![]() When combined with results of Aldous and Diaconis (1986), this analysis suggests 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.
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