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."

Re:TGIF

[fuzzyfuzzyfungus]

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.)

How is this random?

[Phanatic1a]

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.

Re:How is this random?

[RingDev]

I thought about spending several paragraphs and a couple of examples explaining this, but from past experience I have learned that probability is sometimes counter-intuitive and some people just never get it.

No joke, you ever try to explain the Monte Hall logic of changing doors? I've had people fight to the bitter end on that one. I've drawn pictures. I even wrote a little .Net app with three doors and a picture of a goat just to help people comprehend...

-Rick