We will try to answer the above question by analyzing the stopping times (which is the time after which the deck of cards is completely random) of the card shuffling process. If i get time i will generalize some of the analysis for random walks on groups.
*Reference:*
*Shuffling cards *and *stopping times* -
*stanford.edu [PDF] *
D Aldous, P Diaconis - American Mathematical Monthly, 1986 - jstor.org
Does Anything Happen at Random? (YouTube video of a talk by Persi Diaconis without much math)