We analyze the effects of two different types of shuffling on a deck of cards. The number of possible orderings of the deck under these two types of shuffles is shown to be bounded by looking at the group structure formed by the two shuffles and by looking at various restrictions imposed by the shuffling types. One such restriction for even-sized decks is that if one card is a particular number of cards away from the top before shuffling, the card that is the same number of cards away from the bottom before shuffling will always be the same number of cards away from the bottom as the other card is away from the top after any amount of shuffles.
Benham, Heidi and Lamont, Riley, "Possible Orderings of a Deck Using Two Types of Shuffles" (2020). Academic Excellence Showcase Proceedings. 194.
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