In shuffle

In shuffle

An in shuffle is a type of "perfect" shuffle done in two steps:
#Split the cards exactly in half (a bottom half and a top half) and then
#Interweave each half of the deck such that every-other card came from the same half of the deck.

If this shuffle moves the top card to be 2nd from the top then it is an in shuffle, otherwise it is known as an out shuffle.

Example

For simplicity, we will use a deck of six cards.

The following shows the order of the deck after each in shuffle. Notice that a deck of this size returns to its original order after 3 in shuffles.::

Mathematics

The number of in shuffles required to return a deck of cards of even size "N", to original order is given by the multiplicative order of 2 modulo ("N" + 1).

For example, for a deck size of "N" = 2, 4, 6, 8, 10, 12 ..., the number of out shuffles needed are: 2, 4, 3, 6, 10, 12, 4, 8, 18, 6, 11, ... (This is the integer sequence [http://www.research.att.com/~njas/sequences/A002326 A002326] ).

For a standard deck of 52 playing cards, the number of in shuffles required to return the deck to its original order is 52.

References

*cite journal
last = Diaconis
first = P.
authorlink =
coauthors = R.L. Graham, and W.M. Kantor
title = The mathematics of perfect shuffles
journal = Advances in Applied Mathematics
volume = 4
issue = 2
pages = 175–196
publisher =
date = 1983
url = http://www-stat.stanford.edu/~cgates/PERSI/papers/83_05_shuffles.pdf
doi = 10.1016/0196-8858(83)90009-X
id =
accessdate =
*cite journal
last = Kolata
first = Gina
authorlink =
coauthors =
title = Perfect Shuffles and Their Relation to Math
journal = Science
volume = 216
issue = 4545
pages = 505–506
publisher =
year = 1982
month = April
url = http://links.jstor.org/sici?sici=0036-8075%2819820430%293%3A216%3A4545%3C505%3APSATRT%3E2.0.CO%3B2-K
doi =
id =
accessdate =
*cite book
last = Morris, S.B.
first = S. Brent
authorlink =
coauthors =
title = Magic Tricks, Card Shuffling and Dynamic Computer Memories
publisher = The Mathematical Association of America
date = 1998
location =
pages =
url =
doi =
isbn = 0883855275
ISBN status = May be invalid - please double check


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Shuffle! On the Stage — Shuffle! Shuffle! est la première visual novel produite par l éditeur japonais Navel. Alors que la version PC est un eroge, le jeu est également sorti sur Playstation 2 sous la forme d un remake tous publics, Shuffle! On the Stage. Le jeu a été… …   Wikipédia en Français

  • Shuffle! — Некоторые героини аниме Shuffle! Жанр романтическая комедия, фэнтези …   Википедия

  • Shuffle — Shuffle! Героини аниме Shuffle! Шафл! (неоф. рус.) Жанр романтическая комедия, фэнтези, гарем Манга «Shuffle! Days in the Bloom» Автор Сирой Кусака …   Википедия

  • Shuffle! — シャッフル！ (Shaffuru!) Género Fantasía, Ecchi, Harem, Romance Novela visual Desarrollador Navel …   Wikipedia Español

  • Shuffle! — Originaltitel シャッフル！ Transkription Shaffuru! …   Deutsch Wikipedia

  • Shuffle track — Shuffle tracking is an advantage gambling technique where a player tracks certain cards or sequences of cards through a series of shuffles. Shuffle tracking is typically done in blackjack games, although it can be done in other card games.… …   Wikipedia

  • Shuffle offense — as an offensive strategy in basketball, developed in the early 1950s by Bruce Drake at the University of Oklahoma. It was later used by Bob Spear, who fast the first head basketball coach of the United States Air Force Academy from 1957 71. The… …   Wikipedia

  • Shuffle Along — steht als eines der ersten erfolgreichen „all black musical“ am Broadway am Anfang einer Epoche afroamerikanischer Emanzipation im Bereich der bildenden Künste und des Kulturbetriebs, die Harlem Renaissance genannt wird. Shuffle Along wurde am 23 …   Deutsch Wikipedia

  • Shuffle (game show) — Shuffle was a game show that aired on The Family Channel. It ran from March 7, 1994 to June 10 of that year. Wink Martindale hosted, and Randy West announced.Wink Martindale and Bill Hillier created and produced four interactive games for FAM,… …   Wikipedia

  • shuffle — [shuf′əl] vt. shuffled, shuffling [Early ModE, prob. < or akin to LowG schuffeln, to walk clumsily, shuffle cards < base of SHOVE] 1. a) to move (the feet) with a dragging or shoving gait b) to perform (a dance) with such steps 2. to mix… …   English World dictionary

  • Shuffle — Shuf fle, v. i. 1. To change the relative position of cards in a pack; as, to shuffle and cut. [1913 Webster] 2. To change one s position; to shift ground; to evade questions; to resort to equivocation; to prevaricate. [1913 Webster] I myself …   The Collaborative International Dictionary of English

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”