Mathematics in Games, Sports, and Gambling

Ronald J. Gould received a B.S. in Mathematics from the State University of New York at Fredonia in 1972, an M.S. in Computer Science in 1978 from Western Michigan University, and Ph.D. in Mathematics in 1979 from Western Michigan University. He joined the faculty of Emory University in 1979. Professor Gould specializes in Graph Theory with general interests in discrete mathematics and algorithms. He has written over 170 research papers and one book in this area. Professor Gould serves on the Editorial Boards of several journals in the area of discrete mathematics. Over the years he has directed over 25 master’s theses and more than 25 Ph.D. dissertations. Professor Gould has received a number of honors including teaching awards from Western Michigan University (1976) and Emory University (1999), as well as the Mathematical Association of America’s Southeastern Section Distinguished Teaching Award in 2008. He has also received alumni awards from both SUNY Fredonia and Western Michigan University. He was awarded the Goodrich C. White Chair from Emory University in 2001.

Basic Probability
Introduction
Of Dice and Men
Probability
The Laws That 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
Puzzles on the Chessboard
Guarini’s Problem
Martin Gardner’s No 3-in-a-Line Problem
The Knight’s Tour
Domination and Independence
Attacking Placements and Independence

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
Relations and Functions
Standard Normal Distribution Table
Student’s t-Distribution
Solutions to Problems
Solutions to Selected Exercises
Bibliography

Index