We examine how almost winning in roulette affects subsequent betting behavior. Our main finding is heterogeneity in gambler behavior with some gamblers less likely to bet on numbers that were near misses on the prior spin and other gamblers more likely to bet on near miss numbers. Using a unique data set from the game rapid roulette, we model the likelihood of a gambler betting on a near miss number while controlling for the favorite number bias and the likelihood of a number being a near miss. We also find no evidence that near misses in roulette leads to gamblers extending the time spent gambling or to the placing of more bets.

Oppenheimer and Monin (2009) recently found that subjectively rare events are taken to indicate a longer preceding sequence of unobserved trials than subjectively common events, an effect which they refer to as the retrospective gambler’s fallacy. The current paper extends this idea to the situation where participants judge the likelihood of streak continuation. Participants were told about a streak produced by a random process (coin flips) or human performance (basketball shots), and either predicted the next outcome or inferred the immediately preceding outcome. For the coin scenarios, participants tended to expect streak termination – the gambler’s fallacy — and this effect was the same for predictions and retrospective inferences. In the basketball scenarios, no overall bias was found in either prospective or retrospective judgments. The results support Oppenheimer and Monin’s suggestion that reconstruction of the past entails the same heuristics as prediction of the future; they also support the idea that the nature of the data-generating process is a key determinant of whether people fall into the gambler’s fallacy. It is suggested that the term retrospective gambler’s fallacy be used to describe situations where a streak is taken to indicate that the preceding unobserved outcome was of the opposite type, and that the phenomenon discovered by Oppenheimer and Monin be referred to as retrospective representativeness, or a retrospective belief in the law of small numbers.

Runs of gains and losses are particularly salient to decision makers because of their perceived departure from randomness, as well as their immediate impact on the financial status of the decision makers. Past research has focused on decision making biases that relate to faulty conceptions of chance and luck, such as the gambler’s fallacy and the hot hand effect. Participants in the current study bet on the outcomes of a long sequence of simulated coin tosses. Risk preferences were found to change as a function of run valence (i.e., losses vs. gains), run length, and financial status. Individuals were found to differ in the effect of all of these factors, in their responses to runs of gains and losses in sequential risky choice.

Previous research has reported that the gambler’s fallacy could be detected in goalkeepers’ behavior during penalty shootouts. Following repeated kicks in the same direction, goalkeepers were more likely to dive in the opposite direction on the next kick. We employ here a unique data collection approach and accurately measure the exact location of each ball when crossing the goal plane. This allows us to analyze how different definitions of the goal center width affect the results, and we show that this width indeed affects whether a gambler’s fallacy in goalkeepers’ diving behavior exists. We further augment the data with additional kicks from top international competitions and analyze the extended dataset. We also question whether previous treatments of kicking sequences adequately represent what goalkeepers consider as a run of consecutive kicks to the same side. A different representation of kicking sequences is provided and applied to the data. Overall, we find some evidence for the gambler’s fallacy after sequences of two or three kicks to the same side.

The gambler’s fallacy (Tune, 1964) refers to the belief that a streak is more likely to end than chance would dictate. In three studies, participants exhibited a retrospective gambler’s fallacy (RGF) in which an event that seems rare appears to come from a longer sequence than an event that seems more common. Study 1 demonstrates this bias for streaks, while Study 2 does so with single rare events and shows that the appearance of rarity is more important than actual rarity. Study 3 extends these findings from abstract gambling domains into real world domains to demonstrate the generalizability of the effects. The RGF follows from the law of small numbers (Tversky & Kahneman, 1971) and has many applications, from perceptions of the social world to philosophical debates about the existence of multiple universes.

The gambler’s fallacy and the hot hand belief have been classified as two exemplars of human misperceptions of random sequential events. This article examines the times of pattern occurrences where a fair or biased coin is tossed repeatedly. We demonstrate that, due to different pattern composition, two different statistics (mean time and waiting time) can arise from the same independent Bernoulli trials. When the coin is fair, the mean time is equal for all patterns of the same length but the waiting time is the longest for streak patterns. When the coin is biased, both mean time and waiting time change more rapidly with the probability of heads for a streak pattern than for a non-streak pattern. These facts might provide a new insight for understanding why people view streak patterns as rare and remarkable. The statistics of waiting time may not justify the prediction by the gambler’s fallacy, but paying attention to streaks in the hot hand belief appears to be meaningful in detecting the changes in the underlying process.

The representativeness heuristic (RH) has been proposed to be at the root of several types of biases in judgment. In this project, we ask whether the RH is relevant in two kinds of choices in the context of gambling. Specifically, in a field experiment with naturalistic stimuli and a potentially extremely high monetary pay-out, we give each of our subjects a choice between a lottery ticket with a random-looking number sequence and a ticket with a patterned sequence; we subsequently offer them a small cash bonus if they switch to the other ticket. In the second task, we investigate the gambler’s fallacy, asking subjects what they believe the outcome of a fourth coin toss after a sequence of three identical outcomes will be. We find that most subjects prefer “random” sequences, and that approximately half believe in dependence between subsequent coin tosses. There is no correlation, though, between the initial choice of the lottery ticket and the prediction of the coin toss. Nonetheless, subjects who have a strong preference for certain number combinations (i.e., subjects who are willing to forgo the cash bonus and remain with their initial choice) also tend to predict a specific outcome (in particular a reversal, corresponding to the gambler’s fallacy) in the coin task.

We explore people’s preferences for numbers in large proprietary data sets from two different lottery games. We find that choice is far from uniform, and exhibits some familiar and some new tendencies and biases. Players favor personally meaningful and situationally available numbers, and are attracted towards numbers in the center of the choice form. Frequent players avoid winning numbers from recent draws, whereas infrequent players chase these. Combinations of numbers are formed with an eye for aesthetics, and players tend to spread their numbers relatively evenly across the possible range.