Kolmogorov complexity

Consider flipping a coin 50 times to obtain the binary string000101000001010100010000010101000100000001010000010.Can we call this random? The string has rather an abundance of 0s,and on closer inspection every other bit is 0. We wouldn’t expect evena biased coin to come up with such a pattern. Still, this stringhas probability $2^{-50}$, just like any other binary string of the same length,so how can we call it any less random?

Kolmogorov Complexity provides an answer to these questions in the formof a measure of information content in individual objects. Objects with lowinformation content may be considered non-random.The topic was founded in the 1960s independently by three people:Ray Solomonoff, Andrei Kolmogorov, and Gregory Chaitin.

See Kolmogorov complexity function and invariance theorem for more details.