An Amazing Card Trick

This remarkable card trick is an example of how a concealed mathematical structure will enter into clumping and produce a result that seems miraculous.

Red/Black Pattern

  1. What strategies could be used to achieve a red and black repeated pattern after the cards have been riffle shuffled?

Strategy:______Strategy:______

# of Riffle Shuffles / Results
1
2
3
4
5
6
7
# of Riffle Shuffles / Results
1
2
3
4
5
6
7
  1. Did any your strategies work consistently? Why do you think your strategy worked or didn’t work?
  1. How many riffle shuffles does it take to destroy the pattern?

Extension: Suited Pattern

  1. What strategies could be used to achieve a repeated suited pattern?
  1. Is the pattern related to the repeated black/red pattern?
  1. How many riffle shuffles does it take to destroy the pattern?

Extension: Number Pattern

  1. What strategies could be used to achieve a repeated suited pattern?
  1. Is the pattern related to the repeated black/red pattern? Is the pattern related to the suited pattern?
  1. How many riffle shuffles does it take to destroy the pattern?

Extension: this activity can lead into discussions about probability, odds, and generalizations.

Black Red Pattern Trick - Stack the cards in a red and black alternating pattern. Cut the deck in half so that the bottom cards of each half are different. Riffle shuffle the two halves together. Take the cards from the top in pairs. Each pair should contain one red and one black card. Pg. 126

Suited Pattern Trick - Arrange the deck in a sequence of suits, such as SHCD, SHCD, SHCD, and so on. Deal from the top to form a pile of about 26 cards. This dealing automatically reverses the order of the cards. Now riffle shuffle the two halves together. Take the cards from the top if quadruplets. Each set should contain one card from each suit. Pg. 127

Number Pattern Trick- Arrange the deck in four sets of 13 cards each, with the cards of each set in the order of Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K (suit does not matter). Follow Deal from the top to form a pile of about 26 cards. This dealing automatically reverses the order of the cards. Now riffle shuffle the two halves together. Take the cards from the top in sets of 13. Each set should contain one card of each value. Pg. 27

Ultimate Card Trick - Arrange two decks of cards in the exact same order. Put one deck on top of the other. Deal off the top to form a pile of 52 cards. Deal out the cards and you will have two complete decks of cards. Pg. 27