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Perkins Special user 950 Posts |
I don't make it to this corner of the Café all that often, but I ran across something that I thought was fascinating. Perhaps common knowledge for numerical warlocks, such as yourselves, but here's a link in case you are interested.
Regards, Perkins http://boingboing.net/2014/04/05/there-a......nge.html
The Séance Party
http://www.theseanceparty.com |
vindar New user Paris, France 62 Posts |
Hi,
There is already a thread about it on the worker forum : http://www.themagiccafe.com/forums/viewt......&forum=2 Yes, it is a very nice little video |
landmark Inner circle within a triangle 5194 Posts |
So... here's my question. Since all decks start off in some form of NDO aren't we really dealing with a pseudo random shuffled deck rather than a random shuffled deck?
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
vindar New user Paris, France 62 Posts |
This is a very interesting question that was investigated by the famous... Persi Diaconis !
Indeed, given an initial configuration of the deck, it is not possible to obtain every other configurations after only one riffle shuffle (for instance, the top card cannot become the bottom once). Thus, after one riffle shuffle, the order is not uniform among all the possible ordering of the deck. However, with repeated riffle shuffles, the arrangement of the cards become more and more "random"... To turn this remark into a mathematical statement, one can consider the so-called "distance in total variation norm" of the random distribution of the cards after n shuffles. It turns out that very few shuffles are needed to make this distance very small, i.e. to make the order of the card almost indiscernible from a real uniform random arrangement. For a deck of 52 cards, the number of riffle shuffles considered safe is (I think) n = 7. More generally, for a deck of m cards, when m gets large, one need about n = (3/2)log2(m) shuffles to really mix the cards. Of course, the number of shuffles needed depend on the kind of shuffle considered. In the case of the riffle shuffle, the result here is only asymptotic and the distribution is never exactly uniform (it get closer and closer but it is never perfect). However, it is possible to consider a uniform random permutation and then use it to construct a really perfectly shuffled deck, provided one can get really random number from, say, quantum mechanic experiment. Here is little survey which seems quite good: http://www.ams.org/samplings/feature-column/fcarc-shuffle Cheers, |
landmark Inner circle within a triangle 5194 Posts |
Diaconis--I should have known! Thanks a lot for that.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
Perkins Special user 950 Posts |
Excellent, Vindar. Thanks. Bit of a mind melter for a fella like myself, but wonderful none the less.
The Séance Party
http://www.theseanceparty.com |
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