  In card games, in casino games with multiple decks of cards and in
cryptography, one is sometimes faced with the following problem: how can a
human (as opposed to a computer) shuffle a large deck of cards? The procedure
we study is to break the deck into several reasonably sized piles, shuffle each
thoroughly, recombine the piles, do some simple deterministic operation, for
instance a cut, and repeat. This process can also be seen as a generalised
Bernoulli-Laplace urn model. We use coupling arguments and spherical function
theory to derive upper and bounds on the mixing times of these Markov chains.
