Probability Decisions and Games 1st Edition by Abel Rodríguez, Bruno Mendes ISBN 1119302605 9781119302605

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Product details:

ISBN 10:       1119302605
ISBN 13: 978-1119302605
Author:         Abel Rodríguez, Bruno Mendes 

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.

Probability, Decisions and Games 1st Table of contents:

1. An Introduction to Probability

• 1.1 What is Probability?
• 1.2 Odds and Probabilities
• 1.3 Equiprobable Outcome Spaces and De Méré’s Problem
• 1.4 Probabilities for Compound Events
• 1.5 Exercises

2. Expectations and Fair Values

• 2.1 Random Variables
• 2.2 Expected Values
• 2.3 Fair Value of a Bet
• 2.4 Comparing Wagers
• 2.5 Utility Functions and Rational Choice Theory
• 2.6 Limitations of Rational Choice Theory
• 2.7 Exercises

3. Roulette

• 3.1 Rules and Bets
• 3.2 Combining Bets
• 3.3 Biased Wheels
• 3.4 Exercises

4. Lotto and Combinatorial Numbers

• 4.1 Rules and Bets
• 4.1.1 The Colorado Lotto
• 4.1.2 The California Superlotto
• 4.2 Sharing Profits: De Méré’s Second Problem
• 4.3 Exercises

5. The Monty Hall Paradox and Conditional Probabilities

• 5.1 The Monty Hall Paradox
• 5.2 Conditional Probabilities
• 5.3 Independent Events
• 5.4 Bayes Theorem
• 5.5 Exercises

6. Craps

• 6.1 Rules and Bets
• 6.1.1 The Pass Line Bet
• 6.1.2 The Don’t Pass Line Bet
• 6.1.3 The Come and Don’t Come Bets
• 6.1.4 Side Bets
• 6.2 Exercises

7. Roulette Revisited

• 7.1 Gambling Systems
• 7.1.1 Martingale Doubling Systems
• 7.1.2 The Labouchère System
• 7.1.3 D’Alembert Systems
• 7.2 You are a Big Winner!
• 7.3 How Long will My Money Last?
• 7.4 Is This Wheel Biased?
• 7.5 Bernoulli Trials
• 7.6 Exercises

8. Blackjack

• 8.1 Rules and Bets
• 8.2 Basic Strategy in Blackjack
• 8.3 A Gambling System that Works: Card Counting
• 8.4 Exercises

9. Poker

• 9.1 Basic Rules
• 9.2 Variants of Poker
• 9.3 Additional Rules
• 9.4 Probabilities of Hands in Draw Poker
• 9.4.1 The Effect of Card Substitutions
• 9.5 Probabilities of Hands in Texas Hold’em
• 9.6 Exercises

10. Strategic Zero-Sum Games with Perfect Information

• 10.1 Games with Dominant Strategies
• 10.2 Solving Games with Dominant and Dominated Strategies
• 10.3 General Solutions for Two Person Zero-Sum Games
• 10.4 Exercises

11. Rock–Paper–Scissors: Mixed Strategies in Zero-Sum Games

• 11.1 Finding Mixed-Strategy Equilibria
• 11.2 Mixed Strategy Equilibria in Sports
• 11.3 Bluffing as a Strategic Game with a Mixed-Strategy Equilibrium
• 11.4 Exercises

12. The Prisoner’s Dilemma and Other Strategic Non-zero-sum Games

• 12.1 The Prisoner’s Dilemma
• 12.2 The Impact of Communication and Agreements
• 12.3 Which Equilibrium?
• 12.4 Asymmetric Games
• 12.5 Exercises

13. Tic-Tac-Toe and Other Sequential Games of Perfect Information

• 13.1 The Centipede Game
• 13.2 Tic-Tac-Toe
• 13.3 The Game of Nim and the First- and Second-Mover Advantages
• 13.4 Can Sequential Games be Fun?
• 13.5 The Diplomacy Game
• 13.6 Exercises

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