The biological substratum of the Gambler's Fallacy

The Gambler’s Fallacy (GF) is usually defined as one’s fallacious belief that the outcome of a random trial is influenced by the previous outcomes of the respective experiment, in the sense that a certain outcome is more likely to occur if it did not occur over a long series of previous trials. This belief is formed despite the theoretical fact that the trials are independent to each other and the predicted outcome has the same probability of occurrence in the current trial as it has or had in any other trial.

The classical example of the Gambler’s Fallacy comes from roulette (but examples can be provided from any game of chance): Assume one bets on red or black and a long streak of blacks occurred before placing their bet. If the gambler decides to bet on red, as basing on the belief that a red is more likely to occur given that information, then they are subject to the Gambler’s Fallacy.

The Gambler’s Fallacy may manifest as well in other situations of daily life. For instance, a parent having two or three children of the same gender may expect for their next child to be of the opposite gender just because the previous children were not and as such commit a Gambler’s Fallacy.

The misconceptions and errors determining the GF are tightly related to mathematical concepts specific to gambling. The complex concept of randomness grounds probability theory, which applies to the gambling phenomenon. Researchers have found that the GF stems from and is potentiated by a poor or inadequate perception and understanding of the concept of randomness, but also of other statistical concepts such as that of statistical independence, statistical average, and the Law of Large Numbers. 

It may appear then that a good grasp of this gambling mathematics knowledge would have full potential of correcting and preventing the GF. But things are not that straightforward, as research has shown that the GF is also a biological phenomenon, which has its causes in the neurophysiology of the brain. There is a battle between the rational side of the brain and its affective-emotional side, and many times the latter wins and favors the manifestation of the GF, just due to our inner biological constitution.

In 2012, evidence was provided that the GF might be caused by an imbalance between the cognitive and affective systems. Precisely, the manifestation of the GF was negatively correlated with the affective decision-making capacities and positively correlated with the general intelligence and executive functioning. Moreover, lesion and physiological neuroimaging studies have confirmed the involvement of both cognitive and affective systems in the GF and GF-like decisions. 

Based on this evidence, researchers proposed that the GF might be the result of hyperfunction in the cognitive system and hypofunction in the affective system, leading to the win-shift/lose-stay strategy based on a false world model. A possible explanation has been advanced that it takes more cognitive control capacity for individuals to implement the false world model than using the win-stay/lose-shift (WSLS) strategy based on a reinforcing learning mechanism.

At the time of those studies, no other research has provided any neuroanatomical evidence for the relationship between the cognitive/affective systems and the GF.

In 2019, a group of Chinese researchers led by Xiaolu Huang and Hanqi Zhang published a study where they used univariate and multivariate voxel-based morphometry (VBM) analysis to explore the correlation between the GF and brain morphology. This is a neuroimaging technique able to investigate focal differences in brain anatomy, by measuring local concentrations of brain tissues and by voxel-wise comparison of multiple brain images. 

The authors of the study used mediation analysis to find the most relevant regions of the brain mediating the relationship between the GF and cognitive/affective systems, and to show that the grey matter volume (GMV) in these regions accounts for the degree of the GF.

The study was conducted on a sample of 350 individuals from the population of Chinese undergraduate college students.

The Card Guessing Task was administered to the subjects to measure their degree of GF. This task consists of a computer-based game, working as follows: The trial begins with two cards (red and black) shown on the screen in a random position. The computer (C1) randomly chooses one card in one second. The subject (P2) is then asked to guess which card was chosen by the computer by pressing the corresponding button within two seconds. The choices of both the computer and the subject are shown for one second. The subject wins one credit (in real money) for each correct guess and loses one credit for each failure, for motivating them. The computer’s last five choices are displayed on the screen. The entire procedure consisted of two 63-trial sessions.

The authors calculated the percentage of trials in which the subjects used the GF strategy, based on the length of the streaks (1 – 6) generated by the computer. They also used lagged logistic regression analysis to investigate the effect of recorded outcomes (gain vs. loss), streak length (1 – 6), the interaction of the previous two factors, and the cumulative probability of the current card on subjects’ next strategy (GF vs. WSLS). 

The cognitive system of the subjects was measured by two tasks – the 2-back working memory task (WMT) and the Stroop task. The former task consists of a semantic, phonological, and morphological judgment session, and the accuracy of the responses collected in these three sessions was taken to be the index of working memory performance.

In the latter task, subjects were asked to respond as quickly as possible to the printed color using four buttons. The time of reaction between the incongruent and congruent trials was taken as the index of the executive function.

As for the affective system, the Iowa Gambling Task (IGT) was used to measure it. In this task, subjects were asked to choose from four decks of cards. After each selection, they were informed how much money they had won or lost. Two decks out of the four provided higher rewards but higher punishments, and the other two decks provided smaller rewards and smaller punishments. The IGT scores, counted as the differences between the number of selections from the good decks and the number of selections from the bad decks, stood as an index for the affective system.

The results of the administered tasks were consistent with previous research, showing that the degree of the GF increased with streak length. For instance, the percentage of trials using the GF strategy following streaks of length less than 4 (41.72%) was lower than that of those following long streaks of length from 4 upward (59.49%). These results suggested that the subjects were more likely to break the random sequence after long streaks in the choices of the computer. 

There were major individual differences in the degree of the GF following both short and long streaks and no correlation was found between the degree of the GF strategy and gender or age.

For a certain sequence of a given length, the local cumulative probability of a certain card would increase under long streaks and decrease when the sequence gets even longer. In such cases, tracking the cumulative probability and using it for making decisions would be considered rational. 

Overall, the behavioral results revealed important positive correlations between cognitive functions and the degree of the GF, but a major negative correlation between affective functions and the degree of the GF.

The presented study confirmed the results of previous research, indicating that individuals with stronger executive function are more likely to use the GF strategy. It is also consistent with the classical psychological models of the Gambler’s Fallacy, based on the heuristics and biases qualification.

The authors of the study uncovered for the first time the neuroanatomical mechanism underlying the brain functions that are related to the Gambler’s Fallacy. Their findings supported the theoretical model of decision making that emphasizes the cognitive system’s constructive role and the affective system’s destructive role in the Gambler’s Fallacy. In this theoretical framework, the Gambler’s Fallacy seems to stem from the cognitive system’s hyperfunction and the affective system’s hypofunction.

The findings of this study shed light on the anatomic dimension of the Gambler’s Fallacy, which adds to its physiological, psychological, mathematical, and epistemological dimensions, all under ongoing scientific investigation and reflecting the interdisciplinary complexity of this phenomenon.

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