Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition, 2nd Edition (Paperback) book cover

Mathematics in Games, Sports, and Gambling

The Games People Play, Second Edition, 2nd Edition

By Ronald J. Gould

Chapman and Hall/CRC

354 pages | 116 B/W Illus.

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Description

Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With emphasis on mathematical thinking and problem solving, the text draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games.

This updated edition of a widely adopted textbook considers a number of popular games and diversions that are mathematically based or can be studied from a mathematical perspective. Requiring only high school algebra, the book is suitable for use as a textbook in seminars, general education courses, or as a supplement in introductory probability courses.

New in this Edition:

  • Many new exercises, including basic skills exercises
  • More answers in the back of the book
  • Expanded summary exercises, including writing exercises
  • More detailed examples, especially in the early chapters
  • An expansion of the discrete adjustment technique for binomial approximation problems
  • New sections on chessboard puzzles that encourage students to develop graph theory ideas
  • New review material on relations and functions

Exercises are included in each section to help students understand the various concepts. The text covers permutations in the two-deck matching game so derangements can be counted. It introduces graphs to find matches when looking at extensions of the five-card trick and studies lexicographic orderings and ideas of encoding for card tricks.

The text also explores linear and weighted equations in the section on the NFL passer rating formula and presents graphing to show how data can be compared or displayed. For each topic, the author includes exercises based on real games and actual sports data.

Table of Contents

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

About the Author

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.

About the Series

Textbooks in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT011000
MATHEMATICS / Game Theory
MAT025000
MATHEMATICS / Recreations & Games
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis