We all know that gambling is irrational. But many of just can’t help it when it comes to lotteries. A prospective multi-million [insert your local currency here] win seems like a huge pay-off in comparison to the small price of a lottery ticket.
An interesting take on the biases evident in lottery gambling was recently published in The Economist. The odds of hitting the jackpot in the UK lottery by picking six correct numbers out of 49 are about one in 14 million. Lottery balls used in the draws are unbiased and the probability of any given number being drawn is of course the same each week. Yet some websites dedicated to providing lottery information identify “hot” and “cold” numbers, based on the number of times they have been drawn in the past. "The only really sound strategy”, according to The Economist, “is to avoid numbers that others pick, since shared numbers mean shared prizes.” Picks that should be avoided include lower numbers (since birth months and days are popular choices), numbers that represent geometric shapes (e.g. diagonal lines) on the ticket, the “lucky number 7”, and the numbers 1, 2, 3, 4, 5 and 6. Apparently, the latter sequence gets chosen by 10,000 UK lottery players each week. A jackpot in the millions of pounds would amount to a pay-off in the hundreds for each winner if this sequence were ever drawn. “But true randomness is best of all,” the article concludes wisely.
There is a long list of cognitive biases that attract people to the lottery, keep them playing every week and make them pick certain numbers. Paul Rogers published a comprehensive review of the cognitive psychology of lottery gambling in the Journal of Gambling Studies a number of years ago. One of the fundamental problems with lottery (and other) gambling is humans’ unrealistic optimism and our misunderstanding of probabilities. Odds that are as small as those of a lottery win simply lie outside the range of our experience of probabilities in everyday life. We can’t easily grasp them. We’re also more used to thinking in terms of absolute numbers (e.g. 10) than probabilities or proportions (e.g. 0.1%). Research on the ratio bias, for example, has shown that people are swayed more by absolute numbers than probabilities. When people are given the chance of winning money by drawing a red jelly bean out of a bowl, they are more likely to go for the bowl in which 10 out of 100 jelly beans are red than the one in which 1 out of 10 jelly beans is red. That’s despite the fact that the probability of drawing red is the same for both bowls. The perceived likelihood of winning is also influenced by the availability bias. Winning seems more likely if we can easily think of an instance of ‘winning’ or an actual lottery winner. Media publicity focuses on the rare winners not the millions of losers, which makes winning salient in people’s minds.
In addition to the erroneous belief in hot and cold numbers and the superstitious thinking that fuels strategies like picking birth dates or anniversaries, other irrational thinking identified by Rogers includes the gambler’s fallacy – the mistaken belief held by some people that independent events, such as successive lottery draws, are interrelated. Is the number 3 less likely to be a winning number next week because it was drawn in the last two lottery draws already? We know that the answer is no, but our gut feeling may tell us otherwise. Then there’s perceived luckiness – people sometimes think of gambles as a combination of chance (coincidence) and luck (a personal attribute). Finally, some people exhibit an illusion of control. One study found that letting players select their own lottery numbers increased their expectations of success.
So what keeps lottery players going? One specific phenomenon that can serve as an incentive to “try again” is a near miss. For example, if the numbers 4, 12 and 19 are drawn, having picked 3, 11 and 18 can be perceived as a near miss, even though any other random numbers (e.g., 8, 16 and 27) were just as likely to be drawn. A near miss makes the probability of winning more vivid and may give gamblers the illusion of “getting closer”. This example of irrational thinking is particularly prominent in slot machine gambling. Perhaps a far more widespread reason that keeps lottery gamblers going is evident in entrapment or sunk cost bias. As money spent on lotteries accumulates over time, players may justify a continued “investment” in the lottery in order to make good on the losses they have incurred already. I can’t give up now – I’ve been playing the lottery for 20 years!
Lottery expenditures in the U.S. have grown over the last few decades, but the recession does not seem to have deterred Americans from buying lottery tickets. In fact, a recent analysis by Csilla Horváth and Richard Paap looked at trends in casino gambling, lotteries, and parimutuel wagering, and found that lotteries appear to be recession-proof. This may be due to their relatively low price. Small-stakes gambles like lotteries are not only more easily justified by consumers as an expense, but lotteries also offer people some hope to improve their circumstances during times of economic hardship. Hope trumps reason.
Horváth, C., & Paap, R. (2012). The effect of recessions on gambling expenditures. Journal of Gambling Studies, 28, 703-717.
Rogers, P. (1998). The cognitive psychology of lottery gambling: A theoretical review. Journal of Gambling Studies, 14, 111-134.