2nd Edition

Mathematics in Games, Sports, and Gambling The Games People Play, Second Edition

By Ronald J. Gould Copyright 2016
    378 Pages 116 B/W Illustrations
    by Chapman & Hall

    378 Pages
    by Chapman & Hall

    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.

    Basic Probability
    Of Dice and Men
    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
    Let’s Make a Deal — The Monty Hall Problem
    Carnival Games
    Other Casino Games

    Repeated Play
    Binomial Coefficients
    The Binomial Distribution
    The Poisson Distribution
    Streaks—Are They Real?
    Betting Strategies
    The Gambler’s Ruin

    Card Tricks and More
    The Five-Card Trick
    The Two-Deck Matching Game
    More Tricks
    The Paintball Wars

    Dealing with Data
    Batting Averages and Simpson’s Paradox
    NFL Passer Ratings
    Viewing Data — Simple Graphs
    Confidence in Our Estimates
    Measuring Differences in Performance

    Testing and Relationships
    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
    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
    Games as Digraphs
    Blue-Red Hackenbush
    Green Hackenbush
    Games as Numbers
    More about Nimbers

    Review of Elementary Set Theory
    Relations and Functions
    Standard Normal Distribution Table
    Student’s t-Distribution
    Solutions to Problems
    Solutions to Selected Exercises



    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.