Mathematical Card Magic

Mathematical Card Magic: Fifty-Two New Effects

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  • Includes over 52 self-working magic creations, requiring no sleight of hand skills or understanding of advanced mathematical details
  • Presents 50 new mathemagical principles
  • Illustrates card handling techniques with step-by-step color photographs
  • Rates each effect for ease of performance, whether any setup is needed, how much mathematics is involved, and how well it appeals to a general audience
  • Explains card handling conventions and basic mathematical principles in a helpful introductory section
  • Covers Gilbreath shuffles and generalizations as well as palindromic card magic
  • Addresses the growing area of two-person mathemagic, which uses subtle information theory principles to communicate
  • Contains clever applications of algebra, combinatorics, discrete math, and probability

Visit the author’s website, Card Colm.


Mathematical card effects offer both beginning and experienced magicians an opportunity to entertain with a minimum of props. Featuring mostly original creations, Mathematical Card Magic: Fifty-Two New Effects presents an entertaining look at new mathematically based card tricks.

Each chapter contains four card effects, generally starting with simple applications of a particular mathematical principle and ending with more complex ones. Practice a handful of the introductory effects and, in no time, you’ll establish your reputation as a "mathemagician." Delve a little deeper into each chapter and the mathematics gets more interesting. The author explains the mathematics as needed in an easy-to-follow way. He also provides additional details, background, and suggestions for further explorations.

Suitable for recreational math buffs and amateur card lovers or as a text in a first-year seminar, this color book offers a diverse collection of new mathemagic principles and effects.

Table of Contents

Colm: Cool and Collected by Max Maven

Hit the Deck Running

Tips of the Trade

The Ratings Game


Convention Center

Low-Down Triple Dealing
Three Scoop Miracle—Done Magic Before?
Any Card (and Any Magician)
Triple Revelation
Ace Combination

For Richer or Poorer
Alphabetical Triple Addition
Subtler Bracelet
From Alpha to Omega
Volunteer Four Hours

Poker Powers
Ditch the Dud
Worst-Case Scenario
Full House Blues
Poker with Any Ten Cards

More Additional Certainties
Little Fibs
Consolidating Your Cards
Matching Interest Rates
Any Two Cards (No Fibbing)

Off-Centered COATs
Celebrity Selection
Never Forget a Face
Oddly Enough
My Lucky Number Is Seven

Gilbreath Variations
Easy as Pi
Lucky Number between One and Thirteen
Unadditional Love
Tapped Out

Word Row
The Biggest Names in Magic
Twisting the Knight Away
Easy as Tau (I Prefer Pi)
Intrinsically Disordered

Bligreath and Beyond
Matchmaker Instincts
The Guessing Game
Flushed with Embarrassment
Wholesome Threesomes

Flipping Miracles
I’ll Be Lucking Out for You
Coprime Twins
Royal Flush at the Eleventh Hour
Any Mathemagician

Red, Black, Silver, and Gold
Double Location
Top Twenty Hit
What’s Black and Red and Red All Over?
Gold and Silver

Slippery Slopes
Ten Soldiers
Slippery Enough
Erdős Numbers
No Drama Queen

Hamming It Down
A Horse of a Different Color
Multiple Personality
And Now for Something Completely Different

The Hidden Value of Cards
Fitch Cheney’s Five-Card Twist
Eigen’s Value
Ups and Downs
Fitch Four Glory





Author Bio(s)

Editorial Reviews

"This book is a well-written window into the mathematics behind 52 new card tricks as well as an introduction to performing such tricks. The mathematics is presented clearly enough for even the novice mathematician to follow. At the same time, the card tricks are explained thoroughly enough for even a novice magician to perform. … This book will bring out the mathemagician in every reader. … a must read for anyone looking for ways to get students of all ages interested in mathematics."
—Brittany Shelton, Mathematical Reviews, April 2014

"Mathematical Card Magic is a great reference for aspiring magicians who are curious about the mathematics behind card tricks. I am not a magician, nor am I an aspiring magician, but I enjoyed this book nonetheless. What I liked best was taking a peek behind the scenes of the card trick setup. … most tricks are a combination of careful dealing, careful shuffling, an astute memory, distracting the audience, and mathematics. I liked the way the book is organized. Every trick is scored on the sophistication of the underlying mathematics, how entertaining the trick is for the lay audience, how much setup is required, and how hard the trick is to perform. The author is clearly a seasoned pro. He is a skilled mathematician and an expert magician. He also has an easygoing way of explaining clever card tricks, combined with careful diagrams so that the reader can master every trick."
—Kara Shane Colley, MAA Reviews, November 2013

"Printed on glossy paper with many colour illustrations, it is not only fun, but also a pleasure to read. The apprentice magician will have a lot to practice on but even the professional magician will find many things to think about while mastering this wonderful calculus of the card deck."
—A. Bultheel, KU Leuven, The European Mathematical Society, November 2013

"Reading Colm Mulcahy’s book on mathematical card tricks is a lot of fun. It's clever, instructive, and clear. Learn some tricks. Learn some math. Impress your friends."
—John Allen Paulos, Mathematician and Author of Innumeracy, A Mathematician Reads the Newspaper, and other books

"Mathematical Card Magic is filled with many original ideas that will keep mathematicians and magicians busy for a very long time."
—Arthur Benjamin, Harvey Mudd College, and author of Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

"Colm Mulcahy has produced a stimulating collection of novel card magic tricks that not only form a wonderful introduction to important ideas in combinatorics but also contain some very nifty magic effects as well. By reading this book, the reader will be well rewarded in both disciplines."
—Ronald Graham, University of California, San Diego, and co-author of Magical Mathematics

"Colm has invented many important and practical mathematical principles and tailor-made them for card magic. He’s a skilled teacher and creator, and with his book in hand you’ll be able to construct lots of new effects. A must for your magic library."
—Lennart Green, 1991 World Champion in Card Magic, Sweden

"This is an amazing volume! Prof. Mulcahy has left one mystery for his readers to solve: Is it a really good math book, using card tricks to explain the math, or is it a really good magic book, using math to explain the magic? Either way, there’s not a wrong answer to this question."
—S. Brent Morris, PhD, author of Magic Tricks, Card Shuffling, and Dynamic Computer Memories

"In the early 1900s there began a new blossoming of mathematical magic, via such brilliant inventors as Charles T. Jordan, Stewart James, Robert Hummer and Martin Gardner. You’ll meet the above-mentioned people, plus many other worthwhile thinkers, in the book that you are about to read. Colm Mulcahy has joined those ranks. His bi-monthly Card Colm has appeared on the website of the Mathematical Association of America since 2004 … If you have been a Card Colm reader, you already know the quality of his imaginative output. You will find much of the best material from that column here in this collection, revised and improved. You will also encounter a wide variety of previously unreleased material, with some lovely surprises."
—From the Foreword by Max Maven, Magician and Mentalist

"… fantastic [book]! There are so many principles and ideas in it that it is one of those rare books that I will continually look through, study, and use as a reference for as long as I do card magic (which means the rest of my life)."
—Mark Setteducati

"In this delightful book, the author of the bi-monthly online articles Card Colm for the Mathematical Association of America shows just how magical mathematics can be. The mathematics ranges from simple to deep and the magical effects range from subtle to stunning. Most of the mathematical principles underlying the effects are original, and many are appearing in print for the first time in this book. I’m looking forward to using this material to intrigue and inspire young people to learn both mathematics and magic!"
—Neil Calkin, Department of Mathematical Sciences, Clemson University

"This is an amazing book! Like a magician’s well-stacked deck of playing cards, the 13 chapters are packed with 52 punchy effects guaranteed to amaze and amuse. Each chapter deals generously with mathematicians and professional magicians alike. Bursting with new effects, the chapters detail the method and Colm’s favoured presentation—each is ‘pick up and use’ perfect—but also provide a springboard for readers’ imagination to create their own presentations. Those with a more mathematical interest won’t be disappointed either; reading further into each chapter is a fascinating exploration of the mathematical questions underlying the effects. This is a magic book that will get you thinking and entertaining in equal amounts, in essence a perfect shuffle."
—Peter W. McOwan, Vice Principal Public Engagement and External Partnerships, Queen Mary, University of London

"Colm not only provides lucid exposition of how certain mathematical principles work, but he also clearly describes subtle performance pieces that entertainingly illustrate them. Then, to boot, he drills down as to why they work. In other words, he gives you the ‘body’ of everything, plus its ‘x-ray.’ Highly recommended."
—Jon Racherbaumer, Preposterist and Author

"In his book Mathematical Card Magic, Colm Mulcahy, PhD '85, shows that performing card tricks can be as easy as pi. Through visuals, detailed instructions, and a few math lessons, the Spelman College professor explains the mathematical basis of various card tricks, teaching readers to become so-called ‘mathemagicians.’"
—Lyndsay Isaksen, Cornell Alumni Magazine, January/February 2014

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