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BGonline.org Forums
Diaconis on Randomness
Posted By: Colin Owen In Response To: Diaconis on Randomness (Bob Koca)
Date: Wednesday, 22 May 2013, at 12:04 p.m.
Last year, a player at my local club , who is a maths teacher, mentioned something about shuffling 7 times - but no more - otherwise, it is less random!
When I googled it, the various references discussed the importance of 7 riffle shuffles. Looking deeper I found that, by an alternative definition of randomness (or the approach to it) the cards were only about two-thirds of the way to randomness after 7 such shuffles, and that about a dozen such shuffles were needed to attain 99%. What was still notable about the 7th riffle shuffle, with this definition, was that by far the biggest gain occured then.
What I also recall was that, if you give the cards 8 PERFECT riffle shuffles, the cards are in the same order as when you started shuffling. This must be what the maths teacher players memory had confused him about - the research was 20 odd years ago. But I'm glad he brought up the general issue for me.
The same kind of research on the journey to randomness when shaking dice (ie pre roll) would be very interesting, but I guess that mixing dice would be far less straightforward to define than mixing cards.
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