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Mathematics in Games, Sports, and Gambling

- The Games People Play

By Ronald J. Gould

Chapman and Hall/CRC – 2009 – 374 pages

Purchasing Options:

  • Add to CartHardback: $64.95
    978-1-43-980163-5
    July 28th 2009

Description

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

Only requiring high school algebra, the text offers flexibility in choosing what material to cover in a basic mathematics course. It covers permutations in the two-deck matching game so derangements can be counted, 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 equations 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 sports data.

Reviews

A 2010 CHOICE Outstanding Academic Title

…this volume is a wonderful reference for studying probability or statistics … Though this book might serve as the seed for the development of a new mathematics course at some institutions, this reviewer sees its greater value as a reference for mathematicians who are unfamiliar with the probabilities associated with gambling or applying statistics in sports.

—J.T. Noonan, Mount Vernon Nazarene University, CHOICE, Vol. 47, No. 9, May 2010

Contents

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

Author Bio

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.

Name: Mathematics in Games, Sports, and Gambling: - The Games People Play (Hardback)Chapman and Hall/CRC 
Description: By Ronald J. Gould. With an emphasis on mathematical thinking and problem solving, Mathematics in Games, Sports, and Gambling — The Games People Play shows how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and...
Categories: Combinatorics, Probability, Mathematics & Statistics