13 Card Trick

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The “Thirteen” card trick.

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How the Performer Knows the Prediction

The performer secretly peeks at the bottom card of the original 39-card portion before placing the 10 cards beneath it. That card is mathematically guaranteed to always be the one revealed. The peek can happen naturally while “casually” squaring up the deck.

  1. Shuffle & mix the cards from a deck without the Jokers.
  2. Count out 13 cards
  3. Mix them up
  4. Have The Mark selects three cards and place face up
  5. (eg) 2, 8, 10
  6. * Take remaning 10 cards and put them on the bottom of the deck
  7. Add value of cards to each – face down
    • 2 gets 11 cards
    • 8 gets 5 cards
    • 10 gets 3 cards
    • Face cards get 3 cards
  8. Add up the face value of the cards 2+8+10 = 20
  9. Deal face down that many cards
    1. 1, 2, 3…. 19, 20
  10. Hold your hand over the face down cards, and “guess” the top card.
  11. Turn over the top card (eg) K diamonds
  12. Prediction matches the card turned over
  • At the start of the cards, after shuffling and mixing, glance at the bottom card.
  • Count out 13 cards, etc – Steps 2, 3, 4, 5, 6 are just diversions
  • The card turned over is what you “peeked” and wrote down.

The Core Mechanic

It’s pure algebra that always cancels to the same result, regardless of which cards are chosen.

The Setup Math

After pulling 13 cards and the mark picks 3 (values a, b, c), the 10 unchosen cards go to the bottom of the deck. Working deck is now 49 cards.

The Cancellation

Each chosen card gets cards dealt on top of it to complete 13:

  • Card showing a → gets (13−a) cards
  • Card showing b → gets (13−b) cards
  • Card showing c → gets (13−c) cards

Cards consumed by the piles:

(13−a) + (13−b) + (13−c) = 39 − (a+b+c)

Then you deal (a+b+c) more cards face down.

Total cards consumed from the working deck:

[39 − (a+b+c)] + (a+b+c) = 39 exactly — always

The Result

The 49-card working deck always has 39 cards consumed and 10 left over — the same 10 that were placed at the bottom. The revealed card is always the card sitting just above those 10, i.e., position 40 from the bottom of the working deck.

The (a+b+c) terms cancel out completely. It doesn’t matter if the mark picks 2-8-10 or 5-5-5 or any other combination — the math lands on the same card every time.

How the Performer Knows the Prediction

The performer secretly peeks at the bottom card of the original 39-card portion before placing the 10 cards beneath it. That card is mathematically guaranteed to always be the one revealed. The peek can happen naturally while “casually” squaring up the deck.

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