Academic journal article Canadian Journal of Experimental Psychology

Grouping and Gambling: A Gestalt Approach to Understanding the Gambler's Fallacy

Academic journal article Canadian Journal of Experimental Psychology

Grouping and Gambling: A Gestalt Approach to Understanding the Gambler's Fallacy

Article excerpt

Abstract The gambler's fallacy was examined in terms of grouping processes. The gambler's fallacy is the tendency to erroneously believe that for independent events, recent or repeated instances of an outcome (e.g., a series of "heads" when flipping a coin) will make that outcome less likely on an upcoming trial. Grouping was manipulated such that a critical trial following a run of heads or tails was grouped together with previous trials (i.e., the last trial of "Block 1") or was the first trial of another group (the first trial of "Block 2"). As predicted, the gambler's fallacy was evident when the critical trial was grouped with the previous trials, but not when it was arbitrarily grouped with the next block of trials. Discussion centres on the processes underlying the gambler's fallacy and practical implications of these findings.

Consider a person who is betting on coin tosses and the prior outcomes were Heads, Tails, Tails, Heads, Heads, Heads. The gambler's fallacy is the tendency to see a given outcome as less likely if it has just repeatedly occurred, in this case, leading to the choice of Tails following three Heads. It is a fallacy to the extent that the person's expectancy deviates from the true probability of getting heads in a coin toss (50%). The gambler's fallacy has been found in a variety of naturalistic gambling situations including playing blackjack in a casino (Keren & Wagenaar, 1985), betting at the racetrack (Metzger, 1985), and in choosing lottery numbers (Clotfelter & Cook, 1993).

We will argue that there are potentially two errors involved in the gambler's fallacy: perceiving separate and independent events as part of an inter-related sequence or pattern, and mistakenly assuming that random events "balance out" in the short term within the pattern. The former is reflected in a tendency to behave as if a present independent event is somehow related to, and influenced by, prior events. The latter predicts a specific direction of bias - toward expecting random events to "balance out" in the short term. Past attempts to explain the gambler's fallacy have tended to focus on the latter, neglecting the former aspect of the phenomenon, something we will attempt to remedy in this paper.

The primary explanation currently cited for the gambler's fallacy is that the phenomenon arises due to failure to understand probability. Tversky and Kahneman (1971) identified the "law of small numbers," which is the erroneous belief that properties of large samples will also apply to very small samples. In fact, though outcomes should be approximately equal over a large number of trials, it does not follow that they "balance out" in the short term. Thus, the gambler's fallacy could simply reflect the false belief in the law of small numbers - the belief that outcomes will balance out in the short term. Consistent with this, when asked to generate random event sequences, people tend to exaggerate alternations of events, and underrepresent "runs" or repetitions (e.g., see Balkan, 1960; Neuringer, 1986).

Although judgment explanations clarify why we overestimate the probability of alternations or reversals after a run, it does not address the initial error of behaving as if independent events were somehow related. We argue that the gambler's fallacy occurs as a result of a natural tendency for people to organize separate events into larger units, groupings of events that form episodes or meaningful patterns, rather than seeing each event as a separate entity, unrelated to others. This tendency to organize individual elements of experience into larger scale units follows from Gestalt principles (e.g., Koffka, 1935; Wertheimer, 1923), and the effects of grouping are commonly observed in a wide variety of perceptual and memory phenomena. Consistent with this, in a literature review of two-choice probability studies, where participants are asked to choose one of two options repeatedly over many trials, Jones (1971, pp. …

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