I have seen this short, wonderful video about the frequency stability property (also there is another video from this guy under his Kickstarter project ArtOfTheProblem; they are both great, and I highly recommend them).
It basically said that when you have two sequences of 0s and 1s you can determine which of those two sequences was truly generated randomly (using a coin flip procedure) and which one was generated by a human trying to act randomly. The trick to discern the two sequences from one another starts with counting non-overlapping segments of length 3. For any sequence you pick, the proportion of times it occurs should be the same as all the other sequences.
Consider following example
1010001101
Three questions:
1st: Which 3 numbers should we observe? Or in another words, should the window of size 3 overlap? Is this the correct histogram?
2 x 101
1 x 010
1 x 100
1 x 000
1 x 001
1 x 011
1 x 110
Or if the window should not overlap then what to do with last 1:
1x 101
1x 000
1x 110
1??
2nd: Why should be observer 3 subsequent numbers? Does it have something to do that the string consist of two numbers (0 and 1)? What would happen if we observe 4,5,6 ... subsequent numbers?
3rd: Do you know some other channel on youtube like this one?
EDIT: I've done experiments using (non)overlapping window, results are here