Mathematics in Games, Sports, and Gambling

Ronald J. Gould is the Goodrich C. White Professor in the Department of Mathematics and Computer Science at Emory University. The recipient of the Mathematical Association of America’s Southeastern Section Distinguished Teaching Award in 2008, Dr. Gould has authored more than 135 research papers and serves on the editorial board of several journals dealing with discrete mathematics.

Basic Probability
Introduction
Of Dice and Men
Probability
The Laws Which Govern Us
Poker Hands versus Batting Orders
Let’s Play for Money!
Is That Fair?
The Odds Are against Us
Things Vary
Conditional Expectation
The Game’s Afoot
Applications to Games
Counting and Probability in Poker Hands
Roulette
Craps
Let’s Make A Deal — The Monty Hall Problem
Carnival Games
Other Casino Games
Backgammon
Repeated Play
Introduction
Binomial Coefficients
The Binomial Distribution
The Poisson Distribution
Streaks — Are They Real?
Betting Strategies
The Gambler’s Ruin
Card Tricks and More
Introduction
The Five-Card Trick
The Two-Deck Matching Game
More Tricks
The Paintball Wars
Dealing with Data
Introduction
Batting Averages and Simpson’s Paradox
NFL Passer Ratings
Viewing Data — Simple Graphs
Confidence in Our Estimates
Measuring Differences in Performance
Testing and Relationships
Introduction
Suzuki versus Pujols
I’ll Decide If I Believe That
Are the Old Adages True?
How Good Are Certain Measurements?
Arguing over Outstanding Performances
A Last Look at Comparisons
Games and Puzzles
Introduction
Number Arrays
The Tower of Hanoi
Instant Insanity
Lights Out
Peg Games
Combinatorial Games
Introduction to Combinatorial Games
Subtraction Games
Nim
Games as Digraphs
Blue-Red Hackenbush
Green Hackenbush
Games as Numbers
More about Nimbers
Appendix
Review of Elementary Set Theory
Standard Normal Distribution Table
Student’s t-Distribution
Solutions to Problems
Selected Even Exercises
References
Index