Cutoff in total variation for the shelf shuffle

We analyze the mixing time of a popular shuffling machine known as the shelf shuffler. It performs a modified version of a 2m-handed riffle shuffle (m=10 in casinos) in which a deck of n cards is split multinomially into 2m piles, the even-numbered piles are reversed, and then cards are dropped from piles proportionally to their sizes. We prove that 5 4log2mn shuffles are necessary and sufficient to mix in total variation, and a cutoff occurs with constant window size. We also determine the cutoff profile in terms of the total variation distance between two shifted normal random variables.