> Can randomness be quantified?

You can measure some things that will help qualify it.
The statistical distribution of the generated numbers of a
long sequence and the distribution of the numbers in pairs
and triplets of even longer sequences.

There is an incredibly good reference titled
"Statistical Distributions" by NAJ Hastings and J.B.Peacock
John Wiley 1974
ISBN 0-470-35889-0 or ISBN 0-470-26446-2
The LC number is QA273.6.H37

This rare book is essential for anyone doing MonteCarlo
simulations or using Random Number sequences. It
is a collection of simple algorithms for generating
random numbers with specific distributions given a simple
random number generator with good first and second
order distribution .

Walter Banks