  In the Gilbert-Shannon-Reeds shuffle, a deck of $N$ cards is cut into two
approximately equal parts which are then riffled uniformly at random. This
Markov chain famously undergoes cutoff in total variation after
$\frac{3\log(N)}{2 \log(2)}$ shuffles. We establish cutoff for the more general
asymmetric riffle shuffles in which one cuts the deck into differently sized
parts before riffling. The value of the cutoff point confirms a conjecture of
Lalley. Some appealing consequences are that asymmetry always slows mixing and
that total variation mixing is strictly faster than separation mixing.
