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Riffle shuffle of cards
Posted:
Jun 17, 2012 4:33 AM
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In http://mathworld.wolfram.com/RiffleShuffle.html one reads:
An ordinary deck of 52 cards is returned to its original order after
52 in-shuffles, but after only eight out-shuffles!
Aldous (1983) showed that 3/2log_2n (correcting a typo) shuffles are
sufficient to randomize a large n-card deck, yielding eight to nine
shuffles for a deck of 52 cards. When combined with results of Aldous
and Diaconis (1986), this analysis suggests that seven riffle
shuffles are needed to get close to random.
The last sentence certainly can be interpreted to mean that eight
shuffles would be very fine. However that would be extremely bad
according to the first sentence. Isn't there some contradiction?
M. K. Shen
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