Article on Perfect Shuffles for those interested in this sort of thing

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Postby Frank Yuen » 04/18/04 10:04 AM

In this month's issue of Mathematics Magazine, there is an article by Daniel Scully. The article is titled, "Perfect Shuffles through Dynamical Systems" and the exact issue is Volume 77 number 2, April 2004. It is the official publication of The Mathematical Association of America so it may take some searching to find.

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Postby Guest » 04/18/04 07:19 PM

Only the table of contents is available on the web.

Here's the description of the article:
Perfect Shuffles through Dynamical Systems
Daniel J. Scully
101-117
To perform a perfect shuffle on a deck of 2n cards you split the deck into two packets of n cards each and interleave the cards in the two packets together perfectly. Magicians do perform perfect shuffles. They appeal to magicians because they appear random but are not. In this article we present a new way to model perfect shuffles that uses the well-known doubling function from dynamical systems. This model shows the intimate relationship between the orbits of the cards under the perfect-shuffle permutations and the binary expansions of certain rational numbers from the unit interval. We exploit that relationship to show connections between the various perfect shuffles on the various sized decks, and we use it to link deck sizes to orbit lengths. The model generalizes nicely to k-handed perfect shuffles, and we use the model to describe more general (less-than-perfect) riffle shuffles.
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Postby Guest » 04/19/04 03:03 AM

This is probably a similar article:

http://mathworld.wolfram.com/RiffleShuffle.html

Faro enthusiasts might find the following online tool of interest:

http://www.natedog.com/cards/faro.html
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Postby Bill Mullins » 04/19/04 02:13 PM

The "similar article" isn't, really.

Dr. Scully was kind enough to send me a PDF of his paper, and said I could pass it on to whoever. So, if you want a copy, email me and I'll forward it.

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