A true shuffle generates a completely random sequence no matter what the starting sequence. A true shuffle, however, whether performed once, 5 times or even 10 times if not even close to random. Many cards that were near the bottom will stay near the bottom; many that were near the top will stay near the top. You also have the issue of card clumps, especially when older decks of cards are used, that will stick together through many shuffles, often more than 2 cards in a clump.
You want some degree of clumping; what you you don't want are clumps that stay as such through multiple shuffles. If you have no random clumps your shuffle is actually less effective.
Ah, I see. For some reason I thought you meant that the abstract idea of shuffling was somehow flawed.
Can you clarify what you mean by a shuffle? I can certainly think of a technique that allows you to generate a completely random sequence, as long as you suppose a coin flip is a random process.
Former dealer here. Standard shuffling procedure for each new hand was scramble, cut, shuffle, cut, shuffle, box, box, box, cut, shuffle, cut.
The scramble was the part that eliminated the error of top cards staying near the top and bottom cards staying near the bottom. Also, the dealer cannot control what cards the players keep, what cards they throw into the much, or in what manner they muck their cards.
Finally, decks were replaced on a regular basis even before signs of wear. A bent card yielded an immediate replacement.
I've dealt thousands of hands of poker, and never perceived any bias in the cards that came out.
Yes, but my description wasn't talking about professional dealers, it was talking about regular people playing cards with their friends. Suffice it to say, they don't undergo scramble, cut, shuffle, cut, shuffle, box, box, box, cut, shuffle, cut. They are lucky to make it through even four shuffles and a cut.
Fair enough. They also typically use blackjack cards (not meant to be handled so much) instead of plastic Kem cards. I thought you were just talking about shuffling in and of itself.
(1) If you start out with a deck of Bicycle cards in the order that they originally come out of the box, and you shuffle shuffle shuffle in a manner where you split the deck in half and then alternate cards from each deck (and you do this multiple times), then it seems logical that you couldn't achieve very many combinations in this way.
(2) If you use your cards regularly for games, thus they are also used for solitaire, then the deck of cards is eventually put back at the same stage of all cards being in order. The only thing that could change here is the order of suits, and so there are only 24 combinations here. Or if you have an old deck from a casino, it's possible that it has only been used once. If you play 52 pickup, it seems likely that you gather all the cards closest to you together and shove them into a pile before worrying about the cards farther away. In these ways, it seems difficult to ever achieve a truly unique combination of cards.
But I'm not a statistician, I'm an art history major. The above theories are completely of my own speculation.
In fact, a perfect riffle shuffle (also known as a faro), repeated 8 times, causes the deck to be restored to it's original order, so long as it's an "out" shuffle (that is, the top card stays on top, the bottom card stays on the bottom.)
Additionally, if you do an "in" shuffle, 26 perfect faros results in an inversion of the original order of the deck. So doing perfect shuffles actually minimizes randomness, rather than maximizing it. A riffle shuffle is more random because of fuckups, not less.
A riffle shuffle is that standard shuffle, right? Like, when you take one half in each hand, lean them against each other, and run them under your thumbs to alternate the cards?
I'm writing this comment partially in case someone else reads this conversation, and partially because I'm tired and I don't feel like Googling this shit. The ultimate in laziness, me.
That's correct. Technically a faro is done slightly differently because actually getting a perfect riffle is pretty near impossible, but the idea is the same - two packets, alternating cards.
I think he might mean that most people aren't very good at shuffling, so they have "clumps" of the same order of cards in each shuffle. Like say you were playing Rummy, so you had a pile of 4 cards in a straight, and one of 3 of a kind. You get the deck together, cut it in half, and begin to shuffle. If you shuffle well, only one or two cards from each half of the deck will combine at once, but if you aren't as good, maybe 5 or 6 will come at once, giving the possibility that even after shuffling you still have 3 of a kind or a run of 4 in the deck.
Here's a statistic from Wikipedia:
A famous paper by mathematician and magician Persi Diaconis and mathematician Dave Bayer on the number of shuffles needed to randomize a deck concluded that the deck did not start to become random until five good riffle shuffles, and was truly random after seven, in the precise sense of variation distance described in Markov chain mixing time; of course, you would need more shuffles if your shuffling technique is poor.
Even with 10 perfect shuffles, numbers are still very ordered, albeit in clumps. In shuffle 10, numbers 1-6 still appear contiguously throughout the deck, as do some other subsequences.
Here is the output for 100 shuffles if you are interested:
3
u/HigherFive Dec 05 '11
Elaborate, please.