*A Gentle Introduction using R*

Author: Abel Rodríguez,Bruno Mendes

Publisher: John Wiley & Sons

ISBN: 1119302617

Category: Mathematics

Page: 240

View: 5922

INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAME THEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TO MOTIVATE AND ILLUSTRATE ABSTRACT MATHEMATICAL CONCEPTS Covering both random and strategic games, Probability, Decisions and Games features a variety of gaming and gambling examples to build a better understanding of basic concepts of probability, statistics, decision theory, and game theory. The authors present fundamental concepts such as random variables, rational choice theory, mathematical expectation and variance, fair games, combinatorial calculus, conditional probability, Bayes Theorem, Bernoulli trials, zero-sum games and Nash equilibria, as well as their application in games such as Roulette, Craps, Lotto, Blackjack, Poker, Rock-Paper-Scissors, the Game of Chicken and Tic-Tac-Toe. Computer simulations, implemented using the popular R computing environment, are used to provide intuition on key concepts and verify complex calculations. The book starts by introducing simple concepts that are carefully motivated by the same historical examples that drove their original development of the field of probability, and then applies those concepts to popular contemporary games. The first two chapters of Probability, Decisions and Games: A Gentle Introduction using R feature an introductory discussion of probability and rational choice theory in finite and discrete spaces that builds upon the simple games discussed in the famous correspondence between Blaise Pascal and Pierre de Fermat. Subsequent chapters utilize popular casino games such as Roulette and Blackjack to expand on these concepts illustrate modern applications of these methodologies. Finally, the book concludes with discussions on game theory using a number of strategic games. This book: · Features introductory coverage of probability, statistics, decision theory and game theory, and has been class-tested at University of California, Santa Cruz for the past six years · Illustrates basic concepts in probability through interesting and fun examples using a number of popular casino games: roulette, lotto, craps, blackjack, and poker · Introduces key ideas in game theory using classic games such as Rock-Paper-Scissors, Chess, and Tic-Tac-Toe. · Features computer simulations using R throughout in order to illustrate complex concepts and help readers verify complex calculations · Contains exercises and approaches games and gambling at a level that is accessible for readers with minimal experience · Adopts a unique approach by motivating complex concepts using first simple games and then moving on to more complex, well-known games that illustrate how these concepts work together Probability, Decisions and Games: A Gentle Introduction using R is a unique and helpful textbook for undergraduate courses on statistical reasoning, introduction to probability, statistical literacy, and quantitative reasoning for students from a variety of disciplines. ABEL RODRÍGUEZ, PhD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC), CA, USA. The author of 40 journal articles, his research interests include Bayesian nonparametric methods, machine learning, spatial temporal models, network models, and extreme value theory. BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA. BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA.INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAMETHEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TOMOTIVATE AND ILLUSTRATE ABSTRACT MATHEMATICAL CONCEPTSCovering both random and strategic games, Probability, Decisions and Games features a varietyof gaming and gambling examples to build a better understanding of basic concepts of probability,statistics, decision theory, and game theory. The authors present fundamental concepts such asrandom variables, rational choice theory, mathematical expectation and variance, fair games,combinatorial calculus, conditional probability, Bayes Theorem, Bernoulli trials, zero-sum games andNash equilibria, as well as their application in games such as Roulette, Craps, Lotto, Blackjack, Poker,Rock-Paper-Scissors, the Game of Chicken and Tic-Tac-Toe. Computer simulations, implementedusing the popular R computing environment, are used to provide intuition on key concepts and verifycomplex calculations.The book starts by introducing simple concepts that are carefully motivated by the same historicalexamples that drove their original development of the field of probability, and then applies those conceptsto popular contemporary games. The first two chapters of Probability, Decisions and Games: A GentleIntroduction using R feature an introductory discussion of probability and rational choice theory in finiteand discrete spaces that builds upon the simple games discussed in the famous correspondence betweenBlaise Pascal and Pierre de Fermat. Subsequent chapters utilize popular casino games such as Rouletteand Blackjack to expand on these concepts illustrate modern applications of these methodologies. Finally,the book concludes with discussions on game theory using a number of strategic games. This book:• Features introductory coverage of probability, statistics, decision theory and game theory, and hasbeen class-tested at University of California, Santa Cruz for the past six years• Illustrates basic concepts in probability through interesting and fun examples using a number ofpopular casino games: roulette, lotto, craps, blackjack, and poker• Introduces key ideas in game theory using classic games such as Rock-Paper-Scissors, Chess,and Tic-Tac-Toe.• Features computer simulations using R throughout in order to illustrate complex concepts andhelp readers verify complex calculations• Contains exercises and approaches games and gambling at a level that is accessible for readerswith minimal experience• Adopts a unique approach by motivating complex concepts using first simple games and thenmoving on to more complex, well-known games that illustrate how these concepts work togetherProbability, Decisions and Games: A Gentle Introduction using R is a unique and helpful textbook forundergraduate courses on statistical reasoning, introduction to probability, statistical literacy, andquantitative reasoning for students from a variety of disciplines.ABEL RODRÍGUEZ, PhD, is Professor in the Department of Applied Mathematics and Statisticsat the University of California, Santa Cruz (UCSC), CA, USA. The author of 40 journal articles, hisresearch interests include Bayesian nonparametric methods, machine learning, spatial temporalmodels, network models, and extreme value theory.BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at theUniversity of California, Santa Cruz, CA, USA.