=+state where all c permutations are equally likely. Let be the uniform distribution and Xn be

=+state where all c permutations are equally likely. Let π be the uniform distribution and πXn be the distribution of the cards after n shuffles.

The probability Pr(T ≤ n) is the same as the probability that c balls

(digit strings) dropped independently and uniformly into 2n boxes all wind up in different boxes. With this background in mind, deduce the bound

πXn − πTV ≤ 1 −

c

−1 i=1



1 − i 2n

.