sleightless.

The Si Stebbins Stack

A deck in a secret order that looks, when you riffle it, exactly like a deck somebody shuffled. Learn two small sums and you know the card underneath any card named, the card at any position, and where in the deck a named card is sitting — without a glimpse, a mark or a move.

Published under this name by William Coffrin, who performed as Si Stebbins, in 1898. The arrangement itself is far older — versions of it turn up in books from the 1590s. It is out of copyright, out of secret, and still the first stack most card workers learn, because it is the only one you can rebuild from scratch in front of a mirror in ten minutes.

Ask it a card

Pick any card. This is the sum you would be doing in your head.

Rank

Suit

Try it without the sum in front of you

You see a card. Name the one that follows it. Four choices, and the wrong ones are the near misses you would actually make.

How to build it

1. Two rules, and that is the whole stack. Every card is three higher than the one before it, and the suits run in a fixed rotation: Clubs, Hearts, Spades, Diamonds.
2. Counting past the King wraps around. Ace is 1, Jack 11, Queen 12, King 13. King plus three is sixteen, and sixteen minus thirteen is three — so a King is followed by a 3.
3. Start with the Ace of Clubs and just keep going. Ace of Clubs, 4 of Hearts, 7 of Spades, 10 of Diamonds, King of Clubs, 3 of Hearts, and on round. After fifty-two cards you arrive back at the Ace of Clubs, which is what makes the deck a loop rather than a list.
4. Build it from a new deck in about a minute. A fresh pack is already sorted by suit, so you are dealing rather than searching. Do it a dozen times and you stop needing to think about it.

The whole thing, in order:

Why does the Si Stebbins stack work?

Because 3 and 13 share no factors, and 4 suits divide 52 exactly.

Adding three each time and wrapping at thirteen walks you through all thirteen ranks before it repeats — 1, 4, 7, 10, 13, 3, 6, 9, 12, 2, 5, 8, 11 — because three and thirteen have no common factor. Any step size that shared a factor with thirteen would land you back where you started early and leave ranks unused. Thirteen being prime means every step from 1 to 12 works; three is chosen because adding three is a sum you can do while talking.

Meanwhile the suits cycle every four cards. Thirteen ranks and four suits, with the two cycles running at different lengths, means a rank does not meet the same suit again until fifty-two cards have gone by. That is the whole construction, and it is why it closes into a loop exactly at the end of the deck.

What you know	The sum	What it gives you
A card someone names	rank + 3, next suit along	the card beneath it
A card someone names	see below	its position in the deck
A position	3 × position, next suit along	the card sitting there

Why does it look shuffled?

Because the eye looks for suits, and no two neighbours share one. A deck sorted by suit is obvious from across a room; this one has clubs, hearts, spades, diamonds repeating so steadily that it reads as noise. The ranks climb by three, which the eye does not spot either, because it is looking for runs of one.

What gives it away is a long look at the faces, so do not give anybody one. Cut it as often as you like — a cut moves the starting point and changes nothing else, since the deck is a loop. A riffle shuffle destroys it completely.

What it buys you

• Somebody takes a card and you name it, having glimpsed only the card above it.
• You call the deck's order from memory while it sits in your pocket.
• A card is lost in the deck and you cut straight to it.
• It is the doorway to a memorized deck, which is the same idea without the sums — and considerably faster, because there is nothing to work out.

More

The 21 card trick needs no setup at all and is worth understanding for the opposite reason: the method is trivial and everything rests on the performance.