# How many shuffles of a deck before it's back in the original order? **URL:** \ **Category:** Factual Questions\ **Created:** [November 14, 2025, 5:23pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852 "2025-11-14T17:23:29Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 16, 2025, 11:44pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/41 "2025-11-16T23:44:10Z")
> [@Buck\_Godot](#): > > 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. That was actually the main point of the paper by Bayer and Diaconis that I referenced above. After seven random riffle shuffles, the deck is within 1% of being perfectly random. What is a random shuffle? Well suppose you start by dividing it in two equal pieces (equal isn’t necessary or even desirable, but simplifies the explanation). Now toss a fair coin and if it comes up heads, select the top card of the left pile; otherwise the right. Rinse and repeat 52 times. I assume that if one pile runs out just take the rest of the other one. That’s one random dovetail (the word they use) shuffle. Now do this 6 more times. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 16, 2025, 11:56pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/42 "2025-11-16T23:56:10Z")
That’s not quite the procedure that @Buck_Godot described: He said that the probability of selecting from each pile was proportional to the size of that pile. Always choosing 50-50 between the piles would tend to leave a decent-sized chunk together at the end, where choosing proportionate to the size of the piles would tend to finish both piles at close to the same time. ---
**Author:** ![Jasmine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jasmine/32/2964_2.png) [@Jasmine](https://boards.straightdope.com/u/Jasmine)\ **Post date:** [November 17, 2025, 12:40pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/43 "2025-11-17T12:40:48Z")
> [@Chronos](#): > > Always choosing 50-50 between the piles would tend to leave a decent-sized chunk together at the end, where choosing proportionate to the size of the piles would tend to finish both piles at close to the same time. So, the question I would now pose to you guys is: Is there a skill to dealing (that entails shuffling) in, say, poker? Is there a way of tipping probability in the dealer’s favor? In essence, could “Maverick” actually tip the odds in his favor as he did in the old TV series bearing his name, or was that just Hollywood theatrics? ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [November 17, 2025, 4:14pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/44 "2025-11-17T16:14:35Z")
Oh, absolutely. A good card manipulator can deal whatever he wants without obvious signs that he is manipulating the deck. See for example this spectacular demonstration by the great Ricky Jay where he appears to be shuffling the deck randomly, but actually has full control of the complete order of the deck and can produce selected cards at will. [![](https://i.ytimg.com/vi/UWvRorX0KhQ/hqdefault.jpg "Ricky Jay - Amazing Card Trick/Manipulation") ](https://www.youtube.com/watch?v=UWvRorX0KhQ) ---
**Author:** ![Jasmine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jasmine/32/2964_2.png) [@Jasmine](https://boards.straightdope.com/u/Jasmine)\ **Post date:** [November 17, 2025, 4:17pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/45 "2025-11-17T16:17:16Z")
Astounding! ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [November 17, 2025, 4:20pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/46 "2025-11-17T16:20:05Z")
I don’t pretend to fully understand how he does it, but notice at the beginning of the demonstration he makes eight riffle shuffles. One is a fan shuffle and there’s also a triple cut in there, but it’s probably not a coincidence that there are eight of them. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [November 17, 2025, 5:43pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/47 "2025-11-17T17:43:40Z")
Take a look at some of the work Richard Turner does, he’s been on Fool Us with Penn & Teller a few times. BTW, he’s blind. [![](https://img.youtube.com/vi/Ufvo0HULFos/maxresdefault.jpg "Blind Magician Fools Penn & Teller with Card Magic Tricks | Penn & Teller: Fool Us | The CW") ](https://www.youtube.com/watch?v=Ufvo0HULFos&t=119/) ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 17, 2025, 5:55pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/48 "2025-11-17T17:55:58Z")
> [@Jasmine](#): > > So, the question I would now pose to you guys is: Is there a skill to dealing (that entails shuffling) in, say, poker? The simplest version of this would be fake shuffling and bottom dealing. Put whatever cards you want for yourself at the bottom of the deck, when you riffle shuffle make sure to drop that pile of five (or however many cards) first so they stay on the bottom. When dealing, deal every card off the top of the deck, but the bottom cards to yourself. It takes a lot of practice to make this look like you’re dealing off the top card, but some kids in my high school would make some money in the back of the CTA bus playing cards and bottom dealing themselves the hands they wanted. I’ve seen them do it, and even knowing what they’re doing (I went through a card magic phase at the time), it was next to impossible for me to definitively see them dealing off the bottom. But that’s basic beginners card manipulation. Or at least intermediate. It’s nothing like what real magicians can do. ---
**Author:** ![Jasmine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jasmine/32/2964_2.png) [@Jasmine](https://boards.straightdope.com/u/Jasmine)\ **Post date:** [November 17, 2025, 6:04pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/49 "2025-11-17T18:04:33Z")
> [@pulykamell](#): > > The simplest version of this would be fake shuffling and bottom dealing. That would get you shot in the old days! LOL ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 17, 2025, 6:06pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/50 "2025-11-17T18:06:35Z")
Might even get you shot today on the back of a CTA bus. ---
**Author:** ![Jasmine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jasmine/32/2964_2.png) [@Jasmine](https://boards.straightdope.com/u/Jasmine)\ **Post date:** [November 17, 2025, 6:12pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/51 "2025-11-17T18:12:26Z")
They can’t play poker in the back of CTA buses. The chips and cards would be bouncing and sliding all over the place. Then you’d get robbed. THEN you’d get shot. 😄 ---
**Author:** ![muldoonthief](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/muldoonthief/32/3188_2.png) [@muldoonthief](https://boards.straightdope.com/u/muldoonthief)\ **Post date:** [November 17, 2025, 6:28pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/52 "2025-11-17T18:28:17Z")
“You can have the money and the hammer, or you can walk out here. You can’t have both.” ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 17, 2025, 6:57pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/53 "2025-11-17T18:57:48Z")
Oh, they certainly played cards in the back of the CTA bus. I wasn’t making up a story–in high school they’d play cards in the back and occasionally some guy would come by with the shell game to score a few bucks from people who didn’t know better. ---
**Author:** ![Lucas\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lucas_jackson/32/303_2.png) [@Lucas\_Jackson](https://boards.straightdope.com/u/Lucas_Jackson)\ **Post date:** [November 17, 2025, 7:14pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/54 "2025-11-17T19:14:16Z")
> [@markn\_1](#): > > Oh, absolutely. A good card manipulator can deal whatever he wants without obvious signs that he is manipulating the deck. I love Ricky Jay (RIP). But also check out some of this guys stuff, an amazing card manipulator: [![](https://img.youtube.com/vi/G7o8EjTqYv0/maxresdefault.jpg "The Amazing “tHaT cAn’T bE dOnE wiTh siRi” Card Trick-Done with Siri. RULE #1 YOU ARE NOT THE EXPERT") ](https://www.youtube.com/watch?v=G7o8EjTqYv0) ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 17, 2025, 9:45pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/55 "2025-11-17T21:45:20Z")
Persi Diaconis could certainly deal any hand he wanted. Between fake shuffling and funny dealing. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 17, 2025, 11:07pm UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/56 "2025-11-17T23:07:30Z")
The possibility of trick shuffling is why it’s traditional for some other player to cut the deck after it’s shuffled. There are still ways to cheat, of course, but cutting makes it harder. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [November 18, 2025, 2:38am UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/57 "2025-11-18T02:38:03Z")
> [@Hari\_Seldon](#): > > That was actually the main point of the paper by Bayer and Diaconis that I referenced above. Sorry I guess I missed your post. Yes that was probably the paper I was thinking of. I definitely recognize Diaconis as an author. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [November 18, 2025, 2:58am UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/58 "2025-11-18T02:58:35Z")
I was introduced to this cipher in Stephenson’s Cryptonomicon ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [November 18, 2025, 3:34am UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/59 "2025-11-18T03:34:09Z")
Yes, Schneier created the cipher at the request of Stephenson for use in that book. It was an unusual case of an innovative cryptographic technique created for a piece of fiction. It reminds me of the [Futurama Theorem](https://theinfosphere.org/Futurama_theorem), a novel theorem in group theory created by mathematician Ken Keeler for use in a Futurama episode. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [November 18, 2025, 3:41am UTC](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852/60 "2025-11-18T03:41:32Z")
> [@Telemark](#): > > Take a look at some of the work Richard Turner does, he’s been on Fool Us with Penn & Teller a few times. BTW, he’s blind. My guess is that the cards in the deck are marked by feel in some way (e.g. vary slightly in length). While he is talking about Penn interpreting he is manipulating the deck to feel the kings put and then does some more shuffles to put them in the order he wants them. Then he could false deal (like he showed at the start) to give the cards to the people he wanted to. However it also could be that it was a fair deal but there was some choice manipulation such that regardless of whether 5, 6, or 7 hands were chosen the trick would work. I notice for example that even though 6 hands were dealt he chose Teller was the 5th hand. He also could have chosen Penn to be the one which had the good cards. He also could choose whether to burn cards and how many to burn, and it didn’t have to be 4 kings, it could have been 4 queens, or a straight flush so there may have been multiple interspersed winning hands. That would win depending on how many players were chosen. Still amazing work on Turners part [Previous page](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852.md?page=2) [Next page](https://boards.straightdope.com/t/how-many-shuffles-of-a-deck-before-its-back-in-the-original-order/1024852.md?page=4)