How to do the down-under deal card trick

In the down-under deal, cards are dealt alternately onto the table and under the packet until only one is left. With the right number of cards, you know in advance which card that will be. Deal sixteen cards and the bottom one always survives, so a chosen card can find itself with no sleight of hand at all.

What does the audience see?

Someone picks a card, remembers it and puts it back. They count a small pile of cards onto the table themselves, then deal through it with a simple rule: one card down, one card under. Cards disappear onto the table until a single card is left in their hand. They turn it over, and it’s the card they chose.

Because the spectator does every deal, it feels as if the cards are choosing for themselves. That’s what makes it a good first self-working trick, alongside classics like the key card trick and the 21-card trick.

What is the down-under deal?

Hold a packet face down. Deal the top card onto the table. Move the next card from the top to the bottom of the packet. Repeat, “down, under, down, under”, until one card remains.

Mathematician Tanya Khovanova notes that the similar under-down deal, which starts by moving a card to the bottom instead, is mathematically equivalent to the Josephus problem, an old counting puzzle. The two versions give different survivors, so always start with “down” for this trick.

How do you do the trick?

1. Have a card chosen. Shuffle, spread the deck and let someone take any card. Ask them to show it to everyone except you.
2. Get it on top. Square the deck and ask them to place their card face down on top.
3. Count sixteen. Ask them to deal sixteen cards one at a time into a pile on the table, counting out loud. Dealing one at a time reverses the order, so their card, which started on top, is now at the bottom of the pile. Put the rest of the deck aside.
4. Do the deal. They pick up the pile face down and deal it down-under: one card onto the table, the next to the bottom, and so on.
5. Reveal. When one card is left, ask them to name their card, then turn it over.

Why does it work?

Sixteen is a power of two, and with a power of two the card that starts at the bottom is always the last one left. You can see why by following one pass. In the first trip through sixteen cards, every card in an odd position is dealt away, so eight cards are left, and the original bottom card is still at the bottom. The same thing happens with eight, then four, then two, until it’s the only card remaining.

For other packet sizes there is a simple rule. Find the largest power of two that is not bigger than your packet. Subtract it, double the result, and that’s the starting position, counted from the top, of the card that survives.

Cards in the packet	Card that survives (position from the top)
8	8th (the bottom card)
10	4th
12	8th
14	12th
16	16th (the bottom card)

Try it face up with ten cards and you will see the fourth card left at the end. Colm Mulcahy explains the same rule in his card-trick column for the American Mathematical Society, and the NRICH maths site sets it as a puzzle for students.

How do you make it stronger?

• Let them shuffle first. A full shuffle before the selection makes everything that follows look fair.
• Give the dealing a reason. Call it an elimination game: the cards are “voting off” everyone except the one that belongs to them.
• Don’t rush the count. The counting out loud in step 3 is what gets their card to the bottom, so make sure the cards really are dealt one at a time.
• Practise the rhythm. Saying “down” and “under” out loud keeps the spectator from mixing up the order halfway through.

What helps you take it further?

• Mathematical Recreations and Essays by W. W. Rouse Ball, free from our public-domain library. The classic Cambridge collection includes arithmetical card tricks, the Josephus problem and the three-pile problem.
• Ultimate Self Working Card Tricks: Cameron Francis Edition. Eleven card routines from Cameron Francis’s own repertoire that need no sleight of hand, including a triple prediction and a full-deck colour separation.

For more ideas, browse our card tricks or try the 1089 number trick, another self-working classic built on maths.

Frequently asked questions