Editing Shuffling (section)

===Research===
Following early research at [[Bell Labs]], which was abandoned in 1955, the question of how many shuffles was required remained open until 1990, when it was convincingly solved as ''seven shuffles,'' as elaborated below.<ref name="kolata" /> Some results preceded this, and refinements have continued since.

A leading figure in the mathematics of shuffling is [[mathematician]] and [[stage magic|magician]] [[Persi Diaconis]], who began studying the question around 1970,<ref name="kolata" /><!-- 20 years before 1990 is 1970 --> and has authored many papers in the 1980s, 1990s, and 2000s on the subject with numerous co-authors. Most famous is {{Harv|Bayer|Diaconis|1992}}, co-authored with mathematician [[Dave Bayer]], which analyzed the [[Gilbert–Shannon–Reeds model]] of random riffle shuffling and concluded that the deck did not start to become random until five good riffle shuffles, and was truly random after seven, in the precise sense of [[Total variation distance of probability measures|variation distance]] described in [[Markov chain mixing time]]; of course, you would need more shuffles if your shuffling technique is poor.<ref name="kolata">{{Cite web
| title = In Shuffling Cards, 7 Is Winning Number
| first = Gina
| last = Kolata
| date = January 9, 1990
| work = [[The New York Times]]
| access-date = 2012-11-14
| url = https://www.nytimes.com/1990/01/09/science/in-shuffling-cards-7-is-winning-number.html
}}</ref> Recently, the work of Trefethen et al. has questioned some of Diaconis' results, concluding that six shuffles are enough.<ref>{{Harv|Trefethen|Trefethen|2000}}</ref> The difference hinges on how each measured the randomness of the deck. Diaconis used a very sensitive test of randomness, and therefore needed to shuffle more. Even more sensitive measures exist, and the question of what measure is best for specific card games is still open.{{Citation needed|date=February 2007}} Diaconis released a response indicating that you only need four shuffles for un-suited games such as [[blackjack]].<ref name=science_news>{{cite magazine
 | url = http://www.sciencenews.org/view/generic/id/38434/title/Shuffling_the_cards_Math_does_the_trick
 | title = Shuffling the cards: Math does the trick
 | date = November 7, 2008
 | access-date = 14 November 2008
 | magazine = Science News
 | archive-url = https://web.archive.org/web/20090111090252/http://www.sciencenews.org/view/generic/id/38434/title/Shuffling_the_cards_Math_does_the_trick
 | archive-date = 2009-01-11
 | quote = Diaconis and his colleagues are issuing an update. When dealing many gambling games, like blackjack, about four shuffles are enough.
 }}</ref><ref name=persi_at_stanford>{{cite web
 | url = http://www-stat.stanford.edu/~cgates/PERSI/papers/redblack.pdf
 | title = A Rule of Thumb for Riffle Shuffling
 | access-date = 14 November 2008
 | last = Assaf
 | first = Sami
 |author2=Persi Diaconis |author3=K. Soundararajan
  | publisher = t.b.a.
 }}</ref>

On the other hand, variation distance may be too forgiving a measure and seven riffle shuffles may be many too few. For example, seven shuffles of a new deck leaves an 81% probability of winning [[New Age Solitaire]] where the probability is 50% with a uniform random deck.<ref name="vzs2004" /><ref>{{Harv|Mann|1994|loc=section 10}}</ref> One sensitive test for randomness uses a standard deck without the [[joker (playing card)|joker]]s divided into suits with two suits in ascending order from ace to king, and the other two suits in reverse. (Many decks already come ordered this way when new.) After shuffling, the measure of randomness is the number of rising sequences that are left in each suit.<ref name="vzs2004" />