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?