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Fewer Shuffles Suffice
An anonymous reader writes "You may have heard that it takes about seven shuffles to mix up a deck of cards to near randomness. Turns out, though, that most of the time, perfect randomness is more than you need. In blackjack, for example, you don't care about suits. The same mathematician who developed the original result now says that for many games, four shuffles is enough. And the result isn't only important for card sharks. It helps reveal the math underlying Markov Chain Monte Carlo simulations, telling applied mathematicians when they can stop their simulations."
My reply was shuffled 4 times and it's now at a completely random position!
4 shuffles should be enough for everyone.
...deck shuffles you.
Quick, somebody report a bug to Microsoft. Free Cell and Hearts need a patch!
I realize that you are joking; but the link between probability theory and mathematicians with raging gambling habits is about as old as probability theory. In fact, I suspect that, given a suitable supply of wit, an analog to the philosopher's drinking song featuring mathematicians and gambling could be constructed without substantial violence to the truth.(Heck, just look at Pascal, he couldn't put the dice down when he was writing about Theology.)
"We're all enthusiastic," Diaconis says, "because you can describe it to your mom, the math is hard, and the results are interesting."
RTFA just for it to turn out to be a Your-Mom joke. Thanks guys. You really got me.
Not so obligatory link: http://xkcd.com/221/
Any life is made up of a single moment, the moment in which a man finds out, once and for all, who he is.
never ascribe to a heck of a shuffling that which can be adequately explained by stacking the deck and bottom dealing.
Do you even lift?
These aren't the 'roids you're looking for.
I've seen this assertion, and never quite understood it. I mean, if you're doing a perfect interleave shuffle, dividing the cards into two piles A and B and then weaving them together ABABABAB and so on, in what sense is that random? No matter how many times you iterate, it's still a purely deterministic process and you can easily predict the order of cards in the deck post-shuffle. So how do you get a random non-predictable card order out of this?
I can understand that in real life, you're not going to shuffle perfectly, there'll be a few more cards in one pile than the other, your interleave will occasionally do something like ABBBAABA instead of being perfect, and so forth, but in that case I don't see how you can say "Oh, it'll be random after 7 shuffles," because it'll depend on the amount of imperfection. And even then, this still doesn't strike me as actual random behavior; it's still deterministic, it just doesn't matter because a human observer isn't capable of observing the information he'd need to predict card order. But that information's still *there*, and a theoretical perfect observer will still be able to know what the card order is. With a truly random sequence, there is *no* way to determine the order, even given a perfect observer.
welcome our new less-thoroughly-shuffled overlords. (I am truly sorry for that, but I couldn't resist)
What we really need is a ten day waiting period and a background check before you can buy a congressman.
First! (this shuffling really works!)
Extreme Programming - Redundant Array of Inexpensive Developers
I've played far more than my share of cards, from CCGs and other proprietary games to standard 4-suit 52-card playing cards (learning to shuffle 200-card decks in Magic:TG before we discovered that a 60 card deck was optimal sure made me good at shuffling!), and let me say this: some people shuffle better than others.
Quality of shuffling varies widely; If I concentrate, I can get a clean broken-in deck to shuffle perfectly alternating cards from each half (though this is undesirable as it is not random). On the other end of the spectrum, many people shuffle very large chunks alternating, which is only as random as the cards are clean (which is to say, usually not very random).
Methods of shuffling also vary. There is the standard "Riffle" shuffle that was probably used in this study, there is overhand shuffling (taking small piles of cards from one or both sides of the deck and assembling them in a different order elsewhere), and there are several other methods. Because my riffle can sometimes be too precise, I will actually alternate riffle and overhand shuffles, performing three of each when I shuffle a deck.
In Magic: The Gathering, it is common to table-shuffle, which is essentially dealing out the cards into a set number of piles (usually 4-6 as they each divide a 60 card deck evenly, thus letting you ensure the cards are all there). This assures absolutely no clumping of dirty cards. Since it isn't very random, it should be followed by proper shuffling. (M:TG tournament rules now require three riffle shuffles since some people insist upon table-shuffling to preserve their expensive cards.) I use this method when dealing with dirty standard cards, too.
The WikiPedia page on Shuffling is actually amazingly informative, covering different shuffling methods, fake shuffle tricks (for magic tricks or cheating), shuffle-tracking (for gamblers), and far more math than the article linked in this sciencenews.org article. Give it a gander.
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Riffle shuffling is "professional-grade" in that it is the most thorough, and it is standard in the States. Throughout Asia and other parts, the "Hindu shuffle," which is very similar to the overhand method, is the most prevalent (as explained at WikiPedia:Shuffling#Hindu shuffle).
Most of the Asians and Australians I've played with actually use Hindu rather than overhand, so I'd guess that's what you saw. The difference is in the delivery of the cards from one pile to the other; in overhand, you're dropping them from one stack to the other (so the hand holding the original stack is doing all the action), whereas in Hindu, the action is in your free hand, which takes the cards from the main stack and slaps them back in a different position. This is typically done horizontally whereas overhand can be done in almost any position (usually at an almost vertical angle to use gravity).
Hmm, that's a better description than on Wikipedia. I'll be right back...
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