St Petersburg paradox

Pierre-Louis Dumesnil, Interior with Card Players, c1752 , Metropolitan Museum, N.Y.

The "St  Petersburg Paradox" is a classic problem in probability theory first formulated in the early 18th century by the Swiss Mathematician Nicolas Bernoulli.  It first came to widespread attention in 1738 when Daniel Bernoulli, another of the Bernoulli dynasty, presented it to the Imperial Academy of Sciences in St. Petersburg.  D'Alembert described it in the Encyclopédie article "Croix ou pile" in 1754 and returned to it repeatedly in later writings. Buffon claimed to have been introduced to it independently as early as 1730 by the Genevan professor Gabriel Cramer and to have reached conclusions similar to those of Daniel Bernouilli.

D'Alembert loses at roulette...

Our experience and understanding of the laws of nature teach us that the same event never happens many times in a row, and it is by virtue of this acquired knowledge that we dismiss the repetition of "heads" or "tails" many times consecutively.

(d'Alembert, Opuscules mathématiques, 1780, p.48)

If Google hits are anything to go by, d'Alembert is remembered chiefly today as the author of a codified gambling staking plan.  Although there is no documentation, the d'Alembert System probably dates from the late 18th or early 19th century and was not "invented" by d'Alembert at all, though it is loosely based on his speculations on the mathematics of probability.

Philidor takes on The Turk

Here is Wolfgang von Kempelen's  famous chess-playing automaton, the Turk. There is loads and loads written on it. This account of the Turk's tour to Paris in 1783 and its encounter with the great Philidor is taken mostly from Thomas Standage's book of 2002 The Mechanical Turk (p.42-46).

Jean-Jacques plays chess

Chess set in the "Régence" style which was standard in France in the 18th and 19th century.  The design was possibly that of  the furniture make Charles Cressent  (1685-1768).  See http://ccifrance.com/77.html

 Rousseau discovers chess

Of all the Enlightenment lovers of the game, it was Jean-Jacques Rousseau who was the most enthusiastic chess player.  According to the Confessions he was introduced to chess at Chambéry, during his séjourn with Madame de Warens, in about 1737 by a Genevan called Gabriel Bagueret who had perhaps been employed by Peter the Great as a secret agent - according to Rousseau ,he was  a "rogue" and one of the biggest fools he had ever met:

He got the idea of proposing to teach me chess, which he could play a little.  I tried almost against my will, and after i had more or less learned the moves, my progress was so rapid that before the end of our first sitting I could give him the rook which at first he had given me. 

Rousseau being Rousseau, he instantly became a chess fanatic, bought himself a board and a copy of Gioachino Greco's manual and sat up night and day committing chess moves to memory. He relates that, nonetheless, when he went to the local café, he was repeatedly beaten by Bagueret:

Every time I have tried to practise by studying games with Philidor's book or Stamma's the same thing has happened to me; I have completely worn myself out and found my play weaker than before.  For the rest, whether I have given up chess for a time or kept myself in practice by playing, I have never improved a jot since that first sitting; I have always found myself just where I was when I got up from it.  I might practise for thousands of centuries, and at the end I should be capable of giving Bagueret his rook, but that is all.  Time well spent, do you think?
Confessions Book 5 (Penguin Classics ed. p.211)



Rousseau - chess champion in the making

In 1742 Rousseau came to Paris  with the hope of making his fortune with a new scheme of musical notation and, when, that fell through, briefly fancied he could make a name for himself as a chess player. He seems to have played chiefly not at the Régence, but at the Café Maugis in the rue Saint-Séverin (remembered today only because it featured in a police report). 

There I made the acquaintance of M. de Légal, of M. Husson, of Philidor, and of all the great chess players of that time, without however improving my game thereby. But I had no doubt that in the end I should be better than any of them; and that, in my opinion, would a sufficient resource."
Confessions Book 7 (Penguin Classics ed. p.271)

The over-confident Rousseau's potential career as a chess player was cut mercifully short when he left for Venice in 1743 as secretary to the French ambassador.

On his return in 1745 Rousseau turned once more to music and managed to fall out with the amicable Philidor who arranged his opera, Les Muses galantes, for performance in the private theatre of the financier La Pouplinière at Passy.  The work was a disaster, though Grimm admired Philidor's overture. Family tradition has it that Philidor conscientiously wrote his musical accompaniment to showcase Rousseau's melodies,but the score has long since disappeared. Rousseau jealously disparaged his contribution and complained that Philidor failed to commit himself to the work.(Allen Life of Philidor p.14-17) 

Philidor - continued

By Charles- Nicolas Cochin, 1772
http://gallica.bnf.fr/ark:/12148/btv1b8423528b/f1.item

In the 1750s Philidor,  once more back in Paris, began to make a name for himself as a composer of comic operas.  According to his son, it was Rameau who advised him to abandon Church music to devote himself to the music of the stage. It was at this time too that he came into contact with Diderot, with whom he was probably acquainted from the circles of the financier  La Poupelinière, and with Grimm.  In 1760 he married Angélique-Henriette-Elisabeth Richer, daughter of a composer and herself an accomplished singer.  The couple had four surviving sons and a daughter. In 1766 Philidor composed an operatic tragedy, Ernelinde, princesse de Norvège, which, despite mistakes by both  musicians and performers, was a great success; he was subsequently awarded a royal pension of twenty-five louis d'or.

Philidor - chess phenomenon

The career of the musician and virtuoso chessmaster François-André Danican Philidor is interesting both in itself and for the light it shines on 18th-century society, its systems of patronage and modes of sociability, and the opportunities it afforded to an exceptional gifted individual.

Cavagnole - a "cheating game"

Gambling was another of Emilie's passions.  Her quick mind enabled her to calculate chances effectively (though it did not save her from spectacularly losing over 80,000 livres at the royal table at Fontainebleau in 1747).  On her death Voltaire lamented loss a "great man" who translated Newton and Virgil, but was known among women only for her "diamonds and cavagnole" ( to Baculard d’Arnaud, letter of 14th  October 1749)

Gaspare Traversi," The Card Party"  (Metropolitan Museum of Art)

"Cavagnole" was indeed a surprisingly unintellectual pastime for an intelligent woman. Usually played for low stakes, it was easy to cheat at and boringly simple to play.  It was looked upon with contempt by courtiers like Voltaire, who were obliged to suffer stifling evenings at the gambling table:

On croirait que le jeu console ; 
Mais l'ennui vient , à pas comptes ,
A la table d'un carvagnole , 
S'asseoir entre des majestés

[They believe that the game amuses / but boredom arrives, step by step/ at the cavagnole table / to take a seat between their Majesties].