''Essay d'analyse sur les jeux de hazard'' (''Essay on the Analysis of Games of Chance'') is a book on

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and mathematical

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

written by Pierre Remond de Montmort published in 1708 with an expanded second edition in 1713. It was the first comprehensive text published on probability theory. With ''Essay'', Montmort intended to incorporate and build upon

Jacob Bernoulli Jacob Bernoulli (also known as James in English or Jacques in French; – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibniz ...

's unfinished ''

Ars Conjectandi (Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Nicolaus I Bernoulli. The seminal work consolidated, ap ...

'', which remained unpublished at the time of Jacob's death. Both works applied theories of combinatorics and probability to analyze

games of chance A game of chance is in contrast with a game of skill. It is a game whose outcome is strongly influenced by some randomizing device. Common devices used include dice, spinning tops, playing cards, roulette wheels, numbered balls, or in the case ...

popular at the time. ''Essay'' additionally solved problems posed by

Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...

' treatise ''De ratiociniis in ludo aleae'' (''On Reasoning in Games of Chance'', 1657) and proposed the solutions for new and more complex problems. ''Essay'' greatly influenced the thinking of Montmort's more famous contemporaries,

Nicolaus I Bernoulli Nicolaus Bernoulli (also spelled Nicolas or Nikolas; in Basel – 29 November 1759 in Basel) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. Biography Nicolaus Bernoulli was born on in Base ...

and

Abraham De Moivre Abraham de Moivre FRS (; 26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He move ...

Continuation of Montmort's work

In 1710, Montmort began a three-year correspondence with Nicolaus I Bernoulli, Jacob Bernoulli's nephew, which was incorporated into the second edition of ''Essay'' published in 1713. The correspondence covers many topics, particularly the probability questions that arose from the original edition of the book. Also that year, Nicolaus published Jacob's ''Ars Conjectandi'', eight years after Jacob's death. The second edition of ''Essay'' is twice as long as the first edition and is divided into five sections: # A Treatise on Combinations; # Problems on Games of Chance; # Problem on Quinquenove; # Various Problems; and # Correspondence The second section studies the card games: Pharaon, Lansquenet, Treize, Bassette, Piquet,

Triomphe Triomphe (French for triumph), once known as French ruff, is a card game dating from the late 15th century. It most likely originated in France or Spain (as triunfo) and later spread to the rest of Europe. When the game arrived in Italy, it shared ...

, L'Ombre,

Brelan Brelan () is a famous French vying game with rapidly escalating bets from the seventeenth to nineteenth century, and hence also a name for a card player, gambler or the name of the place where the game was played. The game is quite similar to the ...

, Imperial and Quinze. The third section examines games played with dice: Quinquenove, Hazard, Esperance,

TricTrac Trictrac (also tric trac or tric-trac) is a French board game of skill and chance for two players that is played with dice on a board (game), game board similar, but not identical, to that of backgammon. It was "the classic tables game" of Franc ...

, Trois Dez, Rafle, Trois Rafles, and Noyaux. The fourth section solves problems posed in Huygen's ''De ratiociniis in ludo aleae'' and poses four unsolved problems. The fifth section contains Montmort's correspondence with Nicolaus Bernoulli and introduces the St. Petersburg paradox and the

Waldegrave problem In game theory, the Waldegrave problem is a problem first described in the second edition of Pierre Raymond de Montmort`s '' Essay d'analyse sur les jeux de hazard'', which is the first discussion of a mixed strategy to derive a solution in game the ...

References

Sources

* * * {{authoritycontrol 1708 non-fiction books 1708 in science 1714 non-fiction books Probability books Combinatorics Books about games