Given a binary sequence, how can I calculate the quality of the randomness?
Following the discovery that Humans cannot consciously generate random numbers sequences, I came across an interesting reference:
- "A professor of probability would have half of his class write down a list of zeros and ones from a bunch of coin tosses and the other half write down a list of zeros and ones that they would try to make look random. The professor could sort out the papers with only a glance at each paper."
What method would be suitable to replicate the professor's act, i.e. judging which sequence is likely to be generated by a random process?
A method I have in mind is: for a given sequence-length $ n $, establish the frequencies of each possible sub-sequence in the population of all possible sequences and than compare these with a particular sequence.
As this very quickly becomes impractical (the number of sub-sequences grows exponentially with $ n $) the method may, instead, only measure a subset of all sub-sequences, e.g. all sequences of same digit.
How good would such a method work? What are some better methods?