Card Trick Strategy

Solution & Explanation

The card trick strategy hinges on a clever collaboration between the dealer and a partner who sees all five cards you draw. This trick uses a combination of suit matching, card ordering, and permutation encoding to reveal the card you keep.

Step-by-Step Breakdown:

1. Initial Setup:

   • You draw five cards at random from a standard 52-card deck.
   • A partner, who works with the dealer, examines these five cards.

2. Identifying Matching Suits:

   • Among the five cards, there will always be at least two cards that share the same suit. This is due to the pigeonhole principle, as there are only four suits.

3. Choosing a Card to Keep:

   • The partner selects one card from the matching suit pair to give back to you.
   • The card given to you is strategically chosen to be the one that is "beaten" by the other card in the same suit.

4. Returning Cards to the Dealer:

   • The partner returns the remaining four cards to the dealer, with the first card being the one that "beats" the card you kept.
   • This first card indicates the suit of your card and narrows down the possibilities to six potential cards within that suit.

5. Encoding the Card Rank:

   • The remaining three cards are returned in a specific order to encode the rank of the card you kept.
   • The order of these three cards represents permutations, which correspond to the values +1, +2, +3, +4, +5, and +6. These values are added to the rank of the first card given to the dealer to determine your card's rank.

Example:

• Drawn Cards: 10♣, 5♠, 5♦, Q♣, K♠

• Partner's Decision:

  • Partner keeps 5♠ and returns K♠ as the first card.
  • K♠ "beats" 5♠, indicating the suit and narrowing it down to six possibilities: A♠, 2♠, 3♠, 4♠, 5♠, 6♠.

• Encoding the Rank:

  • The partner orders the remaining cards (10♣, 5♦, Q♣) to encode the number +6.
  • The order might be High, Middle, Low, where 5♦ > Q♣ > 10♣.

• Dealer's Deduction:

  • The dealer receives K♠ and deduces the card in hand is K♠ + 6, which is 5♠.

Conclusion:

This strategy relies on the partner's ability to communicate card information through strategic selection and ordering. By leveraging suit matching and permutation encoding, the dealer can accurately deduce the card you retained, making it appear as if they possess an uncanny ability to read minds.