  By a well-known result of Bayer and Diaconis, the maximum entropy model of
the common riffle shuffle implies that the number of riffle shuffles necessary
to mix a standard deck of 52 cards is either 7 or 11--with the former number
applying when the metric used to define mixing is the total variation distance
and the latter when it is the separation distance. This and other related
results assume all 52 cards in the deck to be distinct and require all $52!$
permutations of the deck to be almost equally likely for the deck to be
considered well mixed. In many instances, not all cards in the deck are
distinct and only the sets of cards dealt out to players, and not the order in
which they are dealt out to each player, needs to be random. We derive
transition probabilities under riffle shuffles between decks with repeated
cards to cover some instances of the type just described. We focus on decks
with cards all of which are labeled either 1 or 2 and describe the consequences
of having a symmetric starting deck of the form $1,...,1,2,...,2$ or
$1,2,...,1,2$. Finally, we consider mixing times for common card games.
