This is a simple question really. If you have a shuffled deck and you want to put it into Mem Deck order, what's the fastest way to do so? I'm not talking about setting it up during a performance or on the fly. I mean you're at home and you want to stack your deck. Is there a system for doing so other than just going one by one? I personally do it in groups of 3, but I feel like there's probably something faster that someone smarter has worked out. Anyone?

I make 5 heaps on the table.
1-9, 10-19, 20-29, 30-39, 40-52
Then I sort each heap.

Bob Farmer recently released his Tarodiction toolbox. That describes a method for this. Also Patrick Redford recently released his method (available to owners of his new book Temporarily out of order). There are threads for both here in Shuffled not stirred.

It would be nice if we could collectively find an efficient solution to that challenge There are a lot of sorting algorithms which are very efficient with abstract data but fail miserably with physical objects (for obvious reasons.)

Going from a shuffled deck to a stack order or to NDO is actually the same process; the numbering of the cards, 1 to 52, is the same, only the card values are different. Therefore you could use NDO and suits for your experimenting sessions.

Like many people, I usually deal out four piles of 13 cards (1-13,14-26,27-39,40-52); I then fan each pile and sort each sequence using no particular method. It’s not that bad, but there must be a way to improve on that.

So, how about using an algorithm similar to the Patience Sorting Algorithm ?

Method

Hold the shuffled deck face up.

Phase 1: Dealing

1. Initially, there are no piles. The first card dealt forms a new pile consisting of the single card.
2. Each subsequent card is placed on the leftmost existing pile whose top card has a value greater than the new card's value, or to the right of all of the existing piles, thus forming a new pile.

Phase 2: Collecting

3. Pick up the smallest card. It will always be on top of the left-most pile.
4. Keep picking up cards in order. The next card will always be on top of one of the piles.

I have tried with 26 numbered cards and it’s pretty quick once you’re used to it. It takes some time to make the decisions without thinking. The issue I’ve found is that you sometimes need a lot of table top space.

So what do you think? Is it possible to improve this sort/merge algorithm, or are there much better ones out there?

Table space is indeed another parameter to take into account. If you have a large table you can directly deal the cards into their normal position if you draw a grid of 13x4 or 10x6 for example. You just deal the cards onto the grid and collect.


Maybe if people are ready to try different versions they could also indicate their sorting time (after some sufficient training) ?

Yes, the tabletop space issue is a big problem with the quicksort like method I posted above. A couple of times I had 14 packets. Too many for comfort.

jmbulg is onto something there with the notion of fixed positions. I vaguely remembered a sort algorithm that uses a fixed number of slots and I went to my favourite website Stackoverflow (I'm a coder by profession) and I have found what I think is a workable method: A radix sort.

It's possible to sort a 52 deck of cards in two passes by always using 10 slots (2 rows of 5 slots, for example) on the first run and 6 on the second. I've tried and it's very quick.

I'll post more about it later, but if you're in a hurry, navigate to this site: sorting an actual deck of cards and search for radix sort.

Patrick Redford can get into Redford Stack from a shuffled deck in the process of doing a few tricks that almost automatically stack the deck for him.

Ben

Just depends on which stack your using. I use the "Redford" stack now after many many years of using mnemonica. I can get from a completely shuffled deck into "Redford" stack all in the hands using no table in less than 2 minutes using the Chinese shuffle. Very quick and convenient. This is all taught in Patrick Redfords new book "temporarily out of order"

OK, here’s the method. As from my previous post it’s based on The Radix Sort.

For training purpose, It’ll be easier to number a deck of cards, in your stack order, on its face. You’ll be able to see better how the deck gets ordered.

Least significant digit radix sort

Hold a shuffled deck, face up.

Imagine you have 10 spaces (buckets, spots, etc.) on the table numbered from 0 to 9 where you’re going to build the card piles.

1st round: rightmost digit sort

On the first round you will consider only the rightmost digit of you card position in the ordered memdeck and deal the card face up on its spot.

So for instance: 2, 12, 22, 32, 42, and 52 are dealt to to spot 2, and 10, 20, 30, 40, 50 to spot 0.

Once you’re through dealing the pack, you’ll have 10 piles having each 5 to 6 cards.

Gather the deck from right to left, i.e. starting from the rightmost pile (spot 9) that you put on top of pile 8, then on pile 7 up to pile 0.

2nd round: leftmost digit

Here you have to remember that cards numbered from 1 to 9, should be thought as numbered as 01 to 09 and therefore will go to pile 0.

Hold the deck face up and visualize 6 spaces, numbered from 0 to 5 and deal the cards to their correct pile based on their leftmost digit.

So, for example, 1 to 9 will go to pile 0, whereas 40, 41, 42, 43... and 49 will go to pile 4.

Once again gather the deck from right to left and the deck is in memorized order with 1st card on top of the face-down deck.

A few hints:

It'll take some time before you get used to the idea, but if you manage to deal the cards without thinking, the method is rather fast.

If you’d rather visualize the piles ranging from 1 to 0 (think of them as 10), instead of 0 to 9, it’s fine, but when you gather make sure that the 0 pile is picked up last.

It might be better, during the 1st round of dealing, to form 2 rows of 5 piles each, as it will be easier to find the relevant pile to put down a card.

Something I have just realised is that after round 1, your deck is setup for the excellent Aronson effect Histed Heisted.

Finally I’ve got some ideas to considerably speed up and limit errors during the dealing procedure and reduce the number of piles. I’ll post them if I manage to finalize them.

Thank you for posting this Claudio!

Sometimes an in-the-hands-sort is useful. I use the following mainly as an in-the-hands sort for NDO. I've used it as well for Aronson, but it can be generalized to any stack:

Run through deck upjogging all black cards. Pull out black cards to face of deck.

Run through deck upjogging all spades and diamonds. Pull out this half to face of deck.

Spread the bottom 13 spades and arrange in order with right hand as if arranging a bridge hand. Cut those 13 cards to the top of deck. Repeat with the next three suits. You are now in Bicycle NDO.

To generalize for any stack:

1) upjog all cards within the ranges of 14-26 and 40-52, and cut to face of deck.
2) upjog all cards within the ranges of 27-52 and cut to the face of the deck.
3) Spread 13 cards at a time and put in ascending order, then cut to back of deck. Repeat three more times.

Hope this is useful to someone.

I use two methods.

Method One:
If there's a table, I'll sort into piles 1-13, 14-26, 27-39, 40-52. Then I fan each one to put them in order. This is similar to the first reply in this thread.

Since I get into my stack from NDO, I also have an in-the-hands method, but it's slightly more efficient than Landmark's above post.

Method Two:
First, I like to begin with a (low) diamond on the face, and another diamond (any value) at the rear (i.e., the top of the deck). I'll explain why in a minute.

Similar to Landmark, I upjog all of the black cards, HOWEVER, the spades are pushed higher than the clubs (the clubs are only upjogged half-way).
Next I spread the cards into a kind of fan, and remove the spades one at a time* beginning with the king and ending with the ace, so they're in New Deck order (K-A).
I repeat with the clubs but start with the ace and end with the king (A-K).

Now I spread through the pack again, fully upjogging A-7H, and mid-jogging 8-K. I again spread and remove the cards and, starting with the ace, remove them one at a time.
Now I'm left with the diamonds on the face, which I'll fan out and put in K-A order.

This is not quite New Deck Order because the spades and diamond suits are switched, but I need them switched for my particular stack (which is just four faros away). And the reason for having diamonds on the top and bottom is because I save the diamond suit for last, so they make for clamp the cards in place (e.g., if a spade were at the rear of the deck and I upjogged it, it could drop to the floor. Since a diamond is on top, it will keep the cards secure).

Using this method I can get into stack order (without a table) in under two minutes (that's counting the four faros). Obviously it's not something that should be done in front of spectators. This method of half-jogging also suggests another solution: ujpog, mid-jog, and downjog, so that the suits can be sorted in one pass rather than two. I've experimented with it, but the sloppiness isn't worth the effort, especially since this is only done for myself. I'm sure someone could make it work with practice (this is essentially what Lennart Green does with a modified angle jog allowing for a quad-separation. Then again, the guy has hands like catcher mitts).

*I said I remove the cards one at a time, but that's not necessarily the case. If the five and six are adjacent to one another (and in the proper order e.g., the five is on top of the six), I can pull them both out at once.

I don't have any work by Redford, but what you describe sounds very much like a Bro. John Hamman concept explained in his effect The Chinese Miracle. It uses a series (up to 6) of culls/out-jogs, aka "chinese shuffles" to get from a shuffled deck to NDO, though obviously the concept can be applied to any stack.

Is that the case?

The question was about getting to stack openly. If you want to get to stack in a covert way (by skill or cover of trick(s)), there's a lot of material out there.

I know that Doug McKenzie has a method to get from a shuffled deck to any stack in just 3 culls! He says that he could order up to 64 cards in 3 culls. That should give a clue as to the method.

Keep track of four positions without a table? That's impressive.

Yes, he is! #thumbsup

As mentioned about the Bammo Tarodiction Toolbox, there's a full-deck stack sort in that book that requires 8 piles dealt only twice. I think it's detailed in the second addendum.

- Richard

As one of the easter eggs to Temporarily Out of Order I shared a way to get into any full deck stack by dealing the deck out twice (that doesn't use any binary or markings). There are two methods I shared to do so.

I also have some work with the Chinese Shuffle that's taught in the project as well.

I hope this clarifies!

For the best work on Radix sorting, get in touch with Tomas Blomberg.

A few years back, Shoot Ogawa put out a DVD set: Busters. He can order a deck in hands in about 60 seconds.

In a nutshell, the cards are upjogged by different amounts based on the value of the cards, then collected out of the deck in order.

I usually sort the deck back into NDO, and then shuffle it into mnemonica