Mathematics of Keno and Lotteries

Mark Bollman is Professor of Mathematics and chair of the Department of Mathematics & Computer Science at Albion College in Albion, Michigan, and has taught 111 different courses in his career. Among these courses is "Mathematics of the Gaming Industry," where mathematics majors carefully study the math behind games of chance and travel to Las Vegas, Nevada, in order to compare theory and practice. He has also taken those ideas into Albion's Honors Program in "Great Issues in Humanities: Perspectives on Gambling," which considers gambling from literary, philosophical, and historical points of view as well as mathematically. Mark’s previous book is Basic Gambling Mathematics: The Numbers behind The Neon.

"Keno is a gambling game in which the house randomly selects a subset of numbers from a given range. Players choose a subset and bet on the size of the intersection. Occasionally order matters. Payo s for various matches are specified in advance, always with a house advantage. State lotteries work the same way.The author uses his passion for the history of Keno and Keno-like games and lotteries to teach the traditional combinatorics of permutations and combinations and the calculation of expected values. He documents the real examples in the text and exercises with 167 references, including one to a paper of Euler's and one to a lottery instance when the house advantage was momentarily a disadvantage.The treatment is essentially elementary. Just a little algebra sufices. The text shows how to use Excel for some tasks."- Ethan D. Bolker - Mathematical Reviews Clippings - March 2019

• Chapter 1. Historical Background. 1.1 History of. 1.2 History of Lotteries. Chapter 2. Mathematical Foundations. 2.1 Elementary Probability. 2.2 Addition Rules. 2.3 Conditional Probability. 2.4 Random Variables and Expected Value. 2.5 Combinatorics. 2.6 Binomial Distribution. Chapter 3. Keno. 3.1 Standard Keno Wagers. 3.2 Game Variations. 3.3 The Big Picture. 3.4 Video Keno. 3.5 Keno Side Bets. 3.6 Keno Strategies: Do They Work?. Chapter 4. Lotteries. 4.2 Passive Lottery Tickets. 4.3 Lotto Games. 4.4 Games Where Order Matters. 4.5 Powerball. 4.6 Lotto Strategies: Do They Work?