Games, Gambling, and Probability: An Introduction to Mathematics, 2nd Edition

Length: 516 pages
Edition: 2
Language: English
Publisher: Chapman and Hall/CRC
Publication Date: 2021-06-23
ISBN-10: 0367820439
ISBN-13: 9780367820435
Sales Rank: #2021973 (See Top 100 Books)

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.

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.

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
List of Figures
List of Tables
Preface
1. Mathematics and Probability
	1.1. Introduction
	1.2. About Mathematics
	1.3. Probability
		Language
		Probability
		Adding Probabilities
		Multiplying Probabilities
		Shortcuts
		The Monty Hall Problem
	1.4. Candy (Yum)!
	1.5. Exercises
2. Roulette and Craps: Expected Value
	2.1. Roulette
		Odds
		Expected Winnings (Expected Value)
	2.2. Summations
	2.3. Craps
		Free Odds
		Other Wagers
	2.4. Exercises
3. Counting: Poker Hands
	3.1. Cards and Counting
		Poker Hands
		Combinations (Binomial Coe cients)
	3.2. Seven Card Pokers
	3.3. Texas Hold'Em
	3.4. Exercises
4. More Dice: Counting and Combinations, and Statistics
	4.1. Liar's Dice
		Binomial Distribution
		Spread
		Using Tables
	4.2. Arkham Horror
	4.3. Yahtzee
		Permutations
		Multinomial Distribution
		Mini-Yahtzee
	4.4. Exercises
5. Game Theory: Poker Bluffing and Other Games
	5.1. Bluffing
		Optimal Bluffing
	5.2. Game Theory Basics
		Dominance and Saddle Points
		Mixed Strategies
		Larger Games: 2 x m and n x 2
		Larger Games: 3 x 3 and Beyond
	5.3. Non-Zero Sum Games
		Movement Diagrams
		Nash Equilibrium Explored
		Prudential Strategies
		Pareto Optimality
		Prisoner's Dilemma Revisited
	5.4. Three-Player Game Theory
	5.5. Exercises
6. Probability/Stochastic Matrices: Board Game Movement
	6.1. Board Game Movement
		Probability Matrices
		Steady-States
		Yahtzee, Revisited
		Cyclic Boards
	6.2. Pay Day (The Board Game)
	6.3. Monopoly
		The Properties' Real Values
		The "Long Jail" Strategy
		Fixing the Model
	6.4. Spread, Revisited
	6.5. Exercises
7. Sports Mathematics: Probability Meets Athletics
	7.1. Sports Betting
		Moneyline and Spread Betting
		Horse Racing
	7.2. Game Theory and Sports
	7.3. Probability Matrices and Sports
	7.4. Winning a Tennis Tournament
		Game Win Probability
		Set Win Probability
	7.5. Repeated Play: Best of Seven
	7.6. Exercises
8. Blackjack: Previous Methods Revisited
	8.1. Blackjack
		Gameplay
		Card Counting
		Decision Making, Probability Trees, and Basic Strategy
	8.2. Blackjack Variants
		Rule Variations for Normal Blackjack
		Blackjack Switch
	8.3. Exercises
9. A Mix of Other Games
	9.1. The Lottery
		Pick 3
		Mega Millions
	9.2. Bingo
		Counting Cards
		Bingo Probabilities
	9.3. Uno
	9.4. Baccarat
	9.5. Farkle
	9.6. Scrabble
	9.7. Backgammon
		Probabilities for Hitting a Piece
		The Doubling Cube
	9.8. Memory
	9.9. Zombie Dice
	9.10. Exercises
10. Betting Systems: Can You Beat the System?
	10.1. Betting Systems
		Martingale System
		(Loss) Streaks
		Anti-Martingale System
		The Kelly Criterion
	10.2. Gambler's Ruin
		Minimizing the Probability of Ruin
	10.3. Exercises
11. Potpourri: Assorted Adventures in Probability
	11.1. True Randomness?
	11.2. Three Dice "Craps"
	11.3. Counting "Fibonacci" Coins "Circularly"
	11.4. Compositions and Probabilities
	11.5. Sicherman Dice
	11.6. Traveling Salesmen
	11.7. Random Walks and Generating Functions
		Random Walks
		Generating Functions
	11.8. More Probability!
Appendices
	A. Probabilities with Infinity
	B. St. Petersburg Paradox
	C. Binomial Distribution versus Normal Distribution
	D. Matrix Multiplication Review
Tables
Answers and Selected Solutions
Bibliography
Image Credits
Index