In this paper a mathematical model of card shuffling is constructed, and used to determine how much shuffling is necessary to randomize a deck of cards. The crucial aspect of this model is rising sequences of permutations, or equivalently descents in their inverses. The probability of an arrangement of cards occuring under shuffling is a function only of the number of rising sequences in the permutation. This fact makes computation of variation distance, a measure of randomness, feasible; for in an n card deck there are at most n rising sequences but n! possible arrangements. This computation is done exactly for n = 52, and other approximation methods are considered.