perfect shuffle

An out-shuffle, also known as a perfect shuffle, is a riffle shuffle in which the top half of the deck is placed in the right hand, and cards are then alternatively interleaved from the right and left hands. In other words, an out-shuffle on a deck of 2n cards separates the bottom n cards from the top n cards and precisely interleaves them, with the bottom card remaining on the bottom. Using an out-shuffle, a deck originally arranged as 1 2 3 4 5 6 7 8 would become 1 5 2 6 3 7 4 8. The ordering of a deck of 52 cards after an out-shuffle is given by 1, 27, 2, 28, 3, 29, ... (OEIS A059953). Out-shuffling an even number n cards n - 2 times when n - 1 is prime results in the original order.

in-shuffle | Kimberling sequence | riffle shuffle | shuffle