What is randomness? Probability is based on the idea of randomness. Without 
randomness there is no probability but only certainty. Probability 
distributions are not always flat with equal chances for all results, but 
this does not make randomness any less of a factor.  Some people may think 
there is no such thing as randomness because everything is determined by 
initial conditions, but this is not true.

Not everything is determined by initial conditions. In quantum physics, this 
statement would be equivalent to the claim that there are hidden variables. 
And it has been proven that there are no hidden variables. Experiments have 
proven that Bell's inequality does not hold so local realism or absolute 
determinism is out. This means deterministic reductionism is dead. Either 
things are not merely the sum of their parts or not all events are determined 
by initial conditions. On a local level this amounts to the same thing. 
Events are not determined by localized initial conditions. The point is that 
quantum physics wins the day and the indeterminacy which it describes is 
unchallenged. 
The important consequence of chaotic dynamics, proven by Ilya Prigogine, is 
that the causal determination of events requires knowing the initial 
conditions to an infinite degree of precision. Since this is impossible, 
randomness makes sense. In addition, this means that Schrodinger was wrong 
and that quantum indeterminacy has macroscopic consequences. Quantum 
indeterminacy means that initial conditions to an infinite degree of 
precision are not only not known but they simply do not exist. Nonlinear 
systems amplify these causally deficient wave collapse events to macroscopic 
consequences. 

Quantum mechanics is deterministic for the most part. Some people like to 
emphasize that the time evolution of wave functions is all deterministic. 
They want to overlook the one part of quantum physics which is not 
deterministic. This is the wave collapse. This happens when you make a 
measurement of something which is represented in quantum physics by a wave 
and probability distribution. The probability distribution tells you the 
probability of the different possible results of your measurement but what 
measurement you actually get is completely undetermined. It was the result of 
such measurements and the wave collapse that mechanistic determinists like 
Einstein hoped could be explained by hidden variables. This is what Einstein 
meant when he argued that Quantum physics was incomplete. 

Schrodinger thought and argued that quantum indeterminacy had no effect on 
macroscopic consequences. But the fact of the matter is that every time you 
make a measurement as described above you are amplifying a quantum wave 
collapse to a macroscopic event which you can see. And that is before you 
take the advent of chaotic dynamics into account. Illya Priogogine proved 
that non linear far from equillibrium processes require the specification of 
the initial conditions to an infinite degree of precision, in order for their 
results to be determined. Quantum physics says that such an infinite 
precision doesn't even exist and if you force it you get a wave collapse. The 
result is that such naturally occuring complex systems which are far from 
equillibrium also amplify the quantum wave collapse to macroscopic events.