Given a sequence of N bits, what metric would give you something akin to "how unlikely it is that the sequence resulted from random (p=.5) generation"?
I know there are measures of the 'complexity' of sequences (Kolmogorov complexity, for one). I don't really know how they work, but I know they exist. But they don't really seem like they answer the specific question.
My curiosity was piqued by this sequence: (The history of the MLB All-Star game)