An Introduction to Gilbreath Numbers

Abstract

This chapter mathematically analyzes the behavior of a card trick described by an undergraduate math major at the University of California, Los Angeles, named Norman Gilbreath. Stated succinctly, this trick can be performed by handing an audience member a deck of cards, letting them cut the deck several times, and then having them deal a number of cards from the top into a pile. The audience member takes the two piles (the cards in hand and the set now piled on the table) and riffle-shuffles them together. The magician now hides the deck (under a cloth, perhaps, or behind the back) and proceeds to produce one pair of cards after another in which one card is black and the other is red.