I think the problem here is that the ground rules regarding "random" may not have been clearly stated.
Damianoakley, it may be useful to re-state them, so that recent readers dont have to re-read all 11 pages of this thread !!
My understanding is that random is dependant on time-frame.
Yes, each coin-flip is random. The result is NOT affected by the previous flips.
However, over a large enough trial, they WILL tend towards 50/50.
Dice throws ARE random. You CANNOT guess which number, from 1-6 will fall.
But, over a large enough set of trials, the numbers WILL tend towards 1/6.
Radio-active decay IS random. But it can be quantified mathematically. ( go figure )
This is the great paradox of randomness. There IS order from chaos.
We have the ability to mathematically quantify something that is, wait for it, random.
We CAN quantify randomness mathematically.
SO, damian, please restate your definitions, and continue.