The algorithmic (Kolmogorov) complexity definition of randomness states that a random string is incompressible, yet 11111111 would not be considered random because you can compress it easily.
On the other hand, we know that each sequence has the same probability when we take the frequentist definition, so the above sequence would be as random as, let's say, 01101010.
My question: Isn't this a contradiction? How to square both approaches with each other?