# what does total variation difference mean when, and how can certain values be interpreted

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I know a post about this has been made already over 5 years ago, but there wasnt a singular comment under it. what im trying to understand is what it is, how it should be interpreted, and how outcomes should be interpreted. like i saw a video about card shuffling, and they mentioned that after like 7 shuffles you have a total variation distance of about 0.3 and this is very good, but i have trouble really understanding how good and all it is. so as a clear question: what is total variation distance, and how should it and its results be interpreted.

(of course if any clarification is needed please let me know)

In: Mathematics

Card shuffling isn’t really random.  Cards can move up or down in position by one

If you give a brand new deck of cards 1 shuffle; you can deduce every cards position after 2 or 3 cards are shown – no randomness achieved

The more times you shuffle the deck the “more random” it becomes.  After 7 shuffles the deck is mathematically random in order