Lotteries in the real world

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  • Journal of Risk and Uncertainty, 4:227-232 (1991) 1991 Kluwer Academic Publishers

    Lotteries in the Real World

    CHARLES T. CLOTFELTER Institute of Policy Science, Duke University, 4875 Duke Station, Durham, North Carolina 27706

    PHILIP J. COOK Institute of Policy Science, Duke University, 4875 Duke Station, Durham, North Carolina 27706

    Key words: lotteries, beliefs, patterns of play, advertising, normative issues


    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.

    In this article, we will focus our remarks on two issues of particular interest. ] First, state lotteries offer a rich source of field data for testing theories of risk-taking and decision-making under uncertainty. Second, the policies of lottery agencies, especially with regard to information they provide players about the games, raise interesting and important normative issues. Before addressing these issues, we provide a quick descrip- tion of the state lottery operations. ]

    1. The lottery landscape

    Until 1964, lotteries were illegal in every state in this country. Today they are operated in 32 states and the District of Columbia. They are also a worldwide phenomenon: there are 100 countries where lotteries are legal. Their growth in the U.S. has been very rapid: per capita expenditures on lotteries in lottery states have increased (in 1989 dollars) from $22 in 1975 to $108 in 1989, an annual growth rate of 12%. In 1989, total sales in all U.S. state lotteries totaled $17 billion. Of that total, roughly 50% was returned to players in

    The authors gratefully acknowledge the research support of the National Bureau of Economic Research. This article is based on an informal presentation the authors gave at the Fifth International Conference on the Foundation and Application of Utility, Risk, and Decisions Theories at Duke University, June 11, 1990. l. Supporting evidence and documentation for the factual statements that follow are in Clotfelter and Cook (1989, 1990).


    the form of prizes and another 10% went to pay operating costs (including commissions to retail ticket outlets), leaving an average of 40% of total revenues that went into state treasuries. Yet despite this rapid growth and high profit rate, lotteries still constitute only about 4% of total own-state revenues in states that have them.

    State lotteries now offer three major products. Usually the first to be introduced by any new lottery is the instant scratch-off game, sold for a dollar, which gives players the chance to rub off a covering to find out--instantly--whether they are winners. Unlike the other two major products, instant games do not require an on-line communications network and therefore can be launched quickly. The second product is the numbers game, a replica of illegal numbers games in which a player picks a three- or four-digit number. Among the various bets that are offered on this daily drawing, the most popular is the so-called straight bet, offering a 1A00o probability for a three-digit game. The typical payout on such a bet is $500, reflecting the average 50% "payout rate." The third major game, lotto, has generated most of the excitement and publicity, owing to the enormous prize jackpots that have been generated. In this game players choose six numbers out of a field of, say, 44 numbers. The probabilities of successfully picking all six are infinites- imal (one in 7.1 million for 6/44 games; one in 14 million for 6/49 games), but the prizes are correspondingly large. If there is no winner in a drawing, the jackpot "rolls over" to the next drawing. A series of rollovers have on occasion produced jackpots worth tens of millions of dollars.

    2. Patterns of play

    As any gambling sophisticate knows, the lottery's payout rate of 50% is considerably lower than that offered by other forms of commercial gambling. For example, horse racing has an average payout rate of 81% and slot machines 89%. Lotteries are a crummy bet, but people still play, and some of them play a lot.

    Many players appear to take the job of picking a number quite seriously. To them, all numbers are not created equal. We observe, for example, that the distribution of bets over all combinations is far from random. In Maryland's three-digit numbers game, the numbers 333 and 777 were bet nine times the average rate; the numbers 086 and 092 were bet only once for every 35 times those popular numbers were. People bet their children's birthdays, their pet's birthday, their address, their favorite ballplayer's uniform number, and so forth.

    Acting like investment analysts, players use new information to inform their betting decisions. For example, they bet on the day of the month or on numbers linked to public events. This kind of behavior has long been associated with the illegal numbers game. For example, the illegal numbers games were flooded with bets on 715 when Hank Aaron was on the verge of breaking Babe Ruth's record of 714 home runs. In the same way, betting on the number 2880 in the Illinois lottery had to be stopped in 1982 after hitting the agency's $5 million betting limit. Why? That was the lot number of the Tylenol capsules that had been laced with cyanide.


    Many players consult outside sources for information on numbers to play. There are gadgets ranging from key chain novelties that select six numbers for lotto bets to expen- sive computer programs that do much the same thing. There are "dream books," inex- pensive pamphlets that contain lists of objects and occurrences that might appear in dreams, each with the number or numbers believed to correspond with it. Their anteced- ents reach back at least to colonial times and into the murky history of sorcery and numerology. Dream books are sold on newstands in lottery states across the country today: for example, we bought the PrinceAli Lucky Five Star 200 feet from Harvard Yard, in the cradle of rationality. This book gives the following numbers: apples, 416; bugs, 305; grave, 999, priest, 001. Of course these numbers won't work for just anybody. A former illegal numbers operator on Chicago's South Side, when interviewed, said most players used dream books. He then added, with caution worthy of an attorney, "It tells you everything, but there's an art in using it."

    There are a host of "lottery advisors," ranging from all-purpose astrologers to special- ized lottery experts. Publications such as The National Enquirer and The Globe carry numerous ads and articles purporting to help individuals improve their odds of winning the lottery. More specialized publications include lottery-oriented newsletters and books. Many of these advisors claim to be employing the ancient arts of astrology, nu- merology, or dream interpretation. Readers of the weekly pulp newspapers are provided with lottery advice from a number of different perspectives. For example, issues of The Globe that our research assistant examined during the summer of 1987 carried astrologer Katherine Singer's "Astroguide," with several "winning" numbers for each day of the month; they carried articles on numerology with titles like "Your Telephone Number is Your Secret Hot Line to Good Fortune," and "Your Zip Code Could Put You on Easy Street." They provided, for each state, lists of numbers for each state that were "overdue' and those that had won the most times. (At first we were inclined to dismiss this as the behavior of a small fringe group--until it came out that an astrologer was telling the President of the U.S. when to travel and when to hold news conferences in the White House.)

    Before turning to a consideration of policy, we would like to share two other observa- tions on betting behavior. One relates to the notion of "overdue" numbers. It turns out that the "gambler's fallacy" is alive and well among lottery players. Although the proba- bility of any number being selected is quite independent of past drawings, players evi- dently believe lightning can't strike the same number twice in a short period. We looked at betting on three-digit numbers in Maryland before and after the number was drawn. On the day after a number hit, the amount bet on it dropped by about a fourth; and it dropped to about half its previous level on the second day.

    This form of irrationality didn't cost players anything, however, because Maryland offers a fixed payout of $500 for any winning bet. But some states use aparimutuel basis for their numbers payouts, so betting on popular numbers will not bring as big a prize as betting on unpopular numbers. Players respond by spreading their bets more uniformly in states with parimutuel payouts. We found an appreciably flatter distribution of bets across all numbers in the parimutuel system than in the fixed-payout system.


    3. Normative issues

    The issue raised by the state lotteries is not just whether this type of gambling should be tolerated. The states have moved far past mere tolerance. In creating the lotteries, they have leaped from prohibition to active promotion.

    A lottery places the state in a new business--promoting an actMty that has no public or private virtue. Indeed, for centuries, gambling has been considered a