This is a good thought experiment, but I don’t think even the most skilled with cards could do 8 much less 52 perfect shuffles so that not even one card is out of place. Just one errant card ruins the possibility.
Jasmine asketh, YouTube giveth: The perfect shuffle done 8 times is magic
There are card players and magicians/illusionists who are mindbogglingly good at this stuff. I’m not one of them… whenever I try to shuffle, gravity takes care of the randomization for me.
Thanks for all the responses. Only 8 times ( for the right kind of shuffle) boggles the mind. Like I said I wondered if it was much lower than I expected, but never thought the answer would be single digits.
I noticed that after just 3 shuffles, the cards went from A-2-3-4-5….etc to A-A-A-A, 2-2-2-2,3-3-3-3…etc which tickled my fancy a bit. I can imagine someone practicing enough that they could execute 2 perfect shuffles in a row, leaving them with a deck that may appear to a bystander to be fairly randomly distributed but is in fact in a VERY precisely known order. A large number of magic tricks could them be executed from there.
Jasmine, I have to say your first response ( and the subsequent good natured pile on) made me laugh. I did indeed specify a perfect shuffle in my OP, even called it that although I didn’t know it was a real term that meant anything. I guess even the best of us can fall into a comprehension blind spot once in a while LOL.
After 1 out-shuffle, the cards are shuffled 1,27, 2,28, 3,29 … 24,50, 25,51, 26,52
After 1 in-shuffle, the cards are 27,1, 28,2, 29,3, … 50,24, 51 25, 52,26 (each pair is reversed)
As linked to in this thread, very skilled magicians can absolutely do eight perfect Faro shuffles in a row. This is a skill that can be honed through much practice.
Wait, so is it 8 shuffles using only out-shuffles, and also 8 if using only in-shuffles?
Eight out-shuffles or 52 in-shuffles, as noted by @Wendell_Wagner in the first reply.
Oh, thanks - I was misinterpreting it somehow.
I think there was some rounding error or something in whatever tool you used to calculate this. The correct value (52!) is
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
And yes, any moderately skilled card manipulator would be able to perform 8 consecutive perfect Faro shuffles. It doesn’t require Ricky-Jay-level skills.
What about those mechanical card shufflers and dealers? How close do they come to performinig a perfect shuffle?
This guy apparently did 3200 perfect Faros in a row:
Given what I’ve learned in this thread, am I correct in saying that the number of cards in the deck does not matter (as long as it’s even)? That 8 perfect Faro out shuffles will return a deck to its original order?
If I took just the hearts and spades, for example….26 cards. Am I still doing 8 shuffles to restore the deck to its original order? What about a double deck (104 cards)?
No, not at all. We’re all assuming that “a deck of cards” means 52. In fact, the number of out-shuffles needed for 50 cards is exactly the same as the number of in-shuffles needed for 52.
It would be easy to design a card shuffling machine that does perfect Faro shuffles, but such a machine would be useless because it would do a very poor job of randomizing the deck. In fact, as discussed in this thread, if it shuffled the deck a multiple of 8 times, the deck would remain its original order.
Most modern shuffling machines are computer controlled. The computer uses a pseudorandom number generator to calculate the desired order of cards, and then the mechanics of the shuffler put the cards into that order.
Of course, some shuffling machines are worse than others.
(TLDR: cheaters set up rigged poker games which used modified card shufflers that enabled the cheaters to know the exact layout of the deck after shuffling, as well as other cheating technology.)
Simply not true. For example take the two halves of the deck that you are riffling. The bottom card of one of the halves will end up the bottom card of the deck and one of the top cards of the halves will end up as a top card.
Card-shuffling can be used in cryptography to generate a set key or to create a secure shuffle.
Persi Diaconis might disagree with you. Magician turned mathematician he coauthored a paper on what they called the dovetail shuffle. I met him once and I haven’t the slightest doubt he could do 8 perfect shuffles. He might balk at 52 though. He could throw a coin to come down heads every time. The explanation is that while it seemed to spin it never turned over. But even he could not see that it wasn’t.
Bruce Schneier designed the Solitaire cipher as a modern, high-security cipher whose operation is based on manipulating a deck of cards. Schneier says
I designed it to allow field agents to communicate securely without having to rely on electronics or having to carry incriminating tools. An agent might be in a situation where he just does not have access to a computer, or may be prosecuted if he has tools for secret communication. But a deck of cards…what harm is that?
The cipher’s key is the initial arrangement of the deck, which must be randomized (shuffled) and then shared between the sender and receiver. Schneier notes that “most people are not good shufflers”, so getting the deck into a well-shuffled state is one of the cipher’s weaknesses.
Actually, other mathematical weaknesses in the cipher have been discovered since its creation in 1999, and it is no longer considered very secure in its original form.
As part of a project for my undergrad thesis I read a paper about the random
Even with an imperfect shuffle it still isn’t going to be completely random after one shuffle. Its actually pretty interesting. As part of a project for an undergrad probability class, I read a paper about the approach to randomness of a riffle shuffle.
It defined the shuffle as dividing the deck into two piles (I don’t recall if it was even division or there was some randomness in the size of the stacks) and then a cards were overlaid from one stack or the other with probability proportional to the size of the stack.
What was interesting what that the approach to randomness was very non-linear. For 52 cards, if you shuffle the cards in this way up to five times then some orders of the cards are much much more likely than others. But if you then shuffle another two or three more times, then all orders become approximately equally likely.