The 13 Trick

Key Concepts

• Card trick using a standard 52-card deck
• Counting up to 13 from a card's value
• Pile creation and elimination
• Mathematical principle behind the trick
• Relationship between top card values and remaining cards

Card Trick Demonstration

The presenter demonstrates a card trick that involves a standard 52-card deck. The deck is shuffled, and the trick proceeds as follows:

1. Pile Creation: Cards are drawn from the deck one at a time. For each card, the presenter counts up to 13, placing down additional cards to reach that number. For example, if an "8" is drawn, the presenter counts "8, 9, 10, 11, 12, 13," placing five cards on top of the "8" to complete the pile. Face cards are valued as follows: Jack = 11, Queen = 12, King = 13. A King requires no additional cards.
2. Pile Elimination: This process is repeated until the deck is exhausted or there are not enough cards to complete another pile. The remaining cards are held in the presenter's hand. The presenter then asks someone to choose any three piles. The remaining piles are added back to the presenter's hand.
3. Final Selection and Calculation: The person is then asked to choose two of the three piles. The top cards of these two piles are revealed. The person is instructed to add 10 to the sum of the values of these two cards. For example, if the top cards are "9" and "6," the calculation is 10 + 9 + 6 = 25.
4. The Reveal: The presenter deals out the calculated number of cards (in the example, 25) from their hand. The number of cards remaining in the presenter's hand will match the value of the top card of the remaining pile.

Mathematical Explanation

The presenter explains the mathematical principle that makes the trick work:

1. Pile Structure: Each completed pile contains 14 cards in total: the initial card plus the cards added to reach 13.
2. Initial State: The trick starts with 52 cards.
3. Ideal Scenario: If three complete piles of 14 cards each were created, there would be 14 * 3 = 42 cards on the table. This would leave 52 - 42 = 10 cards in the presenter's hand.
4. The "Skipped" Cards: The value of the top card on each pile represents the number of cards that were not placed in the pile during the counting process. These "skipped" cards remain in the presenter's hand.
5. The Equation: The number of cards in the presenter's hand is equal to 10 (the number of cards that would be left if all three piles were complete) plus the values of the top cards of the three piles.
6. The Deduction: By revealing the top cards of two piles and dealing out a number of cards equal to 10 plus their values, the number of cards remaining in the presenter's hand will be equal to the value of the top card of the remaining pile.

Conclusion

The card trick works because of a consistent mathematical relationship between the number of cards in each pile, the initial number of cards, and the values of the top cards. The trick cleverly uses pile selection and a simple calculation to mask this underlying mathematical principle, creating the illusion of magic. The presenter emphasizes that the value of the top card on each pile tells us how many additional cards are in the presenter's hand.