In 
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/Mann.pdf

My aim is to look at (by algorithms or any method to measure) the
randomness of a deck of cards (permutation?) to determine whether they
are disturbuted randomly or not.

Page 18, it uses "variation distance".
What is that about? Is it a measure of "randomness of cards"?

In the last few pages, there are two more approaches - Birthday Bound
and Markov Chain. Can anyone explain to me briefly what are they
about? Which one is the best approach? Compare with "variation
distance", which one is the best approach?

Appreicated.