1st Edition

Mathematics of Keno and Lotteries

By Mark Bollman Copyright 2018
    338 Pages 62 B/W Illustrations
    by Chapman & Hall

    338 Pages 62 B/W Illustrations
    by Chapman & Hall

    338 Pages 62 B/W Illustrations
    by Chapman & Hall

    Mathematics of Keno and Lotteries is an elementary treatment of the mathematics, primarily probability and simple combinatorics, involved in lotteries and keno. Keno has a long history as a high-advantage, high-payoff casino game, and state lottery games such as Powerball are mathematically similar. MKL also considers such lottery games as passive tickets, daily number drawings, and specialized games offered around the world. In addition, there is a section on financial mathematics that explains the connection between lump-sum lottery prizes (as with Powerball) and their multi-year annuity options. So-called "winning systems" for keno and lotteries are examined mathematically and their flaws identified.

    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?


    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