Analysis and Manipulation of the Kruskal Card Trick

Abstract

In the Kruskal card trick, an audience member has a full suit of cards, ordered ace to King, and the magician has the rest of the deck. The audience member then picks out a card from the magician’s deck of his or her choosing, without showing the magician. The audience member has the single suit of cards facing them, ace on top and then silently spells out the name of the chosen card moving a card to the back of the deck with each letter in the name. For instance, if the audience member had chosen a Jack, the audience member would spell out J-A-C-K moving the ace, two, three, and four to the back of the deck. The top card will then be a five. The audience member repeats again this time spelling out F-I-V-E. The audience will repeat the process a third and final time with the next top card and will end up at his or her final card. The magician then makes a guess as to what the final card is, revealing a King to be the final card. The trick will always end up at the King no matter what card the audience member initially spells out when the cards are arranged in order. We move on to three variations of this card trick: how accurate this trick is when the ordered suit is iterated through more than three times, how accurate this trick is when the thirteen cards are shuffled before they are iterated, and how accurate this trick is when both the cards are shuffled, and the number of iterations are changed. 1 Introduction