Essay d'analyse sur les jeux de hazard
An examination into the heart of chance, penned by Pierre Remond de Montmort, first saw the light of day in 1708. It was a seminal work, a comprehensive treatise on combinatorics and the nascent science of probability. A second, expanded edition arrived in 1713, solidifying its place as the foundational text in probability theory. It’s a shame most people only see the surface of things, the winning hands, the lucky rolls. They don’t appreciate the intricate machinery beneath, the cold logic that governs even the most chaotic-seeming outcomes. Montmort, at least, understood that much.
Montmort’s ambition with Essay was to build upon the unfinished edifice of Jacob Bernoulli's Ars Conjectandi, a work that languished in obscurity until after Jacob’s death. Both men, in their own ways, sought to dissect the popular games of chance of their era using the rigorous tools of combinatorics and probability. Montmort, however, didn’t just build; he challenged. He addressed the puzzles left by Christiaan Huygens in his De ratiociniis in ludo aleae (On Reasoning in Games of Chance, 1657), not merely solving them but proposing new, more complex quandaries. His work resonated, significantly influencing the intellectual currents of his contemporaries, notably Nicolaus I Bernoulli and Abraham De Moivre. It’s rare to find minds that can both appreciate the elegance of a system and simultaneously push its boundaries. Most are content to merely observe.
Continuation of Montmort's Work
The intellectual gears continued to turn. In 1710, Montmort embarked on a three-year exchange of letters with Nicolaus I Bernoulli, nephew of the esteemed Jacob. This correspondence became a crucial component of the second edition of Essay, published in 1713. Their discussions delved deeply into the probabilistic quandaries sparked by the original text, a testament to the fertile ground Montmort had cultivated. It was also in 1710 that Nicolaus finally saw fit to publish his uncle Jacob's Ars Conjectandi, eight long years after Jacob’s passing. One wonders if Jacob would have approved of the delay, or if he’d have been more concerned with the content itself.
The 1713 edition of Essay was a substantial expansion, doubling the original's length and presenting its findings across five distinct sections:
- A Treatise on Combinations;
- Problems on Games of Chance;
- Problem on Quinquenove;
- Various Problems; and
- Correspondence
The second section is a veritable catalogue of the games that occupied the minds of the era’s gamblers and mathematicians alike. It dissects the mechanics and probabilities of Pharaon, Lansquenet, Treize, Bassette, Piquet, Triomphe, L'Ombre, Brelan, Imperial, and Quinze. The subsequent section turns its attention to games of dice, meticulously examining Quinquenove, Hazard, Esperance, TricTrac, Trois Dez, Rafle, Trois Rafles, and Noyaux. Section four revisits Huygens’s challenges, offering solutions to his established problems and, more provocatively, posing four new, as yet unsolved, enigmas. The final section, a collection of Montmort's exchanges with Nicolaus Bernoulli, is perhaps the most intriguing. It’s here that we find the introduction of the St. Petersburg paradox and the Waldegrave problem, concepts that would continue to confound and fascinate mathematicians for centuries. It’s in these dialogues, these back-and-forths, that the true evolution of thought often occurs. The solitary contemplation is valuable, but the friction of opposing intellects? That’s where sparks fly.