Order after 52 in-shuffles, but after only eight out-shuffles!Īldous (1983) showed that (correcting a typo) shuffles are sufficient to randomizeĭeck, yielding eight to nine shuffles for a deck of 52 cards. An ordinary deck of 52 cards is returned to its original

Out-shuffling an even number cards times when is prime results in the original order (Diaconis et al.ġ983, Conway and Guy 1996). Therefore, in-shuffling an even number cards times when is prime results in the original card order. Note that (in the out-shuffle case) this maps the firstĪnd last card to 0, but this makes sense, because they are both fixed points. For an out-shuffle, theįirst card is numbered 0 and the multiplication is done modulo. For an in-shuffle, theįirst card is numbered 1 and the multiplication is done modulo. Moves to the position originally occupied by the th card modulo. The riffle operation is implemented in the Wolfram Riffle shuffles are used in card tricks (Marlo 1958ab, Adler 1973), andĪlso in the theory of parallel processing (Stone 1971, Chen et al. UsingĪn out-shuffle, the deck order would become 1 5 2Ħ 3 7 4 8. Using an in-shuffle,Ī deck originally arranged as 1 2 3 4 5 6 7 8 would become 5 1 6 2 7 3 8 4. Left and right hands (an in-shuffle) or from the rightĪnd left hands (an out-shuffle).

Is placed in the left hand, and cards are then alternatively interleaved from the A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck ofĬards is divided into two halves.

What is the card game faro