Mathematics in Games, Sports, and Gambling

Mathematics in Games, Sports, and Gambling: - The Games People Play

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Features

  • Presents gaming in mathematics, statistics, and probability as applications
  • Encourages students to think mathematically and apply the fundamentals to real gaming situations
  • Includes real-world examples from sports, games, and gambling situations
  • Explores concepts, such as binomial distributions and combinatorics, through common games and sports, including backgammon, poker, roulette, baseball, football, and hockey
  • Discusses more unusual topics, such as mathematical card tricks and old TV shows
  • Contains many in-class group problems and homework exercises

Summary

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.

Table of 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(s)

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.

Editorial 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

 
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