This thesis considers the effect of riffle shuffling on decks of cards, allowing for some cards to be indistinguishable from other cards. The dual problem of dealing a game with hands, such as bridge or poker, is also considered. The Gilbert-Shannon-Reeds model of card shuffling is used, along with variation distance for measuring how close to uniform a deck has become.; A method is found for approximating the variation distance from uniform when the size of a shuffle is large. This leads to a number of results for specific card games. In particular, the normal cyclic way that bridge is dealt is not optimal: changing to back-and-forth dealing can add as much randomness to the game as performing 3.7 more shuffles. Also: one fewer shuffle is needed to mix a go-fish deck (in which suit is irrelevant) than to mix a deck of 52 distinct cards; shuffling a deck with two types of cards is greatly speeded if the top and bottom cards of the deck initially have the same value; and a poker deck is best cut in such a way that the cards to be played come from the middle of the shuffled pack.; Several Monte Carlo methods are also discussed, for use in estimating values that are beyond the means of current technology to calculate exactly. The results of two large supercomputer simulations for bridge dealing are reported.; Among the other results are methods for computing the transition probability between decks when one of them has special characteristics (in particular, when one of them is sorted, or when the target deck consists of blocks of cards with the same value). This leads to an investigation of the joint distribution of two statistics on the symmetric group, des(pi) and pi(1), and a generalization of the Eulerian numbers. That results in a formula for the number of permutations with a given number of descents and a given initial value, and a proof that the expected value of pi(1), when pi is chosen uniformly from those permutations with d descents, is d + l.
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