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Magician Turned Professor Talks About the Math Behind Shuffling Cards
An anonymous reader writes with this story about magician and professor of mathematics and statistics at Stanford University Persi Diaconis. "Now a professor of mathematics and statistics at Stanford University, Diaconis has employed his intuition about cards, which he calls 'the poetry of magic,' in a wide range of settings. Once, for example, he helped decode messages passed between inmates at a California state prison by using small random 'shuffles' to gradually improve a decryption key. He has also analyzed Bose-Einstein condensation — in which a collection of ultra-cold atoms coalesces into a single 'superatom' — by envisioning the atoms as rows of cards moving around. This makes them 'friendly,' said Diaconis, whose speech still carries the inflections of his native New York City. 'We all have our own basic images that we translate things into, and for me cards were where I started.' In 1992, Diaconis famously proved — along with the mathematician Dave Bayer of Columbia University — that it takes about seven ordinary riffle shuffles to randomize a deck. Over the years, Diaconis and his students and colleagues have successfully analyzed the effectiveness of almost every type of shuffle people use in ordinary life."
to complete randomness, is to leave an open pack sitting on the floor and let loose the kittens.
I'm a very special type of magician, I'm a MATH-emagician
"... that it takes about seven ordinary riffle shuffles to randomize a deck."
This often cited proof depends on a non-unique definition of random-- random relative to a cards original postion in the deck or relative to the position of another card. The number of shuffles varies with this definition. This has been proven.
Brady Haran on Numberphile has a series of interviews with Persi Diaconis: https://www.youtube.com/playli...
Elen sìla lùmenn' omentielvo
If you do 13 perfect shuffles (deck cut in exactly half, one card from each half going on top of the other), you will end up with the same deck. So it's not surprising that 7 "shuffles" would maximize entropy, by how they are measuring it (where does the top card end up, are there adjacent cards still "stuck"). You do end up with interesting pattern on a perfect shuffle using a sorted deck.
--sf
This topic might have warranted a video, considering it's a demo. It would sure beat all the "some dude talks about something for flipping forever" videos Slashdice keeps trying to dump on us instead.
Hmm, I recall learning the seven shuffle result when I was in math grad school in the 80s (from Prof Diaconus himself.) Did he not publish it until '92?
First of all, my respect to devoted professor and mathematician who is able to concentrate into observation and to think it through various aspects.
I have read article carefully and what it says is that certain type of shuffling produces desired random sequence of cards.
Also, consequently, we have mathematician who is trying to prove statistical correlation between how much time is spent mixing (smooching) and the randomness.
It can be proved empirically that this is a correct theory - the longer you shuffle cards, the more random sequence you have.
My question is..... what are the practical applications of this observation and what exactly mathematician is trying to prove.
But that's highly unlikely. I didn't RTFA largely because the summary included the word intuition.
Magician Turned Professor
...into a frog.
systemd is Roko's Basilisk.
Mental Hopscotch
Mental Hopscotch
Mental Hopscotch
Do me shuffle me rill me dump me
This blog post is rather more interesting than the (inaccurate) post above:
https://mathymcmatherson.wordpress.com/2015/04/15/mild-obsessions/
every type of shuffle people use in ordinary life
Which shuffle should I use in my ordinary life then? I'm ashamed that I survived so long without using one.
Most people are not aware that a perfect riffle shuffle on a deck of cards returns the deck to it's original state at eight shuffles. This means an assumption of imperfection for seven shuffles.
It is highly probabilistic that a perfect riffle shuffle never occur. It takes some effort to replicate to perfect shuffle.
My guess is he suspected it but did not have the right tools to prove it. Some people are like that with math. They can 'see it' but not have the correct proof to write it down.
The idea makes sense. Eventually it is random. But *when* is the question.
"Over the years, Diaconis and his students and colleagues have successfully analyzed the effectiveness of almost every type of shuffle people use in ordinary life."
All Shuffles? What about the Truffle Shuffle? After all, that is the most important shuffle I can come up with.
and he won't be available to be cast in this role. When the film version is announced, of course.
Diaconis also did a wonderful study on how human flipped coins aren't fair some years back.
https://statweb.stanford.edu/~susan/papers/headswithJ.pdf
It can be proved empirically that this is a correct theory - the longer you shuffle cards, the more random sequence you have.
Not true. There is a limit to entropy of a collection of objects, and once you reach this limit, any change to the system can only to be a reduction in the degree of entropy in the system. Also, it is entirely possible, (if unlikely) that you can shuffle a randomized deck of cards into sequential order.
HA! I just wasted some of your bandwidth with a frivolous sig!
Proof? Have you seen the data? It's basically a curve, and at some point you say, "yea, x% non-random seems small enough for me": http://www.ams.org/images/fcarc-december2010-dk.graph.2.gif
http://www.ams.org/samplings/feature-column/fcarc-shuffle
For those who are interested in math and/or card tricks, Colm Mulcahy is a professor of mathematics who often writes about math, cards and card tricks. He writes a blog called Card Colm for the Mathematical Association of America (MAA). He has written a book, Mathematical Card Magic: Fifty-Two New Effects, published by CRC Press.
A web site contains other interesting information about Mulcahy and his work, including links to past Card Colms.
Enjoy!
no wonder the education system sucks, it's just rich kids having fun spending public funds on useless crap