Suppose you have a set of digits, for the sake of simplicity we'll make them binary, how would you determine the probability that the set is random? For example, given the following 3 strings of numbers... 1111111111111111111111111111111111111111111111111111111111111111 0010010000111111011010101000100010000101101000110000100011010011 1101011111001000000000011101111011111010010101011111101010110110 The first appears non random while the second and third appear random. In reality, only the third actually is random. Given a truly random string of 1s and 0s all 3 are equally likely. So If I didn't know the origin of the numbers how would I compute a probability that they were generated randomly? For the sake of simplicity assume that if they are random then the probability of 1 is the same as the probability of 0 and that each digit selected without consideration of any other digit.