On the three-person game baccara banque

Baccara banque is a three-person zero-sum game parameterized by $\theta\in(0,1)$. A study of the game by Downton and Lockwood claimed that the Nash equilibrium is of only academic interest. Their preferred alternative is what we call the independent cooperative equilibrium. But this solution exists only for certain $\theta$. A third solution, which we call the correlated cooperative equilibrium, always exists. Under a "with replacement" assumption as well as a simplifying assumption concerning the information available to one of the players, we derive each of the three solutions for all $\theta$.Comment: 22 pages, 4 figures, and a 54-page appendix; new figure and minor corrections in v

Session 3-2-F: A Game-Theoretic Analysis of Baccara Chemin de Fer

Baccara chemin de fer — review of main contributions Baccara was first mentioned in print by Van Tenac in 1847. It was analyzed by Dormoy in 1872 and Bertrand in 1889. Borel called Bertrand’s study “extremely incomplete,” but it motivated Borel to develop game theory in the 1920s. Von Neumann planned to study baccara after proving the minimax theorem in 1928, but he didn’t. The first game-theoretic solution was by Kemeny and Snell in 1957. In 1964, Foster gave a solution based on a new algorithm, unaware of the Kemeny–Snell solution. A solution under more realistic assumptions was found by Downton and Lockwood in 1975 using Foster’s algorithm. Based on the extensive form of the game, the Kemeny–Snell solution was rederived by Deloche and Oguer in 2007

A New Variant of Baccarat for VIP Players

In 2013 baccarat generated over US$41 billion in revenue for the 35 casinos of Macau, of which nearly US$30 billion was attributed to VIP players (high-stakes gamblers). Although the VIP market segment has declined over the past two years, it is still substantial. In this talk we propose a new variant of baccarat that will appeal to and attract VIP players. Its appeal lies in the facts that (a) it has a historical connection to baccarat and (b) it is closer to a fair game than is baccarat

Teaching a University Course on the Mathematics of Gambling

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a course on the mathematics of gambling

The representation of money in film : gold, paper, metal and electronic

This dissertation is a study of the representation of money on screen, in its textual and contextual constructions. Money, itself a representation, has a complex status: it is both an abstract concept, a symbol of value, a social convention, and a concrete object in its embodiment as gold, metal or paper. This study then is that of a representation of a representation. Its starting point is the very paradox of money as both an object endowed with great value while at the same time not worth much more than the substance it is made of or the numbers referring to it in newer forms of electronic money. The paradox is particularly salient in a medium that works through images while at the same time requiring itself so much money. The distinction between the two Latin words moneta and pecunia offers an understanding of money in its main properties and functions, as an exchange tool in constant circulation and as an object of hoarding, as belongings. This distinction is operative in the present study and runs through the thesis, together with the Marxian concepts of use-value and exchange value. The objective is to analyse patterns, peculiarities and meanings linked to the portrayal of money. This thesis does not encompass a comprehensive survey of money represented in all of cinema. Instead, the study is conducted in four groupings of films that are not necessarily thought of in connection with their images of money. Four chapters examine films from different contexts, periods, genres or trends in the cinema of various countries. The groupings are suggested partly by issues outside of money and partly by periods and kinds of money, and focus on case studies while simultaneously referring to a larger corpus. The first chapter examines the issues raised by the topic and surveys the existing literature. The second chapter undertakes an analysis of gold and gold mining in the context of the pioneering West in US films. The third chapter considers paper money and its meanings in neo-realist films. The thesis then proceeds to study films from the 1970s and 1980s. The fourth chapter concerns money in French films on high finance, and the last chapter looks at money as it appears in horror films. The thesis ends with a discussion of the recurrent patterns at work in the representation of money

Le système ESAR : un modèle de classement des jouets et du matériel de jeu à l'intention des éducateurs

Québec Université Laval, Bibliothèque 201

The Conflict of Laws: A Comparative Study, Second Edition. Volume Two. Foreign Corporations: Torts: Contracts in General

The second volume of Ernst Rabel\u27s comparative treatise on the conflict of laws was originally published in 1947. This new edition completes the plan to revise the first two volumes, as arranged with the approval of the author before his death on September 7, 1955. Pursuant to this plan, the present edition has been made possible through the continued support of the work by the University of Michigan Law School and the generous cooperation of the Max Planck-Institut für aüslindisches und internationales Privatrecht in Hamburg, in making available the competent services of a member of the staff of the Institut, Dr. Ulrich Drobnig, who utilized the special facilities at the Legal Research Building in Ann Arbor from July, 1955, to June, 1956. In accordance with the advice of the author, whom Dr. Drobnig fortunately was able to consult before undertaking the revision of the two volumes, the collection and inclusion of new material in the author\u27s text has been strictly limited to the addition of new citations and illustrations. Consequently, alterations of the text proper, as distinguished from the footnotes, have been avoided as far as possible. The additional material covers publications up to July 1, 1956, but with the continued co-operation of the Institut after Dr. Drobnig\u27s return to Germany, account has been taken of later developments up to January 1, 1959.https://repository.law.umich.edu/michigan_legal_studies/1011/thumbnail.jp

The Conflict of Laws: A Comparative Study, Second Edition. Volume Two. Foreign Corporations: Torts: Contracts in General

The second volume of Ernst Rabel\u27s comparative treatise on the conflict of laws was originally published in 1947. This new edition completes the plan to revise the first two volumes, as arranged with the approval of the author before his death on September 7, 1955. Pursuant to this plan, the present edition has been made possible through the continued support of the work by the University of Michigan Law School and the generous cooperation of the Max Planck-Institut für aüslindisches und internationales Privatrecht in Hamburg, in making available the competent services of a member of the staff of the Institut, Dr. Ulrich Drobnig, who utilized the special facilities at the Legal Research Building in Ann Arbor from July, 1955, to June, 1956. In accordance with the advice of the author, whom Dr. Drobnig fortunately was able to consult before undertaking the revision of the two volumes, the collection and inclusion of new material in the author\u27s text has been strictly limited to the addition of new citations and illustrations. Consequently, alterations of the text proper, as distinguished from the footnotes, have been avoided as far as possible. The additional material covers publications up to July 1, 1956, but with the continued co-operation of the Institut after Dr. Drobnig\u27s return to Germany, account has been taken of later developments up to January 1, 1959.https://repository.law.umich.edu/michigan_legal_studies/1011/thumbnail.jp

The Conflict of Laws: A Comparative Study. Volume Two. Foreign Corporations: Torts: Contracts in General

Full application of comparative methods to the law of conflicts requires a working plan of some magnitude. We ought to take stock of the conflicts rules existing in the different countries of the world, state their similarities or dissimilarities, and investigate their purposes and effects. The solutions thus ascertained should moreover be subjected to an estimation of their usefulness, by the standards appropriate to their natural objective. Conflicts rules have to place private life and business relations upon the legal background suitable to satisfactory intercourse among states and nations. They are valuable to the extent that their practical functioning, rather than their legal appearance, serves this purpose. To meet the challenge of this program with limited forces is a risky undertaking. Nevertheless it has to be attempted. The conditions of the law of conflicts are deplorable. It may be said, to the reader\u27s and my own consolation, that the staggering provincialism apparent in the international family law presented in this volume is not equaled in other parts. But if conflicts problems have been cultivated by men of the highest erudition, idealism, and endeavor, they have also been the object of prejudice and dogmatism. Suggestions of almost all needed ideas may be found, but little agreement on a sound choice. The courts of this country dealing with a wealth of interstate cases have prevailingly shown sincere respect for foreign legislation and applied an accomplished method of comparative research. But this admirable attitude, which is the most outstanding model for the practice of private international law, suffers exceptions, and in the field of international relations throughout the world, despite enormous efforts, the simple truth that harmony presupposes mutual understanding and tolerance, has not prevailed in conflicts law more than in foreign affairs.https://repository.law.umich.edu/michigan_legal_studies/1007/thumbnail.jp