REVIEWS
“The book [stands] witness to the remarkable skills of the author, who searched for related material for more than thirty years, from Parisian specialized booksellers to French, English, and American archives. He manages to bring a wealth of connections and characters into the story, such as Voltaire’s scheme to take advantage of an earlier French state lottery aimed at reimbursing state debtors.”
— CHANCE
“In 1758, the French state launched an unusual lottery suggested by famed Italian gambler Giacomo Casanova. It lasted until 1836, with a three-year gap during the French Revolution, providing 4% of national income at its peak. However, every time it was drawn, the state was at risk of losing a large amount, with ‘little more than a mathematical theory to protect it,’ writes statistician Stigler as he tells the lottery’s story for the first time.”
— Nature
“I recommend Stigler’s new book Casanova’s Lottery to anyone interested in the history, economics, ethics, and politics of modern-day lotteries. Among other things, Stigler not only traces the history of the French Loterie, the first large-scale commercial lottery in history, he also examines the mathematics of risk, including the epic back-and-forth debate over the ‘maturity of chances,’ or so-called gambler’s fallacy, and the politics of legalized gambling generally.”
— Prior Probability
“Stigler’s statistical expertise enables him to undertake an analysis beyond the skill of many (maybe most) historians. . . . Casanova’s Lottery will be of interest to historians of gambling, finance, and probability, not least for the clearly explained statistical analyses. Moreover, Stigler’s lucid and elegant prose makes the book an engaging read for a wide audience.”
— European History Quarterly
“This excellent book blends compelling mathematical content with fascinating historical context as it describes the remarkable story of the French lottery (Loterie) established in 1757. . . . Stigler relies on a rich array of primary source materials, including rediscovered original lottery documents, for evidence of sound mathematical calculations that supported the French state’s willingness to risk significant loss during each individual draw due to the assurance of longer-term gains.”
— British Society for the History of Mathematics Neumann Prize Committee
“Casanova’s Lottery captivates with the variety of its contents and the questions it puts forth to historians. Stigler offers a fascinating history of the Loterie royale ‘from the ground up,’ enhanced with rare and original archival material, part of which had been patiently collected by the author himself over several decades. While the book is written in clear language, making it perfectly intelligible for readers who lack mathematical knowledge . . . the author’s proficiency in probability theory and its history proves to be an invaluable asset for an in-depth study, allowing readers to grasp the concrete money issues that shaped the practices of the bettors and the organizers.”
— Journal of Modern History
"The author’s statistical skills enrich the book with mathematical annotations about the gambler’s fallacy, marginal utility, Laplace’s theorem, theory of risk and other ‘technical’ arguments. This work is an entertaining history and a mathematical study that once again highlights the close links between the emergence of probability calculus and games of chance."
— Choice
"Stigler draws on a particularly fascinating historical case study, about which he has incredibly deep knowledge and which he is able to transmit in meticulous detail and in delightfully lucid prose. The writing is absolutely clear and readable—a wonderful example of the possibility of writing about serious scholarly matters in a way that invites the reader along and allows the reader to share in the author's expertise, rather than either excluding the non-expert reader or talking down. It's remarkable how accessible Stigler makes the technical material on probability and statistics, again without any simplifications that would take away from the seriousness of the treatment. This is truly an unusually well-written book."
— Justin E. H. Smith, author of The Internet Is Not What You Think It Is
"Stigler is unrivaled in his ability to elaborate subtle points of probability and statistics for broad audiences and to integrate discussion of these technical concepts with lively narrative and historical analysis. He masterfully integrates the practicalities of betting strategy and lottery administration with higher-level intellectual debates about risk, probability, and the ethics of gambling. Entertaining and highly informative."
— William Deringer, author of Calculated Values: Finance, Politics, and the Quantitative Age
TABLE OF CONTENTS
Introduction
DOI: 10.7208/chicago/9780226820781.003.0001
[John Law;state lotteries;Genoese lottery;history of probability;raffles]
The French lottery of this book was unusual in scale and in the type of risk accepted by the state, but it did have antecedents. The main other types of lotteries that were held in Europe before 1750 are reviewed, as is the French experience with experimental approaches to finance, including John Law's innovative approaches to a basis for currency, which proved to be too far ahead of its time in 1720. This was also a time ofrapid development in the theory of probability, whose rudimentary concepts go back at least to 3000 BCE in Mesopotamia. Financial necessity in France in the 1750s was thus joined to a newly developed concept of risk in an environment fertile for experimentation, a mix that would be assisted by a chance arrival of an Italian catalyst in the person of Casanova. The story of the undertaking of this study and its challenges is told.
Casanova
DOI: 10.7208/chicago/9780226820781.003.0002
[Genoese lottery;Giacomo Casanova;Giovanni Calzabigi;Madame de Pompadour;Jean D'Alembert;playing cards]
Casanova escaped from a Venetian prison in 1756 and made his way to Paris, where many were eager to hear the story of the escape. He encountered Madame de Pompadour and members of the finance ministry, leading to conversations with the director of the Military School (the École Militaire), who sought a plan to gain financial support for the school. In the process, Casanova met the Calzabigi brothers, joining them in presenting plans for a lottery to the ministry. Casanova played a crucial role is selling the plan, a variation of one he had encountered in Venice, Naples, and Genoa, the drawings to begin in April 1758.
The Genoese Lottery
DOI: 10.7208/chicago/9780226820781.003.0003
[Hua-Hoey Lottery;Game of Thirty-Six Animals;Marco Polo;lotto]
The Genoese lottery evolved from the practice of betting on elections in Genoa in the 1300s. By the late 1600s it was commonly found in several Italian cities in the form of drawing five numbered balls from a wheel of fortune from a set of 90 or 100 or 120 balls that were sequentially numbered. It was even advertised briefly in London in 1662. Other similar lotteries had a long history in China.
The Establishment of the Loterie
DOI: 10.7208/chicago/9780226820781.003.0004
[wheel of fortune;extrait;ambe;terne;Ecole Militaire]
After a series of delays, the lottery of the École Militaire (henceforth the "Loterie") was formally established on 15 October 1757. The decree gave the rules, similar to the earlier Genoese lottery but with slightly more generous payouts, and similar to modern Lotto but with five balls being drawn from a wheel containing 90 sequentially numbered balls, with initially three types of bets permitted. A speculation is offered for the choice of the initial sizes of the payouts.
Problems and Adjustments in the Early Drawings
DOI: 10.7208/chicago/9780226820781.003.0005
[wheel of fortune;orphans;Giovanni Calzabigi;Boucher;Frederick the Great]
The first drawing on 18 April 1758 was financially successful, but it revealed a number of problems with the method of drawing that were hastily dealt with in a new decree in May, before the second drawing 27 June 1758. The decree described the procedure in painstaking detail, with each step broken down and witnessed by both officials and gamblers. A year later some other steps were spelled out regarding the ways bets were recorded, to minimize the possibility of errors, either by fraud or mistakes in recording. By the end of 1760, Casanova and the Calzabigis had departed from France for other adventures. The success of the Loterie seemed assured, and by 1770 there were 80 sales offices in Paris and the surrounding area.
Antoine Blanquet and the Great Expansion of 1776
DOI: 10.7208/chicago/9780226820781.003.0006
[Anne Robert Jacques Turgot;quaterne;quine;déterminé bets]
Near the end of its second decade, the Loterie had enjoyed modest financial success, but it faced increased foreign competition, and the French finance ministry was looking for more sources of revenue. In 1776 the ministry changed the Loterie from being solely dedicated to the École Militaire and expanded its scale with many more sales offices across France, and with several new bets offering larger payoffs in order to meet foreign competition.
The Introduction of Bonus Numbers: Les Primes Gratuites
DOI: 10.7208/chicago/9780226820781.003.0007
[Primes Gratuites;powerball;lottery design]
The 1776 expansion also announced a new way to bet, with extra draws of "Bonus Numbers" at each drawing, a sort of anticipation of modern Powerball drawings. The scheme was hard to administer and was almost immediately declared a failure, ending in February 1777. As compensation for this cancelled opportunity, the bets with largest payouts had their payout scaled up slightly.
The Spread of the Loterie in Europe
DOI: 10.7208/chicago/9780226820781.003.0008
[Giacomo Casanova;Lord North;Klasse Lotteries]
In 1758, the only cities outside of Italy with lotteries on the Genoese plan were Paris and Vienna. By the 1770s there were similar lotteries in Brussels, in Spain, in Denmark, and in 26 German states. The rules varied slightly, and not all lasted very long. Curiously there was no such lottery attempted in England, although Casanova may have made an unsuccessful attempt to repeat there the success of Paris.
Data Security: The Design of the Tickets
DOI: 10.7208/chicago/9780226820781.003.0009
[printing codes;women's names;dungeon]
The Loterie faced unprecedented challenges: in record keeping, in printing secure tickets, and in training a huge sales force. The potential loss in one drawing was unlimited, and threats of fraud (such as backdated or forged tickets) led to innovative recording of bets in many formats and fraud-resistant printing schemes that evolved with accumulated experience.
The Loterie and the Revolution
DOI: 10.7208/chicago/9780226820781.003.0010
[Louis XVI;Napoleon Bonaparte;Château Kirwan;fable of the wolf and lamb]
The Loterie did not miss a drawing through the early years of the French Revolution; only in the Terror a month after the execution of Marie Antoinette was it suppressed, on 15 November 1793. Three years later it was resumed, as the new regime needed its support. After 1800 it was greatly expanded, eventually with three drawings in each of Paris and four other French cities, and with over 1000 sales offices in France. The net profit in 1776 was about 2 million francs; in 1810 at the peak of the Empire it was more than 10 times that. The Loterie thrived through five changes in regime, including two revolutions.
Was the Loterie Fair?
DOI: 10.7208/chicago/9780226820781.003.0011
[wheel of fortune;Menut de St. Mesmin;birthday problem;Emmanuel-Etienne Duvillard]
Each drawing of the Loterie consisted of five numbers being selected from the first 90 integers. The meticulous records of the drawings and the longevity of the Loterie offer a chance to check on the randomness of the draw. A record of 6606 drawings from 1758 to 1834 is examined using a variation on the modern Chi-Square test of equiprobability, and the drawings pass that test, as do smaller sets of drawings for some German lotteries. A manuscript table from 1818 shows that concerns about fairness occurred at that time as well, but the informal tabulations made would have been reassuring then as well.
Dreams and Astrology: The Bettors and the Loterie
DOI: 10.7208/chicago/9780226820781.003.0012
[tax on stupidity;dream books;August von Kotzebue;quick picks;Comte de Cagliostro]
The drawings were random, but the choices made by bettors were not. In this chapter the choices are studied from two perspectives: a random survey of the numbers bet, and the sources of advice on number choice that were available. The choices made tended to be on smaller numbers, round numbers, jumeaux (22, 33, etc). Lotteries are famously called a "tax on stupidity", but the data suggest the tax was avoided generally; poor long odds bets were played much less frequently than others. Advice books and pamphlets offered ways to choose based on your dreams, by astrology, or by formulas that produced numbers from your name or a famous name. A look at the Loterie in literature shows how the advice may have been followed.
The Number 45 and the Maturity of Chances
DOI: 10.7208/chicago/9780226820781.003.0013
[maturity of chances;martingale;Sébastien Antoine Parisot;Laplace;John Law;insuring tickets;Honoré de Balzac]
Another approach to learning what bettors chose is to study the few scattered surviving tickets, knowing that those are necessarily all losing tickets. From studying them in relation to the record of previous drawings at the time of purchase, it is clear that many bettors believed in the Law of the Maturity of Chances; namely, that numbers become more likely, the longer the time had passed since their most recent appearance in a drawing. Some striking examples are given, and the mathematical support for this Law is discussed in light of the works of Parisot and Laplace. None of that directly addresses the bettor's real question, because the standard mathematical theory of probability already assumes the converse: The game itself has no memory. That Law did provide Balzac with a memorable character. John Law and the practice of insuring lottery tickets is briefly considered.
How Much Did They Bet, and Where?
DOI: 10.7208/chicago/9780226820781.003.0014
[gambling;risk aversion;lottery]
A database of Loterie winners gives a chance for principled inference about how much bettors bet, how that changed over time, and where did they bet, among the thousand sales offices available for most of the period 1798-1834. In that period there were over 167,000,000 bets placed upon one type of bet, the quaterne, where four numbers are specified by the gambler, the great majority betting very small sums. The total number of bets of all types was likely near two and a half billion. The bets were spread over the urban population of France, the areas that were the wealthiest, the best educated and the most industrialized. Paris was the most active of all, on a per capita basis, and the interest in the Loterie remained at a high level to 1830.
Muskets, Fine-Tuned Risk, and Voltaire
DOI: 10.7208/chicago/9780226820781.003.0015
[Jean de Hautefeuille;Voltaire;Charles Marie de La Condamine;classis lottery]
The eighteenth century was a golden age for lottery innovation. There were hundreds of different state lotteries under different plans, most were in some way unique, and no other had the experience of long consistency of plan that the Loterie enjoyed. Many hundreds of others were conceived but never executed. The French economist Hautefeuille invented a scheme where the winning numbers would be selected by firing a musket at a large spinning disk on a boat on the Seine, as spectacular a "drawing" as has ever been suggested. Others invented new ways to package risk. The British with the Classis Lottery of 1711 tried to lessen the disappointment of non-winners; a century later the British painter Tomkins inadvertently came up with a lottery scheme that maximized disappointment. And in 1729, one of the most unsuccessfully designed lotteries in history was exploited by Voltaire and his collaborator La Condamine, who won millions of francs over several months, remarkably without risk, before the loophole in the state lottery was discovered by the finance minister.
The Loterie in Textbooks and Manuals
DOI: 10.7208/chicago/9780226820781.003.0016
[Nicolas de Condorcet;Silvestre François Lacroix;Laplace;Adolphe Quetelet;expected utility]
The Loterie played a role in two very different educational programs. In one, the calculation of odds became a relatively simple exercise in combinatorial mathematics, and even mathematicians who disapproved of the Loterie (essentially all mathematicians) could not resist including it in their textbooks. From the 1780s on, the treatment would begin with the simple calculations, often followed by an expression of disapproval of the enterprise. Condorcet and Lacroix tried to scare the readers with vivid ways of expressing how small the chance of a large prize was. Laplace reached back to Daniel Bernoulli's argument that with decreasing marginal utility even a "fair" lottery had a negative expectation. The second program was for the education of the Loterie's thousands of agents. This ranged from teaching handwriting (ways of writing digits unambiguously), to how to price complicated bets.
The Suppression of the Loterie in 1836
DOI: 10.7208/chicago/9780226820781.003.0017
[Thomas Gataker;Maurice de Talleyrand;Adam Smith;Laplace;Émile Pereire]
All lotteries from their beginning inherited an entrenched opposition to gambling in any form. Even in 1581 there was a principled charge that gambling was addictive, but most early opposition was on religious grounds. The claim was that gambling was immoral, that God controlled even chance events, and to bet on them was contrary to His wishes. By the 1700s such charges were joined by those based on the poor payoffs and low expected gain of many lotteries. By 1789 these concerns were being directed at the Loterie by Talleyrand, and in 1819 by Laplace. Soon economic objections were being raised, when the receipts decreased slightly as the public interest diminished and a new class of bureaucrats from the banking industry gained political power. Rather than permit the enterprise to continue, they would suppress the Loterie and encourage people to put their money in savings banks. The process of shutting down the Loterie was begun on 22 February 1829 and completed as of 1 January 1836.
Conclusion
DOI: 10.7208/chicago/9780226820781.003.0018
[utility theory;Giacomo Casanova;Milton Friedman;Jimmie Savage;Louis-Sébastien Mercier;Jeremy Bentham;Alfred Marshall;risk in Hindu law;Honoré de Balzac]
The Loterie was suppressed in 1836 and no similar lottery was offered in France in the remainder of that century. No other European lottery on that scale with known but unlimited exposure to risk was successful then or later. The moral arguments that had been unsuccessful in closing it for nearly a century had only weakened over time and cannot be accepted as the cause of suppression. Rather, slowing interest in an old institution combined with a new political generation with competing interests carried the day. The attraction of gambling was undimmed, however, even if that attraction remained theoretically unexplained until, perhaps, when Friedman and Savage showed in 1948 how it could fit in with modern utility theory. Meanwhile, governments have remained more open to risks that are not transparent than to those that are. Casanova's success in selling the Loterie to the finance ministers was remarkable.
