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The Math of Card Shuffling

Riffling from factory order to complete randomness.

If this procedure is repeated, eventually the top card will be placed at the very bottom of the deck, shifting the K♦ to the penultimate position. Continuing this procedure, the original bottom card, the K♦, will eventually rise to the top of the deck and be riffled. Notice how it takes many riffles to move the K♦ up just a few positions, but once the K♦ starts rising towards the top of the deck, it accelerates.

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