Casanova’s Lottery [book review]

This “history of a revolutionary game of chance” is the latest book by Stephen Stigler and is indeed of an historical nature, following the French Lottery from its inception as Loterie royale in 1758 to the Loterie Nationale in 1836 (with the intermediate names of Loterie de France, Loterie Nationale, Loterie impériale, Loterie royale reflecting the agitated history of the turn of that Century!).

The incentive for following this State lottery is that it is exceptional by its mathematical foundations. Contrary to other lotteries of the time, it was indeed grounded on the averaging of losses and gains on the long run (for the State). The French (Royal) State thus accepted the possibility of huge losses at some draws since they would be compensated by even larger gains. The reasoning proved most correct since the Loterie went providing as far as 4% of the overall State budget, despite the running costs of maintaining a network of betting places and employees, who had to be mathematically savy in order to compute the exact gains of the winners.This is rather amazing as the understanding of the Law of Large Numbers was quite fresh (on an historical scale) thanks to the considerable advances made by Pascal, Fermat, (Jakob) Bernoulli and a few others. (The book mentions the Encyclopedist and mathematician Jean d’Alembert as being present at the meeting that decided of the creation of the Loterie in 1757.)

One may wonder why Casanova gets the credit for this lottery. In true agreement with Stigler’s Law, it is directly connected with the Genoan lottery and subsequent avatars in some Italian cities, including Casanova’s Venezia. But jack-of-all-trades Casanova was instrumental in selling the notion to the French State, having landed in Paris after a daring flight from the Serenissima’s jails. After succeeding in convincing the King’s officers to launch the scheme crafted by a certain Ranieri (de’) Calzabig—not to be confused with the much maligned Salieri!—who would later collaborate with Gluck on Orfeo ed Eurydice and Alceste, Casanova received a salary from the Loterie administration and further run several betting offices. Until he left Paris for further adventures! Including an attempt to reproduce the lottery in Berlin, where Frederick II proved less receptive than Louis XIV. (Possibly due to Euler’s cautionary advice.) The final sentence of the book stands by its title: “It was indeed Casanova’s lottery” (p.210).

Unsurprisingly, given Stephen’s fascination for Pierre-Simon Laplace, the great man plays a role in the history, first by writing in 1774 one of his earliest papers on a lottery problem, namely the distribution of the number of draws needed for all 90 numbers to appear. His (correct) solution is an alternating sum whose derivation proved a numerical challenge. Thirty years later, Laplace came up with a good and manageable approximation (see Appendix Two). Laplace also contributed to the end of the Loterie by arguing on moral grounds against this “voluntary” tax, along Talleyrand, a fellow in perpetually adapting to the changing political regimes. It is a bit of a surprise to read that this rather profitable venture ended up in 1836, more under bankers’ than moralists´ pressure. (A new national lottery—based on printed tickets rather than bets on results—was created a century later, in 1933 and survived the second World War, with the French Loto appearing in 1974 as a direct successor to Casanova’s lottery.)

The book covers many fascinating aspects, from the daily run of the Loterie, to the various measures (successfully) taken against fraud, to the survival during the Révolution and its extension through (the Napoleonic) Empire, to tests for fairness thanks to numerous data from almanacs, to the behaviour of bettors and the sale of “helping” books. to (Daniel) Bernoulli, Buffon, Condorcet, and Laplace modelling rewards and supporting decreasing marginal utility. Note that there are hardly any mathematical formula, except for an appendix on the probabilities of wins and the returns, as well as Laplace’s (and Legendre’s) derivations. Which makes the book eminently suited for a large audience, the more thanks to Stephen Stigler’s perfect style.

This (paperback) book is also very pleasantly designed by the University of Chicago Press, with a plesant font (Adobe Calson Pro) and a very nice cover involving Laplace undercover, taken from a painting owned by the author. The many reproductions of epoch documents are well-done and easily readable. And, needless to say given the scholarship of Stephen, the reference list is impressive.

The book is testament to the remarkable skills of Stephen who searched for material over thirty years, from Parisian specialised booksellers to French, English, and American archives. He manages to bring into the story a wealth of connections and characters, as for instance Voltaire’s scheme to take advantage of an earlier French State lottery aimed at reimbursing State debtors. (Voltaire actually made a fortune of several millions francs out of this poorly designed lottery.) For my personal instructions, the book also put life to several Métro stations like Pereire and Duverney. But the book‘s contents will prove fascinating way beyond Parisian locals and francophiles. Enjoy!

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE. As appropriate for a book about capitalising on chance beliefs!]

the mechanical [book review]

Read this 2015 book by Ian Tregillis with growing excitement as I was first unsure why I had ordered it. It is a mix of the Baroque Cycle and of the Difference engine, with Huygens playing the central role (rather than Newton). The postulate of the story is that he found [in the 1600’s] a way to create robots (or mechanicals, or yet Clakkers) with autonomy, prodigious strength, and unlimited “life” time. Endowing the Netherlands with such an advantage as to become the unique European power. Except for a small population of French people, living in exile in Montréal, renamed as Marseille-in-the-West, where the descendants of Louis XIV were desperately fighting the Dutch robots with their barely sufficient chemical skills… In addition to this appealing alternate history, where the French are arguing about the free will of the machines, and building underground railways to convey rogue mechanicals outside the Dutch empire, partly for being Catholics and hence following the Pope’s doctrine [and partly to try to produce their own robots], where the Pope is also a refugee in Québec, and where New Amsterdam has not turned into New York, but is a thriving colonial city in America, linked to the mother country by mechanical boats and Zeppelin-like airships, the machines are constrained to obey the humans, with the Queen’s wishes at the top of a hierarchy of constraints. And no Asimov’s law to prevent them from being used as weapons, to the French’s sorrow! But their degree of autonomous thought is such that a mere loosening of a component may remove the compulsion and turn them into rogues, i.e, free willed robots. On the converse side, a nefarious guild in charge of a Calvinist faith and of the maintenance of the robots is attempting to extend this control of the Dutch State over some humans. Which makes for a great setting discussing the blurry border between humans and AIs, with both humans and Clakkers bringing their arguments to the game… I am now eagely waiting for the second and third volumes in the series of The Alchemy Wars to arrive in the mail to continue the story!