The Kruskal Count

Great magicians such as Houdini and David Copperfield are known worldwide and revered for their interesting magic tricks. However, few people take the time to understand the mathematics behind their stunts. Martin Kruskal was a successful mathematician and physicist who lived from 1925 to 2006. Though he mainly worked at Princeton University, and is very well known for his research there, one of his greatest legacies lies in his discovery of an algorithm he called the Kruskal Count. The Count would be used by magicians for decades after its discovery, mainly for a simple card trick made possible by Martin Kruskal.

Magic tricks interest me because there is always a chance that the trick will not work, or that there will be no problems and the trick will amaze

This value will represent the average card number later when we solve for the probability. Second Problem: Finding the Percent Success

In finding the percent success we must first consider our ultimate question: to determine the percent success of the Kruskal Count in a normal deck of cards, given that aces are worth one space, and face cards are worth five. To being this process we must derive a formula that we can use to understand the logic behind the count.

First we must establish that P(success) is the total we are looking for, or the percent success. Next we will use our knowledge of probability to understand that we will say (1-P(failure)) when speaking of the final equation, because by subtracting the percent failure from one, you are solving for the percent success. This is true because percent success plus percent failure must be equal to one.

To begin there must be new variables established: D is a deck of cards, c is coupling time (the part of the deck where the magician and the audience member inevitably land on the same card), and x is the average card number