Cognitive Biases in Playing the Lottery: Estimating the Odds and Choosing the Numbers (original) (raw)
Related papers
Journal of Risk and Uncertainty, 1991
Observed patterns of lottery play suggest that many players believe they can improve their chance of winning by adjusting their bets according to which numbers have won in recent drawings, or in response to their dreams or other portents. This skill orientation is encouraged by state lottery advertising, which tends to be misleading in other respects as well. Patterns of lottery play and the content of lottery commercials provide readily available illustrations of psychological tendencies in risky decision-making that have been documented in laboratory experiments.
Underlying cognitions in the selection of lottery tickets
Journal of Clinical Psychology, 2001
There is evidence that the faulty cognitions underlying an individual's playing behavior maintains and supports their gambling behavior. Sixty undergraduate students completed the South Oaks Gambling Screen (SOGS), a measure to assess pathological gambling, and a questionnaire ascertaining the type and frequency of their gambling activities. Sixteen Loto 6/49 tickets were presented to participants and ranked according to their perceived likelihood of being the winning ticket. The numbers on the tickets were categorized as: long sequences (e.g., 1-2-3-4-5-6), patterns and series in a pseudo-psychological order (e.g., 16-21-26-31-36-41), unbalanced (e.g., six numbers from 1-24 or 25-49), and those appearing to be random (e.g., 11-14-20-29-37-43). Verbal protocols of ticket selections were ranked into eight heuristics. Results revealed that for the entire sample the greatest percentage of tickets chosen for the first four selections were "random" tickets. Further, the most commonly cited reason for selecting and changing a lottery ticket was perceived randomness. The results are discussed with reference to the cognitions used when purchasing lottery tickets.
Judgment Error in Lottery Play: When the Hot-Hand Meets the Gambler’s Fallacy
SSRN Electronic Journal
We demonstrate that lottery markets can exhibit the "hot-hand" phenomenon, in which past winning numbers tend to receive a greater share of the bets in future draws, even though past and future events are independent. This finding is surprising, as works by Clotfelter and Cook (1993) and Terrell (1994) have previously documented the presence of an opposite effect-the "gambler's fallacy"-in the U.S. lottery market. The current literature also suggests that the gambler's fallacy prevails when random numbers are generated by mechanical devices, such as in lottery games (Ayton and Fisher 2004, Burns and Corpus 2004, Caruso et al. 2010). We use two sets of naturally occurring data to show that both the gambler's fallacy and the hot-hand fallacy can exist in different types of lottery games. We then run online experimental studies that mimic lottery games with one, two, or three winning numbers. Our experimental results show that the number of winning prizes impacts behavior. In particular, whereas a single-prize game leads to a strong presence of the gambler's fallacy, we observe a significant increase in hot-hand behavior in multiple-prize games with two or three winning numbers.
The representativeness heuristic and the choice of lottery tickets: A field experiment
Judgment and Decision Making, 2019
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. None...
Lotteries and Probability Theory
2010
Abstract: A variety of decisions seem to require resort to a coin toss, die roll, or the drawing of straws—in other words, a fair lottery. This raises the question of what features distinguish fair lotteries from alternative procedures. The intuitive answer is that a fair lottery generates each of its possible outcomes with equal probability. But probability is a contentious term. There are a variety of conceptions of probability, and it may be the case that equiprobable lotteries are useful for decision-making under some conceptions but not others. This paper considers four of the leading conceptions of probability—the frequentist, objective, subjective, and logical conceptions. It argues that unless the logical conception is adopted, it is impossible to make sense of the contribution that lotteries can make to decision-making.
Lucky numbers: Choice strategies in the Pennsylvania Daily Number game
Bulletin of the Psychonomic Society, 1989
We examined the amount of money bet during a week of Pennsylvania's Daily Number game. In this game, players receive a predetermined payoff for picking the 3-digit number (000 to 999) drawn on that day. The betting distribution was distinctly nonuniform, and we identified several betting patterns, such as picking triples and avoiding double 9s. In addition, we asked separate groups of subjects to rate selected numbers for randomness, luckiness, and perceived history of winning; to categorize numbers; and to free associate to numbers. We propose that people seem to choose highly patterned, available, and]or "lucky" numbers. People apparently do not bet numbers that reflect the random process of the game (they do not utilize a representativeness heuristic).
In search of a fair bet in the lottery
2006
Although state-operated lotto games have the worst average expected payoffs among common games of chance, because the jackpot can accumulate, the maximum expected payoff is potentially unlimited. It is possible, therefore, that lotto can exhibit a positive expected return. This paper examines 18,000 drawings in 34 American lotteries and finds approximately 1% of these drawings provided players with a fair bet. If it were possible for a bettor to purchase every possible combination, however, most lotteries commonly experience circumstances where such a purchase would provide a positive return with 11% of the drawings providing a fair bet to the player. JEL Classification Codes: D81, H71, L83
Special Random Numbers: Beyond the Illusion of Control
Previous research has shown that gamblers prefer numbers they choose themselves because this choice allows them to feel more in control of the (random) outcome. We identify other conditions under which people Wnd numbers "special" (i.e., worthy of betting more on than other numbers). By manipulating gambling task type and assigning participants a number by an endogenous system outside their own control (as is done in numerology, astrology, and other paranormal systems), we Wnd that indeed people prefer to bet on numbers derived from particular special systems. The mechanism underlying this preference is enjoyment with the task-not control. Further, the enjoyment associated with this "specialness" is related to the prevalence of certain types of numbers (i.e., numbers based on dates and names) in the fortune-telling world and not to other factors such as individuality or even belief in the associated system. We replicate these Wndings using actual money and show that this prevalence-to-enjoyment link already exists in memory for dates and names and is activated and strengthened by priming the fortune-telling systems relevant to those special random numbers. Finally, we present a model of special random numbers that integrates our Wndings with other determinants of valuation such as regret and subjective probability. Our results expand the realm of special random numbers beyond control. Our enjoyment model has implications not only for understanding gambling, but also for understanding how reasoning under uncertainty is inXuenced by little-understood phenomena (such as fortune-telling systems) without aVecting subjective probability or actual beliefs.
Computational Intelligence, 1998
The paradox of the preface and the lottery paradox are paradoxes of practical certainty sharing certain features. The paradox of the lottery argues that rational agents are at once practically certain that each ticket in a lottery will lose but also practically certain some ticket will win. The paradox of the preface argues that rational agents are at once practically certain that all facts in a written volume are true, yet are also practically certain that some fact is wrong. A difference between real lotteries and prefaces is that a winning lottery ticket is generally an intended feature of the lottery, whereas incorrect facts are generally unintended. Despite these similarities, Pollock gives a novel argument suggesting that the preface paradox warrants qualitatively different treatment from the lottery, using as a rationale the differences between real lotteries and prefaces. This draws a clear line between the work of Pollock and the work of Kyburg, both of whom have had a prominent influence in recent thinking on nonmonotonic reasoning in AI. This note shows there are real lotteries with the formal structure of the preface paradox and possibly prefaces with the formal structure of lotteries. The surprising conclusion is that within Pollock's framework, the treatment of any problem with a formal structure resembling the lottery (or the preface) depends on the process by which winning tickets (or publishing errors) are generated. The rationales given by Pollock seem to be unrelated to the actual mechanisms implemented.