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Fun (and Fraud Detection) with Benford’s Law Benford’s law is one of those things your high school math teacher would break out on a slow, rainy day when the students’ attention span was even lower than usual. He’d start out by asking the class to look at the leading digits in a list of numbers and then predict how many times each leading digit would appear first in the list. The students would make some guesses and eventually come to the consensus that the probability would be pretty close — about 11% each. Then, the teacher would just sit back, smile, and gently shake his head at his simple-minded pupils. He would then go on to explain Benford’s law, which would blow everyone’s mind — at least through lunchtime. Per Wikipedia : Benford’s law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way. Specifically, in this way: Leading Digit Probability 1

© Copyright 2003, Jim Loy Here are four interesting and famous dice. They are known as non-transitive dice, or Efron's dice. Here is the game we play with them. You can choose any die (singular of dice) that you want, and then I will choose my die; we roll our dice and the higher number wins. Which die would you choose? It turns out that it doesn't matter which one you choose, I will win 2/3 of the time, you will only win 1/3 of the time (in other words, I have a 2:1 advantage). Does that make sense to you? Whichever die you choose, I will choose the one immediately to its left. If you choose the left one, I will choose the right one. The logical way to see if one die beats another is to list the 36 possible outcomes, like this: 4 4 4 4 0 0 3 * * * * 3 * * * * 3