Phase 1: Sandwiching (Steps 1–5)

The chosen pile gets placed between the other two, putting the mark’s card somewhere in positions 6–10 of a 15-card stack.

Phase 2: The Dealing Revelation (Steps 6–7)

Dealing 15 cards into 5 piles distributes them 3 cards per pile, cyclically. Cards from positions 6–10 land as the middle card of each of the 5 piles. So no matter which pile the mark identifies, their card is always the 2nd card of that pile.

Phase 3: Re-stacking to Position 8 (Steps 8–10)

• Chosen pile (3 cards) on top of another pile → target card at position 2 of 6
• That 6 on top of last pile → target card at position 2 of 9
• The remaining 6 cards (two leftover piles) get shuffled and placed on top → target card is now at position 2+6 = 8 of 15

This is the lock. The card is always at position 8, and in the right hand pile, regardless of which card, which pile, or any shuffle.

Phase 4: Binary Elimination (Steps 11–17)

Dealing left-right and discarding left keeps only even-positioned cards each round:

Position 8 = 2³ — a perfect power of two — so it survives exactly 3 rounds of halving. The math is inevitable.

The entire trick is essentially two funnels: the dealing phase guarantees the card is the middle of its pile, and the re-stacking converts “middle of 3” into position 8, which the binary deal then isolates perfectly.

This trick is a classic example of a positional elimination or self-working mathematical card trick. It relies on the precise tracking of a subset of cards through a series of “piles” to ensure the target card always ends up in a specific numerical position.

Here is the breakdown of why the mechanics work:

1. The Stacking Logic (Establishing Position)

By placing the chosen pile (containing the target card) between the other two piles, you are performing a sandwiching technique.

• Piles 2 and 3 each have 5 cards.

• By putting the chosen pile on top of one and the other on top of that, the chosen 5 cards are now located at positions 6 through 10 in a 15-card stack.

2. The Deal (Redistributing)

When you deal the cards face up into 5 piles, you are essentially performing a modular distribution. Since there are 15 cards and 5 piles:

• Pile 1 gets cards 1, 6, 11.

• Pile 2 gets cards 2, 7, 12.

• Pile 3 gets cards 3, 8, 13.

• Pile 4 gets cards 4, 9, 14.

• Pile 5 gets cards 5, 10, 15.

Notice that the “target group” (original positions 6-10) is now distributed so that exactly one card from that group is in each of the 5 new piles. Specifically, they are all the middle cards (the 2nd card dealt) of their respective 3-card piles.

3. The Re-Stacking (The “Lock”)

When “The Mark” points to their pile, you know their card is the middle card of that specific 3-card pile. By placing that pile on top of another pile of 3, and then placing that pile of 6 on top of the last pile of 3, you have moved the target card to position 5 in a 9-card stack.

Note: The trick instructions mention shuffling the “remaining two piles” (the cards not in the 15-card stack) and putting them on top. This is a “convincer”—it adds bulk to the deck (bringing it back to a larger number) but doesn’t change the fact that the target card is now at a fixed, known depth from the top (usually position 8 if you include the 3 cards from the “other” pile and the 5 “extra” cards).

4. The Binary Parity (Elimination)

The final phase uses Successive Elimination (specifically a “reverse Australian deal”). By dealing into two piles and discarding the left one, you are mathematically narrowing the field:

Because the target card was moved to a specific position during the “Which pile?” phase, the “Left-Right” deal acts as a sieve. Every time you discard the left pile, you are discarding cards in positions $2n-1$. The math ensures that the target card’s position is never an “odd” position until it is the only one left.