last1 = Sundali | first1 = J. | last2 = Croson | first2 = R. | year = 2006 | title = Biases in casino betting: The hot hand and the gambler's fallacy | journal = Judgment and Decision Making | volume = 1 | pages = 1–12 | doi = 10.1017/S1930297500000309 | s2cid = 5019574 | doi-access = free }}</ref>

The difference between the two fallacies is also found in economic decision-making. A study by Huber, Kirchler, and Stockl in 2010 examined how the hot hand and the gambler's fallacy are exhibited in the financial market. The researchers gave their participants a choice: they could either bet on the outcome of a series of coin tosses, use an expert opinion to sway their decision, or choose a risk-free alternative instead for a smaller financial reward. Participants turned to the expert opinion to make their decision 24% of the time based on their past experience of success, which exemplifies the hot-hand. If the expert was correct, 78% of the participants chose the expert's opinion again, as opposed to 57% doing so when the expert was wrong. The participants also exhibited the gambler's fallacy, with their selection of either heads or tails decreasing after noticing a streak of either outcome. This experiment helped bolster Ayton and Fischer's theory that people put more faith in human performance than they do in seemingly random processes.<ref>{{cite journal | last1 = Huber | first1 = J. | last2 = Kirchler | first2 = M. | last3 = Stockl | first3 = T. | year = 2010 | title = The hot hand belief and the gambler's fallacy in investment decisions under risk | journal = Theory and Decision | volume = 68 | issue = 4| pages = 445–462 | doi=10.1007/s11238-008-9106-2| s2cid = 154661530 }}</ref>

===Neurophysiology===
While the [[representativeness heuristic]] and other cognitive biases are the most commonly cited cause of the gambler's fallacy, research suggests that there may also be a [[Neurology|neurological]] component. [[Functional magnetic resonance imaging]] has shown that after losing a bet or gamble, known as riskloss, the [[frontoparietal network]] of the brain is activated, resulting in more risk-taking behavior. In contrast, there is decreased activity in the [[amygdala]], [[caudate nucleus|caudate]], and [[ventral striatum]] after a riskloss. Activation in the amygdala is [[Negative correlation|negatively correlated]] with gambler's fallacy, so that the more activity exhibited in the amygdala, the less likely an individual is to fall prey to the gambler's fallacy. These results suggest that gambler's fallacy relies more on the [[prefrontal cortex]], which is responsible for [[Executive functions|executive]], goal-directed processes, and less on the brain areas that control [[Affect (psychology)|affective]] decision-making.

The desire to continue gambling or betting is controlled by the [[striatum]], which supports a choice-outcome contingency learning method. The striatum processes the errors in prediction and the behavior changes accordingly. After a win, the positive behavior is [[Reinforcement|reinforced]] and after a loss, the behavior is [[Operant conditioning|conditioned]] to be avoided. In individuals exhibiting the gambler's fallacy, this choice-outcome contingency method is impaired, and they continue to make risks after a series of losses.<ref>{{cite journal | last1 = Xue | first1 = G. | last2 = Lu | first2 = Z. | last3 = Levin | first3 = I. P. | last4 = Bechara | first4 = A. | year = 2011 | title = An fMRI study of risk-taking following wins and losses: Implications for the gambler's fallacy | journal = Human Brain Mapping | volume = 32 | issue = 2| pages = 271–281 | doi=10.1002/hbm.21015| pmc = 3429350 | pmid=21229615}}</ref>

===Possible solutions===
The gambler's fallacy is a deep-seated cognitive bias and can be very hard to overcome. Educating individuals about the nature of randomness has not always proven effective in reducing or eliminating any manifestation of the fallacy. Participants in a study by Beach and Swensson in 1967 were shown a shuffled deck of index cards with shapes on them, and were instructed to guess which shape would come next in a sequence. The [[Treatment and control groups|experimental group]] of participants was informed about the nature and existence of the gambler's fallacy, and were explicitly instructed not to rely on run dependency to make their guesses. The [[control group]] was not given this information. The response styles of the two groups were similar, indicating that the experimental group still based their choices on the length of the run sequence. This led to the conclusion that instructing individuals about randomness is not sufficient in lessening the gambler's fallacy.<ref>{{cite journal | last1 = Beach | first1 = L. R. | last2 = Swensson | first2 = R. G. | year = 1967 | title = Instructions about randomness and run dependency in two-choice learning | journal = Journal of Experimental Psychology | volume = 75 | issue = 2| pages = 279–282 | doi=10.1037/h0024979| pmid = 6062970 }}</ref>

An individual's susceptibility to the gambler's fallacy may decrease with age. A study by Fischbein and Schnarch in 1997 administered a questionnaire to five groups: students in grades 5, 7, 9, 11, and college students specializing in teaching mathematics. None of the participants had received any prior education regarding probability. The question asked was: "Ronni flipped a coin three times and in all cases heads came up. Ronni intends to flip the coin again. What is the chance of getting heads the fourth time?" The results indicated that as the students got older, the less likely they were to answer with "smaller than the chance of getting tails", which would indicate a negative recency effect. 35% of the 5th graders, 35% of the 7th graders, and 20% of the 9th graders exhibited the negative recency effect. Only 10% of the 11th graders answered this way, and none of the college students did. Fischbein and Schnarch theorized that an individual's tendency to rely on the [[representativeness heuristic]] and other cognitive biases can be overcome with age.<ref>{{cite journal | last1 = Fischbein | first1 = E. | last2 = Schnarch | first2 = D. | year = 1997 | title = The evolution with age of probabilistic, intuitively based misconceptions | journal = Journal for Research in Mathematics Education | volume = 28 | issue = 1| pages = 96–105 | doi=10.2307/749665| jstor = 749665 }}</ref>

Another possible solution comes from Roney and Trick, [[Gestalt psychology|Gestalt]] psychologists who suggest that the fallacy may be eliminated as a result of grouping. When a future event such as a coin toss is described as part of a sequence, no matter how arbitrarily, a person will automatically consider the event as it relates to the past events, resulting in the gambler's fallacy. When a person considers every event as independent, the fallacy can be greatly reduced.<ref>{{cite journal | last1 = Roney | first1 = C. J. | last2 = Trick | first2 = L. M. | year = 2003 | title = Grouping and gambling: A gestalt approach to understanding the gambler's fallacy | journal = Canadian Journal of Experimental Psychology | volume = 57 | issue = 2| pages = 69–75 | doi=10.1037/h0087414| pmid = 12822837 }}</ref>

Roney and Trick told participants in their experiment that they were betting on either two blocks of six coin tosses, or on two blocks of seven coin tosses. The fourth, fifth, and sixth tosses all had the same outcome, either three heads or three tails. The seventh toss was grouped with either the end of one block, or the beginning of the next block. Participants exhibited the strongest gambler's fallacy when the seventh trial was part of the first block, directly after the sequence of three heads or tails. The researchers pointed out that the participants that did not show the gambler's fallacy showed less confidence in their bets and bet fewer times than the participants who picked with the gambler's fallacy. When the seventh trial was grouped with the second block, and was perceived as not being part of a streak, the gambler's fallacy did not occur.

Roney and Trick argued that instead of teaching individuals about the nature of randomness, the fallacy could be avoided by training people to treat each event as if it is a beginning and not a continuation of previous events. They suggested that this would prevent people from gambling when they are losing, in the mistaken hope that their chances of winning are due to increase based on an interaction with previous events.