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Probability, Decisions and Games: A Gentle Introduction using R

ISBN: 978-1-119-30260-5
240 pages
April 2018
Probability, Decisions and Games: A Gentle Introduction using R (1119302609) cover image


This book introduces the basic concepts of probability, statistics, decision theory, and game theory and presents interesting gaming examples to highlight the practical applications and methodologies. The author uniquely utilizes the mathematical analyses of games of chance to develop an understanding of probability and utility (rational thinking) theories.  Based on six years of class-testing, the authors’ approach to games and gambling is accessible for readers with minimal experience.  Ranging from simple games to strategic games, this book features a variety of gaming and gambling examples to build a better understanding of quantitative reasoning, and the authors establish fundamental concepts before moving on to more strategic games that illustrate how multiple concepts fit together.  Organized into thirteen chapters, this book presents equal coverage on the general mathematical analysis concepts found in a wide variety of games as well as the specific theories and problems associated with well-known casino games.  Covering zero-sum games, non-zero-sum games, and sequential games, the authors introduce ideas such as mathematical expectation and variance, bias, combinatorial calculus, conditional probability and Bayes Theorem, Bernoulli trials, and the Binomial distribution.  The first two chapters feature an introductory discussion of utility and probability theory in finite and discrete spaces.  Subsequent chapters utilize popular casino games to illustrate the practical probabilistic methodologies: roulette, which is one of the simplest casino games to play and analyze, is used to illustrate basic concepts in probability such as expectations; lotto is used to motivate counting rules and the notions of permutations and combinatorial numbers that allow for probability computation in large equiprobable spaces; craps and blackjack are used to illustrate and develop conditional probabilities; and poker illustrates how a combination of theories and techniques can be used together.  Finally, the book concludes with discussions on game theory and strategic games.  This book also features computer simulations using Microsoft Office® Excel® spreadsheets throughout in order to illustrate complex concepts and help readers calculate presented problems. 

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Table of Contents



Chapter 1: An introduction to probability

1.1 What is probability?

1.2 Odds and probabilities

1.3 Equiprobable outcome spaces and De Mere's problem

1.4 Probabilities for compound events

1.5 Exercises

Chapter 2: Expectations and fair values 15

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

Chapter 3: Roulette

3.1 Rules and bets

3.2 Combining bets

3.3 Biased wheels

3.4 Exercises

Chapter 4: Lotto and combinatorial numbers

4.1 Rules and bets

4.2 Sharing profits: De Mere's second problem

4.3 Exercises

Chapter 5: Conditional probabilities

5.1 The Monty Hall paradox

5.2 Conditional probabilities

5.3 Independent events

5.4 Bayes Theorem

5.5 Exercises

Chapter 6: Craps

6.1 Rules and bets

6.2 Exercises

Chapter 7: Roulette revisited

7.1 Gambling 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

Chapter 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

Chapter 9: Poker

9.1 Basic rules

9.2 Variants of poker

9.3 Additional rules

9.4 Probabilities of hands in draw poker

9.5 Probabilities of hands in Texas hold'em

9.6 Exercises

Chapter 10: Strategic zero-sum games

10.1 Games with dominant strategies

10.2 Dominant and dominating strategies

10.3 General solutions for two person zero-sum games

10.4 Exercises

Chapter 11: 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

11.4 Exercises

Chapter 12: 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

Chapter 13: Sequential games

13.1 The centipede game

13.2 Tic-tac-toe

13.3 The game of Nim

13.4 Can sequential games be fun?

13.5 The diplomacy game

13.6 Exercises

Appendix: A brief introduction to R

A.1 Installing R

A.2 Simple arithmetic

A.3 Variables

A.4 Vectors

A.5 Matrices

A.6 Logical objects and operations

A.7 Character objects

A.8 Plots

A.9 Iterators

A.10 Selection and forking

A.11 Other things to keep in mind


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