The 2003 Nora And Edward Ryerson Lecture

Stephen M. Stigler
"Casanova's Lottery"
March 6, 2003

Anyone with even a casual interest in the history of probability has heard that gambling motivated early interest in the subject. Yet I suspect many who work in probability and statistics treat this connection as quaint and slightly embarrassing. They tell the story much as they would tell an anecdote about a long-dead ancestor, one who engaged in colorful but ultimately frivolous behavior and should not be taken as representing our present, more serious, purpose. Yes, they might say, we once considered games, but only as simple abstractions; we are really scientists, not deeply concerned with frivolous pursuits.

But were the games our ancestors studied merely frivolous pursuits? Were they only incidental to our history, important only as rhetorical devices that provided a grounding for abstract probability theory? In fact, the history of gambling holds the promise of being immensely informative about human understanding of risk. But the study of the role of gambling in this history is made more difficult by a shortage of documentation. The Oriental Institute Museum has an exquisite collection of dice from 3,500 years ago, but the accompanying Users’ Manual has been lost. From antiquity to Al Capone, gamblers have been poor record keepers, and the story of how they and their customers evaluated and weighed risk is not well-known.

My aim today is to shed some light on this history through a little-known story involving a famous but little-known character, Giacomo Casanova. Casanova was born in Venice in 1725, and he died in Bohemia in 1798. The facts of his life come mainly from his multi-volume Memoirs, published many years after he died from manuscripts written in old age and left in Bohemia. The Memoirs are the basis of his reputation as a lover, and statisticians are always wary of self-reporting, particularly at a time distant from the events reported. But the Memoirs also tell of a long sequence of other adventures, and the basic outlines of many of these have been independently confirmed. The picture that emerges is of a highly intelligent and ambitious Venetian adventurer of great charm, one who was at various times a military officer, a gambler, and a secret agent. In his youth he took religious orders and briefly aspired to be pope. He sought fame and fortune by any means at hand; he even dabbled in mathematics.

Casanova made many enemies, and in late July 1755 he ran afoul of the Venetian Inquisition. Apparently acting on a tip from one of his enemies, the Inquisitor raided his home and found cabalistic books Casanova had been reading for amusement. Casanova tells us that they seized books like The Key of Solomon the King and Instructions on the Planetary Hours, and other mystical and occult literature with incantations for conversing with demons of all sorts, as well as copies of the works of Horace and Petrarch. All of this would be thought pretty tame today, except perhaps for the Petrarch, but in Venice in 1755 it was sufficient for his imprisonment without trial. Casanova was not formally charged or sentenced; he simply was placed in Venice’s dreaded prison in the Doges’ Palace, in a section of seven cells, cells high up under the roof in a section called the Piombi (“The Leads”), so named for the large slabs of lead that formed the roof. After fifteen months in what were dungeon-like conditions, Casanova executed a daring and clever escape at the end of October 1756. He made his way across the pitched and slippery leaden roof at night, reached the ground safely, hailed a gondola to reach mainland, and succeeded in escaping beyond Venetian territorial boundaries. He made his way to Germany and then to France.

Casanova had lived in Paris during 1750 to 1752, and with the assistance of friends he re-established himself there. The international fame he acquired as a result of his spectacular escape made him a lion of French society. Among others, King Louis XV’s mistress, Madame de Pompadour, wanted to hear his dramatic story firsthand, and he gladly obliged. His written account of the escape circulated among French salons too; indeed, it is the only part of his memoirs that was published during his lifetime. It is still a riveting story

As a result of this escape, Casanova made close and consequential contact with the circle of Parisians around Madame de Pompadour, including members of the finance ministry. In the early 1750s, Pompadour had been instrumental in organizing and beginning construction of the Ecole Militaire, a school destined to be the king’s military school, the same school that thirty years later would train the young Napoleon. In 1756, the school was unfinished but already in financial difficulty, and Casanova was invited to discussions on projects to raise money for the school—we would now call it “development.” He opportunistically joined in advancing and supporting a proposal for a lottery, along the lines of one he had seen succeed in Italy.

The lottery he proposed was of a type unknown in Paris, although it had been introduced in the city-state of Genoa in the 1620s. It was an early cousin of Illinois Lotto. In the late 1500s, Genoa was governed by a council of five, the members of the council being selected annually at random from a list of perhaps ninety nobles of the city. The citizens of Genoa took to placing bets on who would be selected— you could bet on any single noble being included in the council or, presumably, on a pair. In 1626, a Genoese entrepreneur had the bright idea that an election was unnecessary in order to have a wager, and he introduced the idea of a lottery where five numbers would be selected by choosing five tokens blindly from a set of ninety sequentially numbered tokens in a rotatable cage called a wheel of fortune, with bets accepted on the outcome. A distant relative to this type of lottery had been popular in China since the Second Han Dynasty (that’s nine hundred years before Casanova), where it was called the Game of Thirty-six Animals, and it is conceivable that Marco Polo’s travel reports played a role in this history, too. In any event, it was just such a lottery that Casanova advocated to rescue the Ecole Militaire from insolvency.

Casanova’s lottery was simple in design: In its initial version, the player had an option of betting on a single number (an extrait), or on a pair of numbers (an ambe), or on a set of three numbers (a terne). The odds of winning varied with the bet and became increasingly unfavorable as the chances of winning became more remote. Later the number of bets available was expanded to reach a maximum of seven different bets, including specifying which place in the drawing a single number would occur (for example, “57” as the third of the 5 numbers drawn, an extrait déterminé), or which places a pair of numbers would occur (an ambe déterminé). They were also permitted to bet on a set of four numbers (a quaterne), or five (a quine). Like our modern lotto, the choice of numbers was up to the bettor. Unlike our modern lotto, there was a choice of bets, and all were priced and treated separately. (See table 1.)

Table 1. Loterie Bets: Five numbers are drawn from 1, 2, 3, ..., 89, 90

At this distance in time it is difficult to understand the reception this idea received from Louis XV’s state council. We might understand them being concerned that the French would not rise to the bait in sufficient numbers to produce much revenue. But even then the lottery should not lose money at those odds, and it could always be cancelled later, if need be. But instead, the council adopted a very conservative stance and worried about major loss.

Figure 1. A handbill for the simplest type of English "blanks" lottery

There were two reasons for this concern. The first is that while this type of lottery was unknown in France, there was another type that was familiar in France, in England, and in America well before 1750, and that type had a mixed and troublesome history. In England it was called a “blanks lottery,” and it was run as a sort of a raffle. (See figure 1.) A scheme of prizes was announced and a set number of tickets was offered for sale. For example, in one English blanks lottery, 13,500 tickets were offered for sale and 2,754 prizes would be awarded. After the sale, a long and complicated drawing was held. The 13,500 ticket stubs were placed in one large barrel, and in another barrel there were placed another 13,500 slips of paper. Of these, 2,754 were marked with prize amounts, and the remainder were blank. Over a period that generally lasted several weeks, two small boys from foundling homes, wearing the blue coats that were the uniforms of those homes, would draw successive tickets from the two barrels and pair them, awarding the lucky winner the prize or the unlucky holder a blank.

The problem with this type of lottery is that to be successful, all the tickets needed to be sold. The nominal price per ticket was £20, too large an amount for many people, and for this reason most tickets were divided into fractions as small as one-sixteenth. Selling that many tickets took a large sales force, which cut into the profits. Tickets were also traded privately during the drawing. Worse, speculators with no connection to the state started offering “insurance” on the tickets—a thinly veiled way of selling tickets they did not hold, but promised to pay off in the unlikely event of a win. With all this going on, there was always the possibility that the sales would fail.

The first such lottery in England was introduced by Queen Elizabeth in 1567 and was a colossal failure: Less than onetwelfth of the tickets were sold, and the queen was forced to cut the prizes after the tickets were sold—not a good way to generate repeat business. In France there were other scandals. The great Voltaire made a fortune in the 1720s by recognizing a flaw in the pricing and sales system that permitted him to wager with certainty of winning.

Of course many lotteries were successful. In America, Harvard, Princeton, Columbia, and Yale Universities financed building plans with the aid of lotteries. Still, with all of this background there was ample reason for the French state council to be worried. And there was one further problem. Unlike modern lotto where the large prizes are not guaranteed but rather are paid from a pari-mutuel pool and the state cannot lose, it was theoretically possible in Casanova’s lottery that the king could lose, even lose big. If a handful of gamblers got lucky and hit a quaterne (paying 75,000 to 1) or a quine (paying 1,000,000 to 1), the week’s receipts would go sharply into the red. No minister would relish the idea of delivering such news to the king

A hearing was held. Casanova argued that the announcement that the lottery was backed by the king, and that the king stood prepared to lose up to a hundred million francs, would dazzle people and guarantee sales. The councilors were taken aback by this prospect, even when Casanova reassured them that before the Crown would lose a hundred million it would receive at least a hundred and fifty million. The reaction, according to Casanova’s account, was still concern.

A councilor asked, “I am not the only person who has doubts on the subject. You must grant the possibility of the Crown losing an enormous sum at the first drawing?”

Casanova replied, “Certainly, sir, but between possibility and reality is all the region of the infinite. Indeed, I may say that it would be a great piece of good fortune if the Crown were to lose a large sum on the first drawing.”

“A piece of bad fortune, you mean, surely?”

“A bad fortune to be desired,” Casanova answered. He argued that the publicity would be invaluable and the odds would safeguard the Crown’s wealth in the long run. He reminded them that all the insurance companies were rich. He offered to prove the soundness of the scheme before all the mathematicians in Europe

A second hearing was held, and Casanova showed himself as adept in seducing the state council as he is believed to have been in other encounters. He answered all objections, and yet another three-hour session was held, one that included testimony by the philosophe Jean le Rond D’Alembert who, in addition to his other accomplishments as co-editor of the Encyclopédie, was a talented and supremely skeptical mathematician. As a result of all this, the project—with the financial backing of the Crown—was approved. Casanova was awarded a pension and six sales offices, five of which he sold for 2,000 francs each. He ran the sixth himself, on Rue St. Denis, with his valet as clerk. Casanova even carried tickets to sell to the salons he visited. His memoirs do not report that he combined sales with his romantic life, however

The state council should not have worried. Casanova soon moved on, leaving the country for what we may euphemistically call “other pursuits,” but his lottery was an enormous success. It held five drawings in 1758, its first year, and soon settled into a routine of monthly draws. Madame de Pompadour died in 1764, and Louis XV died in 1774, succeeded by his grandson Louis XVI. In those years the budget was in poor shape, and in September 1776, a month after Turgot was dismissed as finance minister, the new finance minister was looking for ways to bolster the French treasury. With the king’s permission, he kidnapped the lottery from the Ecole Militaire and made it the “Loterie Royale de France.” It was expanded: Drawings were increased to twice a month. By the 1780s there were regional Loterie sales offices in Lyon, Strasbourg, Brussels, and Bordeaux. When the Bastille fell in July 1789, the Loterie did not miss a draw. When Louis XVI was executed in January 1793, the Loterie did not miss a draw. When Marie Antoinette lost her head in October of that year, the Loterie did not miss a draw.

Table 2. Frequency of Results, 1758–1834

Only in December of 1793, when the Committee of Public Safety and the Reign of Terror held sway, was the Loterie suppressed. Casanova would have understood why. Without civil authority, public faith in payouts plummeted, and with it the receipts of the Loterie! But just four years later, order was restored and the needs of the French treasury inspired its reestablishment under the same rules as before. In 1801, the Loterie expanded further, to three drawings a month, and separate drawings were introduced at each of the four regional offices, for a total of fifteen drawings a month! Parisian gamblers could wager on any of these from Parisian offices, and others in France could wager on either their own region or on the Paris draws. By 1811, the Loterie ran more than 1,000 sales offices across France, and the net proceeds reached as high as 4 percent of the national budget—more than the contribution from postal or customs levies. There were technological and educational benefits as well— to convey the results of the drawings to and from Paris, an energetic communications network with carriages and riders was developed to all corners of France. And the Loterie probably did more for public awareness of—and education in—the calculus of probabilities than any other state effort, before or since.

The Loterie was a frequent topic of discussion in popular culture as well. A home version was marketed already in the 1780s as Loto-Dauphin, essentially a board game. The Loterie was celebrated in novels.

And it was attacked by moralists. Nonetheless, it thrived until May of 1836 when, for reasons I will consider later, the moralists won a significant victory and by law it was permanently suppressed, not to reappear until the twentieth century.

Now, I have a confession to make. Clearly the Loterie was a major force in France between 1758 and 1836, and this was the golden age of French probability. And just as clearly, the Loterie was intimately connected with the laws of probability, and it should therefore be central to any history of probability. Yet it almost escapes notice in all of those histories. The mathematics of the Loterie is mentioned in passing, but the calculation of the odds was an easy chore by then, and the histories tend to dwell instead on more mathematically interesting problems. My confession is that before 1994, I was no more than dimly aware of the Loterie’s past existence. In that year I was reading a circular from a French bookseller when I noticed a listing that advertised a copy of the Almanach Romain sur la Loterie de France, dated 1834. The price was high but so was the stock market, and I ordered it. (See figure 2.)

Figure 2. The “wretched little book”

At first sight the book was a disappointment—it was a wretched little book that was not in good repair. But a second look lifted my spirits: It was packed with data! The book was sold for gamblers, and it had everything they might hope for: The detailed rules of the game, a listing of which numbers were favorably linked with which women’s names or seasons. The Saints’ Days were listed; so were the addresses of all of the 152 sales offices in Paris. But there was more: The book listed the winning numbers of every draw in Paris and all other regions, from Casanova’s first draw in April 1758 through December 1833. An early owner had helpfully added most of the 1834 results as well.

Since the Loterie ran only another yearand-a-half after my wretched little book was published, this was a record of almost all of its history. Clearly there was grist here for a statistical mill, but what to do about it? I wanted to look first into the fairness of the Loterie. After all, statistical procedures for testing uniformity were only developed in the twentieth century—what would they uncover when applied to these old data? But the old typeface did not permit optical character recognition, and I was slowed by the size of the project. Slowed, that is, until one day four years later, when a bright young College student came to see me and asked if I had any project to suggest for her senior year. With her help, and much careful proofreading, all 6,606 draws were put into computer-readable form and subjected to analysis

Table 2 shows one result of this—the distribution of the 33,030 numbers drawn (5 in each of 6,606 drawings, or 5 x 6,606 = 33,030), and it shows that there was a fairly even distribution of the numbers among the 90 possible. But in the science of statistics “fairly even” is not enough—is the spike at number 26 too high? Is that at 87 too low? Subjecting these data to a test is not a standard statistical procedure, because the fact that the five numbers in a draw are chosen without replacement makes the usual chi-square test inappropriate, and I know of no earlier discussion of this than that by my Chicago colleague, Peter McCullagh. By the test he provides, these data pass with flying colors. The visual appearance of evenness is not misleading.

Can we then conclude from this that the Loterie was fair? No. An even distribution does not rule out the possibility the numbers tended to clump, as would be the case if they were insufficiently mixed and as apparently happened with the American Military Draft Lottery in 1970. Technically we would want to verify that all possible combinations of two, three, four, and five numbers appear in the right proportions. But there are nearly 44 million possibilities and only 6,606 draws; the same approach doesn’t work there. A similar chart for combinations of five would be too sparse— 44 million spikes, mostly of height zero.

One approach that does work has a close relationship to what the probabilists call the Birthday Problem. It is usually put this way: How many randomly selected people must you assemble in a room before the chance is at least one-half that at least two of them share the same birthday? The standard answer is 23, and most people consider this surprisingly small. Since 23 is also a usual size for a high school or college math class, it is tempting to demonstrate the problem on the class. And when instructors try this in class, it is their turn to be surprised: Usually (or at least with a frequency well over half), they find duplicate birthdays! What is the explanation? Well, the calculation of the number 23 is based upon an assumption that all 365 birthdays occur with equal frequency. But not only are there seasonal variations, there is also a weekend effect. Obstetricians avoid delivering on weekends and major holidays, and most school classes consist of people of the same age, all born in years with the same weekends! The net effect is to make birthdays unequally frequent and to make it much more likely that there will be a duplication in a class of 23, more like a 70 percent chance. Just so, with the Loterie we can look to see how many times different draws on different days produced the same five numbers, possibly in a different order, or how many times they produced results with four numbers in agreement. The data also pass this test with flying colors—there were 233 pairs agreeing in four numbers, and there was just one pair of draws in agreement in five numbers; both are in line with expectations from a fair draw. The data pass several other tests as well, such as looking for serial dependence or for bias in regional Loterie drawings. The conclusion is that I can pronounce the Loterie fair— remarkably fair, in fact. And there are two significant consequences of this conclusion.

The first is a simple observation: This is evidence that groups of people are sensitive to even very small differences in probabilities when the stakes are high. It is very easy, even in the modern age, for an important and highly visible lottery to be demonstrably imperfect, as the 1970 Military Draft Lottery was. But well before the development of refined statistical measures, the French Loterie achieved a high standard of fairness, disciplined only by close public scrutiny. The king had a high stake in the fairness because the gamblers had much to gain if they discovered any bias, and the results show how well this combination of interests succeeded in accomplishing an unusually good result. “Rational choice” may be a recent topic for study in economics, but it has been practiced for centuries.

The second consequence is more subtle. Let me introduce it by asking a question: How might we learn about the characteristics of the gamblers in a lottery today, say the Illinois Lottery? When tickets are sold, the only record that is kept is the fact of the numbers bet. If we were well-financed, we might try to do a careful survey, employing NORC to randomly select a collection of sales offices, then randomly interview purchasers and try to find where they came from, how much they bet. And we would want to monitor trends, so we would wish to do this over many years and then see what changes, if any, occurred. Of course we cannot afford to do that even now—it would be too expensive and impractical in an era where sensitivity to personal privacy makes the academic investigation of such matters difficult at best. Yet I propose to do exactly that, not for today’s lottery, but for a lottery conducted more than a century before the scientific random sample was invented!

This survey is made possible because my wretched little book includes a list of every major winning bet from 1797 to 1833, including where and when it was placed, which regional Loterie was bet on, and how much was paid out (and from that you can deduce how much was bet). Since we have demonstrated that each draw of the Loterie was a scientifically sound random sample of five numbers from the 90 available, this means that every winning bet is scientifically sampled at random from the bets made on that drawing. If the French had made a duplicate list of all bets and sent them to NORC with the request that a sample be drawn, the sample would perhaps have been larger but it could not have been more random. The French were carrying out a perfectly randomized social survey just as surely as if that had been their conscious intention, and they did so routinely for decades, well over a century before such a concept was introduced. Only a few simple questions were asked in this survey, namely the numbers bet and the size and place of the bet, but nonetheless we can learn something about how risk was regarded two hundred years ago.

The first and simplest issue I addressed is, what numbers were preferred in France just after the revolution? The answer would not surprise students of the modern lottery: simple numbers; low numbers; pairs of digits like 22, 33, 44, 88, 63, 36. (See table 3.) Low numbers could come from birthdates or simple lack of imagination: I understand that one of the most common choices of six numbers in the California Lottery is the numbers 1, 2, 3, 4, 5, 6. There is another suggestion in a short item in the December 28, 1797, issue of the official newspaper the Moniteur Universel. It explains that a citizen bet a total of 1,008 francs (around $5,000) on all 28 ambes(24 francs each) and all 56 ternes (6 francs each) corresponding to the numbers associated with the name “Bonaparte,” with A=1, B=2, etc. He won on one terne and 3 ambes, for a net gain of over 50,000 francs, a considerable fortune! The article concludes with a short notice that General Bonaparte was received the day before as a member of l’Institut Nationale, suggesting that a press agent may have been involved.

Table 3. Bettors’ Numbers

There are eight distinct “Bonaparte” numbers (2, 14, 13, 1, 15, 17, 19, 5), and the question arises, did others imitate the lucky citizen? With a random selection these numbers should occur about 9 percent of the time, but of course they are also among the favored small numbers, so it is not surprising that over the years 1797 to 1814 they occurred as about 11 percent of the choices. Interestingly, in the years after the Battle of Waterloo this increased to 14 percent. Choosing numbers from names in this manner was clearly quite limiting (to the numbers 1 to 26), and an entrepreneur named J. B. Marseille (who billed himself as a “mathematicien”) responded with an extremely complicated cryptological scheme that could yield no end of sets of numbers based upon the same name

Who were the people choosing these numbers? Were they lower or upper class, were they primarily Parisian or spread throughout France? The sizes of the payoffs indicate that the preponderance of bets were small: about 50 percent were for only 2 sous—about 50 cents in today’s currency, and about 80 percent were for 5 sous or less. Only a very small fraction were for large amounts. The largest single bet on a quaterne was 10 francs—about $50—and the largest single bet on a terne was 125 francs—over $600. Of course these were not the only bets placed: My book only reported on the long shots of the time, the quaternes and a few ternes. The longest shot, the quine, was not a permitted bet for most of this period; I suspect the reason for this was the state’s fear of fraud. The successful simpler bets were not recorded. Still, the Loterie’s appeal seems to have been predominantly to the middle class and lower middle class. The sans-culottes would have found even a sou hard to come by, and after the revolution the rich seem to have only dabbled in the Loterie

Where did the people who bet come from? The answer is, all over France, from small towns and large cities. Still, Paris was the center of activity: 43 percent of the bets were placed in Parisian sales offices, this at a time when Paris was home to less than 4 percent of the population of France. At that time, France was predominantly agricultural, with slightly over 7 percent of the citizens of France residing in towns of population 25,000 or greater. Thirty-seven percent of this urban population was in Paris. This means that the bets on the Loterie may not have been far from being uniformly distributed across the urban population of France at that time. With small bets spread broadly over the nation’s urban population, the appeal of the Loterie seems to have been widespread in the cities.

There is one major question remaining. Why was the Loterie permanently suspended in May of 1836? It had been a phenomenal success. The only year it did not make a net profit for the state was 1814, when every army in Europe was crossing France. In that year, the Paris drawings continued, but most other offices were closed for a few months and the office in Brussels moved permanently to Lille, since Brussels was no longer part of France. That year, the cost of administration overran proceeds, and the Loterie lost a third of a million francs, but the net profit over the first quarter of the nineteenth century was generally ten million or more per year.

True, there were voices through the 1820s accusing the Loterie of being a moral scourge upon the nation, that it took money from those least able to pay, for hopes that were false in ways they could never understand. Indeed there was a long tradition to such sentiments. Already in 1776, Adam Smith had written in The Wealth of Nations, “That the chance of gain is naturally overvalued, we may learn from the universal success of lotteries.” Smith did not suggest this tendency to overvalue was limited to any particular economic class, but later writers thought the poor were especially susceptible

In 1819, Pierre Simon Laplace, one of the architects of the modern theory of probability, rose to address a governmental council. In that year the French finances were in excellent shape, and he urged the members to take advantage of the moment of diminished need and abolish the Loterie.

Laplace argued, “The poor, excited by the desire for a better life and seduced by hopes whose unlikelihood it is beyond their capacity to appreciate, take to this game as if it were a necessity. They are attracted to the combinations that permit the greatest benefit, the same that we see are the least favorable.”

He further argued, anticipating Quetelet’s idea of social determinism, that the tax was not really voluntary, as was generally believed:

“No doubt,” he stated, “it is voluntary for each individual, but for the set of all individuals it is a necessity, just as their marriages, births, and all sorts of variable effects are necessary, and nearly the same each year when their number is large, just as the revenues from the Loterie are as constant as is agricultural production.”

And he further claimed that the state’s annual net profit of 10 to 12 million was offset by a hidden tax upon the poor of 40 to 50 million per year in lost investment.

Many others spoke in similarly colored terms. In 1832, one French attorney wrote that “each day it becomes more urgent to put an end to this odious exploitation of the credulity and misery of the people.”

Was, then, the suspension of the Loterie in 1836 simply the result of a moral reawakening in France? Now, I happen to believe that in this one matter Adam Smith was wrong, that in all of these lotteries the true odds were widely known (even widely advertised) to all levels of society, and the hypothesis that their practical implications were misunderstood despite the years of active observation is untenable. But even if you accept the arguments that were presented by Smith and Laplace and others, the question remains: Those voices had been there from the beginning; why were they only heard in the 1830s?

Now, my longitudinal survey of the Loterie provides some revealing evidence bearing on this question. The record of winners allows us to estimate the number of bettors. We can crudely estimate the average number of quaternes bet per sales office for each drawing, and this average decreased from around 200 in 1800 to around 30 in 1833. From 1810 to 1830 the number of quaternes bet in Paris decreased about 25 percent. In the regional Loteries the decrease was greater: In Lyon there was an over 40 percent decline. The public was losing their taste for the Loterie, and by 1836 this shifted the political balance. As the survey shows, the Loterie was never more than an urban phenomenon in a predominantly agricultural country. When profits were running high, the ears of agricultural France were deaf to the moralists’ complaints, but when the urban public began to tire of the Loterie, the arguments became more convincing

The Loterie de France flourished for three-quarters of a century, with a brief hiatus in the 1790s. The persistent demand for the Loterie by a public increasingly well educated in probability shows an attraction to low-cost risk at the individual level that continues today in all societies. The Loterie prospered with the increasingly general knowledge of probability and without doubt contributed to that knowledge; it was a public laboratory for chance where students could see almost daily the application of the techniques they studied in secondary school and university. And education in probability prospered: The great growth in France in the publication of textbooks and treatises on probability dates from 1783 to the 1830s, the period of the Loterie.

The Loterie also serves as an example of the phenomenon of corporate risk aversion by the state. From the resistance Casanova encountered at the founding of the Loterie to the demise of the quine as an option after about 1803, the state was ever mindful of the fact that it always stood the chance of losing on its bets, millions on the quine and hundreds of thousands on the quaterne. No modern state lottery, whether lotto or sweepstakes, accepts such a risk. The odds were so strongly in favor of the state on these bets that it would seem foolish that they would worry, but against that there was always the specter of undiscovered fraud and the administrative manuals of the time show they took this possibility very seriously. It is plausible that this risk aversion, coupled with the slow secular decline in public interest as the Loterie became dated, contributed to the Loterie’s demise.

This type of lottery (with a menu of bets and guaranteed fixed payoffs even for longodds bets) was never widely adopted internationally—only in parts of Italy and Spain, in some German cities, in Vienna, and in France. According to my wretched little book, the payoffs in France were superior to the others; for example, in Germany they paid only 14 times on an bet on a single number and 60,000 times on a quaterne. The Loterie survived the revolution, but by 1836 it had run its course. Nonetheless it left its mark on succeeding generations’ understanding of chance.

The reason for its success—the attraction of risk whether by gambling or speculation—was obvious to Casanova even if it can confound economists to this present day. Casanova wrote his memoirs in retirement in Bohemia, working as a librarian for a duke, but as he vividly recalled the passions of his youth, he wrote, “The passion for gambling was rooted in me; to live and to play were to me two identical things.” Casanova’s lottery inadvertently produced the first scientifically conducted social survey, a curious example of what the late sociologist Robert K. Merton referred to as an “unanticipated consequence of social action.” It is a survey that is very much with us today. The next time you read of a cook or professor winning a hundred million dollars in the Powerball Lottery, do not simply think of that cook or professor as a very lucky person. Rather, you are observing the latest scientific random selection in a survey that dates back nearly 250 years, a survey with a remarkably high cost per observation. And think of Casanova.

About the Lecturer

Stephen M. Stigler is the Ernest DeWitt Burton Distinguished Service Professor in the Department of Statistics, the Committee on Conceptual and Historical Studies of Science, and the College.

He earned his B.A. at Carleton College in 1963 and his Ph.D. from the University of California, Berkeley, in 1967. He served on the faculty of the University of Wisconsin at Madison before coming to the University of Chicago in 1979. He served as chair of the Department of Statistics from 1986 to 1992.

Stigler is an expert on the history of statistics, particularly the implications of problems in the natural and social sciences for the development of statistical methods. His publications include The History of Statistics: The Measurement of Uncertainty before 1900 (1986) and Statistics on the Table: The History of Statistical Concepts and Methods (1999), as well as numerous scientific articles

Stigler is currently president-elect of the International Statistical Institute; he will serve as president of the institute from 2003 to 2005. In addition, he is a fellow of the American Academy of Arts and Sciences.