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Diaconis on Randomness
Posted By: Bob Koca
Date: Wednesday, 22 May 2013, at 11:19 a.m.
In Response To: Diaconis on Randomness (Phil Simborg)
First you need a way to measure randomness. I think how he did that was to say how much better than just guesing one could do predicting the cards one by one i one knew the pre shuffle order. The runs idea is a little similar here.
Then a model of shuffling is needed. I think what he did was to break the deck into 2 based on a binomial model, the number of cards in the left hand has a binomial distribution with 52 and .5 as parameters. Then during the riffle the probability that the next card to fall is from left is the number of cards on the left divided by remaining cards.
With this model there is initially a low slope then a steep slope and then a low slope after the 7th shuffle. Further shuffles do indeed make it more random but to an insignificant degree.
I've seen people who shuffle and the bottom card always stays on the bottom. To that person a cut in the middle is useful. Other than that though cuts are a waste of time, an additional riffle os more effective. Test it yourself. Arrange 2 decks. Give 3 riffles with 3 cuts to one of them and to the other give 4 riffles and no cuts and look at how many runs are preserved.

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