In 1973, Thorp introduced the following card shuffling
procedure. Cut the deck into two equal piles. Drop the first card from the
left pile or the right pile according to the outcome of a fair coin flip;
then drop from the other pile. Continue this way, flipping an independent
coin each time, until both piles are empty.

Despite its simple description, the Thorp shuffle has been hard to
analyze. It is believed that the mixing time is polynomial in log of the
number of cards. We show that this is indeed the case if the number of
cards is a power of 2.