The p-shuffle is a natural generalization of the dovetail
shuffle. It is defined as follows. First, the deck is cut into a top stack
and a bottom stack so that the distribution of the size of the top stack is
Binomial $(N, p)$, where $N$ is the total number of cards in the
deck.Then, conditional on the outcome of the cut,the two stacks are
“riffled” in such a way that all possible riffles (interleavings)
of these two stacks are equally likely. The main result of the paper is an
asymptotic $(N \to \infty)$ bound on the number of repetitions needed
to “randomize” the deck.