Designing Experiments & Games of Chance


Book Description

"During his comparatively brief life (he died at thirty-nine, the age Mozart was to die) Blaise Pascal devoted his unusual talents to mathematics, physics and religion. His religious views are still widely discussed, and the general interest in this aspect of his life may be responsible for the fact that his mathematical and scientific achievements are less known. Those who are familiar with his Pensées, which are fragments of an intended Apology for Christianity, have had little opportunity of acquiring a just appreciation of the originality of his thought in physics and probability theory. This book fills this gap by describing Pascal’s work in a way that is accessible to anyone interested in his contribution to modern science and his attempt to tame Lady Luck. The words “Unconventional Science” in the subtitle of the book are meant as a reminder of the radically different way of looking at nature that was developed by Pascal and his contemporaries. The first seven chapters examine Pascal’s ingenious experiments to show that a vacuum can be produced, an idea that led him to ascend a mountain with a barometer to prove that we lived submerged under a sea of air. Chapter eight considers his bold views on the advancement of science and religion, and chapter nine his new philosophy of experimental science. The concluding chapters offer an insight into his pioneering work in the theory of probability and his willingness to help a friend who was a keen gambler but no mathematician. Pascal even applied his calculation of the odds at games of chance to the problem of personal destiny and the existence of God. Walking in his footsteps, the reader not only discovers the new world of experimental science but learns to play for high stakes."--Publisher's description.




Game Theory and Experimental Games


Book Description

Game Theory and Experimental Games: The Study of Strategic Interaction focuses on the development of game theory, taking into consideration empirical research, theoretical formulations, and research procedures involved. The book proceeds with a discussion on the theory of one-person games. The individual decision that a player makes in these kinds of games is noted as influential as to the outcome of these games. This discussion is followed by a presentation of pure coordination games and minimal situation. The ability of players to anticipate the choices of others to achieve a mutually beneficial outcome is emphasized. A favorable social situation is also influential in these kinds of games. The text moves forward by presenting studies on various kinds of competitive games. The research studies presented are coupled with empirical evidence and discussion designed to support the claims that are pointed out. The book also discusses several kinds of approaches in the study of games. Voting as a way to resolve multi-person games is also emphasized, including voting procedures, the preferences of voters, and voting strategies. The book is a valuable source of data for readers and scholars who are interested in the exploration of game theories.




Games, Gambling, and Probability


Book Description

Many experiments have shown the human brain generally has very serious problems dealing with probability and chance. A greater understanding of probability can help develop the intuition necessary to approach risk with the ability to make more informed (and better) decisions. The first four chapters offer the standard content for an introductory probability course, albeit presented in a much different way and order. The chapters afterward include some discussion of different games, different "ideas" that relate to the law of large numbers, and many more mathematical topics not typically seen in such a book. The use of games is meant to make the book (and course) feel like fun! Since many of the early games discussed are casino games, the study of those games, along with an understanding of the material in later chapters, should remind you that gambling is a bad idea; you should think of placing bets in a casino as paying for entertainment. Winning can, obviously, be a fun reward, but should not ever be expected. Changes for the Second Edition: New chapter on Game Theory New chapter on Sports Mathematics The chapter on Blackjack, which was Chapter 4 in the first edition, appears later in the book. Reorganization has been done to improve the flow of topics and learning. New sections on Arkham Horror, Uno, and Scrabble have been added. Even more exercises were added! The goal for this textbook is to complement the inquiry-based learning movement. In my mind, concepts and ideas will stick with the reader more when they are motivated in an interesting way. Here, we use questions about various games (not just casino games) to motivate the mathematics, and I would say that the writing emphasizes a "just-in-time" mathematics approach. Topics are presented mathematically as questions about the games themselves are posed. Table of Contents Preface 1. Mathematics and Probability 2. Roulette and Craps: Expected Value 3. Counting: Poker Hands 4. More Dice: Counting and Combinations, and Statistics 5. Game Theory: Poker Bluffing and Other Games 6. Probability/Stochastic Matrices: Board Game Movement 7. Sports Mathematics: Probability Meets Athletics 8. Blackjack: Previous Methods Revisited 9. A Mix of Other Games 10. Betting Systems: Can You Beat the System? 11. Potpourri: Assorted Adventures in Probability Appendices Tables Answers and Selected Solutions Bibliography Biography Dr. David G. Taylor is a professor of mathematics and an associate dean for academic affairs at Roanoke College in southwest Virginia. He attended Lebanon Valley College for his B.S. in computer science and mathematics and went to the University of Virginia for his Ph.D. While his graduate school focus was on studying infinite dimensional Lie algebras, he started studying the mathematics of various games in order to have a more undergraduate-friendly research agenda. Work done with two Roanoke College students, Heather Cook and Jonathan Marino, appears in this book! Currently he owns over 100 different board games and enjoys using probability in his decision-making while playing most of those games. In his spare time, he enjoys reading, cooking, coding, playing his board games, and spending time with his six-year-old dog Lilly.




Probability and Statistics


Book Description




Chance, Strategy, and Choice


Book Description

Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague–Grundy theorem and Arrow's impossibility theorem. • Uses an integrative approach to probability, game, and social choice theory • Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies • Contains numerous exercises and examples of varying levels of difficulty • Requires only a high school mathematical background.




Probability, Random Variables, Statistics, and Random Processes


Book Description

Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this book is on the basic principles and practical applications of the fundamental concepts that are extensively used in various Engineering disciplines as well as in a variety of programs in Life and Social Sciences. The text provides students with the requisite building blocks of knowledge they require to understand and progress in their areas of interest. With a simple, clear-cut style of writing, the intuitive explanations, insightful examples, and practical applications are the hallmarks of this book. The text consists of twelve chapters divided into four parts. Part-I, Probability (Chapters 1 – 3), lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables (Chapters 4 – 7), discusses in detail multiple random variables, along with a multitude of frequently-encountered probability distributions. Part-III, Statistics (Chapters 8 – 10), highlights estimation and hypothesis testing. Part-IV, Random Processes (Chapters 11 – 12), delves into the characterization and processing of random processes. Other notable features include: Most of the text assumes no knowledge of subject matter past first year calculus and linear algebra With its independent chapter structure and rich choice of topics, a variety of syllabi for different courses at the junior, senior, and graduate levels can be supported A supplemental website includes solutions to about 250 practice problems, lecture slides, and figures and tables from the text Given its engaging tone, grounded approach, methodically-paced flow, thorough coverage, and flexible structure, Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications clearly serves as a must textbook for courses not only in Electrical Engineering, but also in Computer Engineering, Software Engineering, and Computer Science.




Experimental Games


Book Description

In our unprecedentedly networked world, games have come to occupy an important space in many of our everyday lives. Digital games alone engage an estimated 2.5 billion people worldwide as of 2020, and other forms of gaming, such as board games, role playing, escape rooms, and puzzles, command an ever-expanding audience. At the same time, “gamification”—the application of game mechanics to traditionally nongame spheres, such as personal health and fitness, shopping, habit tracking, and more—has imposed unprecedented levels of competition, repetition, and quantification on daily life. Drawing from his own experience as a game designer, Patrick Jagoda argues that games need not be synonymous with gamification. He studies experimental games that intervene in the neoliberal project from the inside out, examining a broad variety of mainstream and independent games, including StarCraft, Candy Crush Saga, Stardew Valley, Dys4ia, Braid, and Undertale. Beyond a diagnosis of gamification, Jagoda imagines ways that games can be experimental—not only in the sense of problem solving, but also the more nuanced notion of problem making that embraces the complexities of our digital present. The result is a game-changing book on the sociopolitical potential of this form of mass entertainment.




Introduction to Probability


Book Description

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.




Probability, Statistics, and Truth


Book Description

This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.




An Introduction to Statistical Inference and Its Applications with R


Book Description

Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are included. R is used to simplify computation, create figures