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The faro shuffle (American), weave shuffle (British), riffle shuffle or dovetail shuffle is a method of shuffling playing cards. Mathematicians use "faro shuffle" for a shuffle in which the deck is split into equal halves of 26 cards which are then interwoven perfectly.〔Morris 1998, 13〕 Magicians use these terms for a particular technique (which Diaconis, Graham and Kantor call "the technique")〔, Diaconis, Graham, and Kantor 1983, 188〕 for achieving this result. A right-handed practitioner holds the cards from above in the right and from below in the left hand. The deck is separated into two preferably equal parts by simply lifting up half the cards with the right thumb slightly and pushing the left hand's packet forward away from the right hand. The two packets are often crossed and tapped against each other to align them. They are then pushed together on the short sides and bent either up or down. The cards will then alternately fall onto each other, ideally alternating one by one from each half, much like a zipper. A flourish can be added by springing the packets together by applying pressure and bending them from above.〔Morris 1998, 111〕 A game of faro ends with the cards in two equal piles that the dealer must combine to deal them for the next game. According to the magician John Maskelyne, the above method was used, and he calls it the "faro dealer's shuffle".〔Maskelyne 1894, 204〕 Maskelyne was the first to give clear instructions, but the shuffle was used and associated with faro earlier, as discovered mostly by the mathematician and magician Persi Diaconis.〔Morris 1998, 8〕 A faro shuffle which leaves the original top card at the top and the original bottom card at the bottom is known as an out-shuffle; one which moves the original top card to second and the original bottom card to second from the bottom is known as an in-shuffle. These names were coined by the magician and computer programmer Alex Elmsley.〔Morris 1998, 11–12〕 A perfect faro shuffle, where the cards are perfectly alternated, is considered one of the most difficult sleights of card manipulation, because it requires the shuffler to cut the deck into two equal stacks and apply just the right pressure when pushing the half decks into each other. The faro shuffle is a controlled shuffle which does not fully randomize a deck. If one manages to perform eight perfect faro out-shuffles in a row, then the deck of 52 cards will be restored to its original order. If one can do perfect in-shuffles, then 26 shuffles will reverse the order of the deck and 26 more will restore it to its original order.〔Diaconis, Graham, and Kantor 1983, 193〕 ==Computer-science aspects== A faro shuffle is not to be confused with a sorting algorithm. A perfect faro shuffle cycles the order of the cards into a fixed number of states. For a 52-card deck using perfect faro out-shuffles there are 8 possible states in the cycle. That is, a faro shuffle can only be used to return the deck to its order prior to faro shuffling; it will not sort a randomized deck, nor can it return a randomized deck to new-deck order (unless the randomized initial state of the deck just happens to be one of the permutations of faro-shuffling a new deck). In-shuffles and out-shuffles are used in computer algorithms, notably in parallel computing.〔Diaconis, Graham, and Kantor 1983, 191–193〕 Below is a Python 3 implementation of a perfect faro out-shuffle: #! /usr/bin/env python # - *- coding: utf-8 - *- class Deck(object): def __init__(self): self.cards = ( 'A♠', '2♠', '3♠', '4♠', '5♠', '6♠', '7♠', '8♠', '9♠', '10♠', 'J♠', 'Q♠', 'K♠', 'A♦', '2♦', '3♦', '4♦', '5♦', '6♦', '7♦', '8♦', '9♦', '10♦', 'J♦', 'Q♦', 'K♦', 'K♣', 'Q♣', 'J♣','10♣', '9♣', '8♣', '7♣', '6♣', '5♣', '4♣', '3♣', '2♣', 'A♣', 'K♥', 'Q♥','J♥', '10♥', '9♥', '8♥', '7♥', '6♥', '5♥', '4♥','3♥', '2♥', 'A♥' ) def __eq__(self, other): return self.cards == other.cards def faro_shuffle(self): Shuffles the deck using a perfect faro shuffle. r = ): r.append(a) r.append(b) self.cards = r original_deck = Deck() # A deck in new-deck-order we will use for comparison. shuffled_deck = Deck() # A deck we will repeatedly faro-shuffle. for i in range(1, 1000): shuffled_deck.faro_shuffle() if shuffled_deck == original_deck: print("Deck is back in new-deck order after %s shuffles." % i) break The program shuffles a 52-card deck until it returns to its original order. This happens in exactly 8 iterations (shuffles): Below is a Perl implementation of a perfect out-faro shuffle: #!/usr/bin/perl # File: faro_shuffle.pl # Usage: perl faro_shuffle.pl # Purpose: To discover how many out-faro shuffles are required to # revert a deck of 52 cards back to its original order. use strict; use warnings; # Given an input of 52 elements (cards), returns them # as if they were shuffled with an out-faro shuffle: sub faroShuffle # Define a deck in new-deck order that we will use for comparison: my @originalDeck = qw( AH 2H 3H 4H 5H 6H 7H 8H 9H 10H JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C 10C JC QC KC KD QD JD 10D 9D 8D 7D 6D 5D 4D 3D 2D AD KS QS JS 10S 9S 8S 7S 6S 5S 4S 3S 2S AS ); # Create a deck that we will repeatedly faro-shuffle: my @shuffledDeck = @originalDeck; foreach my $i (1 .. 1000) __END__ The program shuffles a 52-card deck until it returns to its original order. This happens in exactly 8 iterations (shuffles): Below is a Perl 6 implementation of a perfect out-faro shuffle: #!/usr/bin/perl6 # File: faro_shuffle.p6 # Usage: perl6 faro_shuffle.p6 # Purpose: To discover how many out-faros shuffles are required to # revert a deck of 52 cards back to its original order. use v6; # Define a deck in new-deck order that we will use for comparison: my @originalDeck = < AH 2H 3H 4H 5H 6H 7H 8H 9H 10H JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C 10C JC QC KC KD QD JD 10D 9D 8D 7D 6D 5D 4D 3D 2D AD KS QS JS 10S 9S 8S 7S 6S 5S 4S 3S 2S AS >; # Create a deck that we will repeatedly faro-shuffle: my @deck = @originalDeck; for 1 .. * -> $i =finish The program shuffles a 52-card deck until it returns to its original order. This happens in exactly 8 iterations (shuffles): 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Faro shuffle」の詳細全文を読む スポンサード リンク
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