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Diaconis on Randomness
Posted By: ah_clem
Date: Wednesday, 22 May 2013, at 3:02 p.m.
In Response To: Diaconis on Randomness (Steve Mellen)
Bayer & Diaconis's paper from 1992 is here: http://wwwstat.stanford.edu/~cgates/PERSI/papers/bayer92.pdf
Brad Mann's "HOW MANY TIMES SHOULD YOU SHUFFLE A DECK OF CARDS?" is here: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/Mann.pdf
Here's the takaway: riffle shuffles will never produce a truly "random" result, but they will approach it in the limit. By the standard of "variation distance", up to five shuffles accomplishes little, a sixth helps considerably, and a seventh drops the variation distance to below .5, which might be considered a minimum standard.
It's not like something magic happens on the 7th shuffle, it's just that some would consider it to be the number where one reaches the point of diminishing returns. 8, 9 or 10 shuffles will increase the degree of randomness.
Total variation distance for m shuffles of 52 cards m IIQmUII 1 1.0 2 1.0 3 1.0 4 1.0 5 .924 6 .614 7 .334 8 .167 9 .085 10 .043

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