Mathematical studies of baccarat before game theory
Session Title
Gambling Mathematics: Classic Games & Odds
Presentation Type
Paper Presentation
Start Date
28-5-2026 12:00 AM
Abstract
The eight most important mathematical works on the game of baccarat prior to the publication of Von Neumann and Morgenstern's (1944) Theory of Games and Economic Behavior (often considered the beginning of game theory) were all in French: ---Théorie mathématique du jeu de baccarat by Émile Dormoy (1873) ---"Étude sur le jeu de baccarat" by Albert Badoureau (1881) ---Traité théorique et pratique du baccara by Laun [pseudonym for Julien-Félix Delauney] (1891) ---Calcul de l’avantage du banquier au jeu de baccara by Jules Louis Henry Lafrogne (1927) ---Nouvel exposé de la théorie mathématique du jeu de baccara by P. Lafaye and Ernest Krauss (1927) ---Le baccara by Georges Le Myre [pseudonym for Andr\'e Sainte-Lagu\"e] (1935) ---La chance et les jeux de hasard, Chapters 15--17, by Marcel Boll (1936) ---Le baccara: chemin de fer --- banque by Marcel Boll (1944) Each of these works has been translated into English, and the mathematical findings have been verified, with a few errors corrected in the process. Our aim in this presentation is to give credit to the early pioneers of the subject for their remarkable insights and daunting calculations done without the benefit of computers. A modern mathematical treatment of baccarat, using computing and game theory, is currently in preparation. ImplicationsOur study reveals that the mathematical works on baccarat between 1880 and 1945 contained a number of new insights that went well beyond Dormoy's initial work and led to a deeper understanding of the game, even before game theory finally yielded the optimal strategy.
Mathematical studies of baccarat before game theory
The eight most important mathematical works on the game of baccarat prior to the publication of Von Neumann and Morgenstern's (1944) Theory of Games and Economic Behavior (often considered the beginning of game theory) were all in French: ---Théorie mathématique du jeu de baccarat by Émile Dormoy (1873) ---"Étude sur le jeu de baccarat" by Albert Badoureau (1881) ---Traité théorique et pratique du baccara by Laun [pseudonym for Julien-Félix Delauney] (1891) ---Calcul de l’avantage du banquier au jeu de baccara by Jules Louis Henry Lafrogne (1927) ---Nouvel exposé de la théorie mathématique du jeu de baccara by P. Lafaye and Ernest Krauss (1927) ---Le baccara by Georges Le Myre [pseudonym for Andr\'e Sainte-Lagu\"e] (1935) ---La chance et les jeux de hasard, Chapters 15--17, by Marcel Boll (1936) ---Le baccara: chemin de fer --- banque by Marcel Boll (1944) Each of these works has been translated into English, and the mathematical findings have been verified, with a few errors corrected in the process. Our aim in this presentation is to give credit to the early pioneers of the subject for their remarkable insights and daunting calculations done without the benefit of computers. A modern mathematical treatment of baccarat, using computing and game theory, is currently in preparation. ImplicationsOur study reveals that the mathematical works on baccarat between 1880 and 1945 contained a number of new insights that went well beyond Dormoy's initial work and led to a deeper understanding of the game, even before game theory finally yielded the optimal strategy.