User:Songm/sandbox

I will be experimenting with my edits for the Gambler's fallacy article below. I plan on dividing the "Psychology of the fallacy" section up into a number of subsections:

Origins
Gambler's fallacy arises out of a belief in the law of small numbers, or 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. Amos Tversky and Daniel Kahneman first proposed that the gambler's fallacy is a cognitive bias produced by a 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. 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", 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 (insensitivity to sample size); Kahneman and Tversky interpret this to mean that people believe short sequences of random events should be representative of longer ones. 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.

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, otherwise known as the just-world hypothesis. Other researchers believe that individuals with an internal locus of control - that is, people who believe that the gambling outcomes are the result of their own skill - are more susceptible to the gambler's fallacy because they reject the idea that chance could overcome skill or talent.

Variations of the gambler's fallacy
Some researchers believe that there are actually two types of gambler's fallacy: Type I and Type II. Type I is the "classic" gambler's fallacy, when individuals believe that a certain outcome is "due" after a long streak of another outcome. Type II 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). 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, therefore people fall prey to the Type II gambler's fallacy. The two types are different in that Type I wrongly assumes that gambling conditions are fair and perfect, while Type II 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. For example, people believe that an imaginary sequence of die rolls is more than three times as long when a set of three 6's is observed as opposed to when there are only two 6's. This effect can be observed in isolated instances, or even sequentially. A real world example is when a teenager becomes pregnant after having unprotected sex, people assume that she has been engaging in unprotected sex for longer than someone who has been engaging in unprotected sex and is not pregnant.

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 the hot-hand fallacy, people tend to predict the same outcome of the last event (positive recency) - that a high scorer will continue to score. In gambler's fallacy, however, people predict the opposite outcome of the last event (negative recency) - that, for example, since the roulette wheel has landed on black the last six times, 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." 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. Usually, 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.

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 be a neurological component to it as well. Functional magnetic resonance imaging has revealed that, after losing a bet or gamble ("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 and ventral striatum after a riskloss. Activation in the amygdala is negatively correlated with gambler's fallacy - 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 (responsible for executive, goal-directed processes) and less on the brain areas that control 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 reinforced and after a loss, the behavior is 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.

Possible solutions
The gambler's fallacy is a deep-seated cognitive bias and therefore very difficult to eliminate. For the most part, educating individuals about the nature of randomness has not proven effective in reducing or eliminating any manifestation of the gambler's fallacy. Participants in an early study by Beach and Swensson (1967) were shown a shuffled deck of index cards with shapes on them, and were told to guess which shape would come next in a sequence. The 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. Even so, 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. Clearly, instructing individuals about randomness is not sufficient in lessening the gambler's fallacy.

It does appear, however, that an individual's susceptibility to the gambler's fallacy decreases with age. Fischbein and Schnarch (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 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 older the students got, 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, however, and none of the college students did. Fischbein and Schnarch therefore theorized that an individual's tendency to rely on the representativeness heuristic and other cognitive biases can be overcome with age.

Another possible solution that could be seen as more proactive comes from Roney and Trick, Gestalt psychologists who suggest that the fallacy may be eliminated as a result of grouping. When a future event (ex: 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, however, the fallacy can be greatly reduced.

In their experiment, Roney and Trick told participants 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. Additionally, the researchers pointed out how insidious the fallacy can be - the participants that did not show the gambler's fallacy showed less confident in their bets and bet fewer times than the participants who picked "with" the gambler's fallacy. However, when the seventh trial was grouped with the second block (and was therefore perceived as not being part of a streak), the gambler's fallacy did not occur.

Roney and Trick argue that a solution to gambler's fallacy could be, instead of teaching individuals about the nature of randomness, training people to treat each event as if it is a beginning and not a continuation of previous events. This would prevent people from gambling when they are losing in the vain hope that their chances of winning are due to increase.

Instances of the gambler’s fallacy when applied to childbirth can be traced all the way back to 1796, in Pierre-Simon Laplace’s A Philosophical Essay on Probabilities. Laplace wrote of the ways men calculated their probability of having sons: "I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls." In short, the expectant fathers feared that if more sons were born in the surrounding community, then they themselves would be more likely to have a daughter.