outshuffle

Outshuffle is a type of perfect shuffle used with an even-numbered deck of cards, typically described as a Faro out-shuffle. In this method, the deck is split exactly in half, and the two halves are interleaved starting with the top card of the first half. The result is that the top card remains on top and the bottom card remains on the bottom, distinguishing it from an in-shuffle where the top card moves down.

Procedure generally involves separating the deck into two equal piles, A (top) and B (bottom). Then N turns are performed by placing the top card from A, then the top card from B, and so on, until all cards are interleaved. The shuffle is deterministic and repeatable, making it a classic example of a perfect shuffle.

Mathematically, the out-shuffle is a permutation of the deck. For a deck of N cards (where N is even), the number of out-shuffles needed to restore the original order equals the multiplicative order of 2 modulo N−1. For a standard 52-card deck, eight consecutive out-shuffles restore the original arrangement, since 2^8 ≡ 1 (mod 51).

Applications and variants include use in magic, cardistry, and combinatorics. The term is commonly paired with Faro to denote the precise interleaving pattern. Its counterpart, the Faro in-shuffle, interleaves starting with the bottom half and places the top card in a different position.