A Good and SIMPLE Measure of Randomness

Question

What is the best algorithm to take a long sequence of integers (say 100,000 of them) and return a measurement of how random the sequence is?

The function should retu

Answer 1

What you seek doesn't exist, at least not how you're describing it now.

The basic issue is this:
If it's random then it will pass tests for randomness; but the converse doesn't hold -- there's no test that can verify randomness.

For example, one could have very strong correlations between elements far apart and one would generally have to test explicitly for this. Or one could have a flat distribution but generated in a very non-random way. Etc, etc.

In the end, you need to decide on what aspects of randomness are important to you, and test for these (as James Anderson describes in his answer). I'm sure if you think of any that aren't obvious how to test for, people here will help.

Btw, I usually approach this problem from the other side: I'm given some set of data that looks for all I can see to be completely random, but I need to determine whether there's a pattern somewhere. Very non-obvious, in general.