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arXiv · 1911.07426

What is the Perfect Shuffle?

James Enouen
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Abstract

When shuffling a deck of cards, one probably wants to make sure it is thoroughly shuffled. A way to do this is by sifting through the cards to ensure that no adjacent cards are the same number, because surely this is a poorly shuffled deck. Unfortunately, human intuition for probability tends to lead us astray. For a standard 52-card deck of playing cards, the event is actually extremely likely. This report will attempt to elucidate how to answer this surprisingly difficult combinatorial question directly using rook polynomials.

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James Enouen. 2019-11-15. What is the Perfect Shuffle?. https://arxiv.org/abs/1911.07426

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