How can I determine the statistical randomness of a binary string?

Question

How can I determine the statistical randomness of a binary string?

Ergo, how can I code my own test, and return a single value that corresponds to the statistical ra

Answer 1

You seem to be asking for a way to find the Kolmogorov complexity of a binary string. Sadly, this is incomputable. The size of your string after running it through a compression algorithm will give you an idea of how random it is, in that more random strings are less compressible.