Mathematics in Games, Sports, and Gambling The Games People Play, Second Edition
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.
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
The Game’s Afoot
Applications to Games
Counting and Probability in Poker Hands
Let’s Make a Deal — The Monty Hall Problem
Other Casino Games
The Binomial Distribution
The Poisson Distribution
Streaks—Are They Real?
The Gambler’s Ruin
Card Tricks and More
The Five-Card Trick
The Two-Deck Matching Game
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
The Tower of Hanoi
Puzzles on the Chessboard
Martin Gardner’s No 3-in-a-Line Problem
The Knight’s Tour
Domination and Independence
Attacking Placements and Independence
Introduction to Combinatorial Games
Games as Digraphs
Games as Numbers
More about Nimbers
Review of Elementary Set Theory
Relations and Functions
Standard Normal Distribution Table
Solutions to Problems
Solutions to Selected Exercises