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Since 1958, mathematicians and magicians have wondered whether Gilbreath shuffling can reliably be applied more than once to a cyclic packet of playing cards and still produce predictable outcomes. Even for the most basic cyclic arrangements (such as an alternating Red/Black organization of the cards) the answer is "no." Yet, there are (in fact) two "perfect" Gilbreath shuffles that can be applied more than once (and, in some cases, many times) and yield predictable results that are a direct generalization of the conclusion of the Gilbreath Principle when a single Gilbreath shuffle is performed on a cyclic arrangement of the cards. To my knowledge, this result is not known (or, certainly, not well-known) in the mathematical or magical communities. As you will learn in this video, I call these two special Gilbreath shuffles "Perfect Gilbreath Shuffles" for an obvious reason and give simple procedures for carrying out both of these "Perfect Gilbreath Shuffles."