A truly random process does exist, such as radioactive decay - which can be averaged and follows a pattern but no scientist can pinpoint the exact time of the decaying

My question is, at what point do we decide a process is random?

I can roll a die and if I had enough data and put it all into a simulation sophisticated enough I could predict the way the die will land at the time I toss it into the air, the die is perfectly predictable but not for a human alone. Thus, I can randomly allocate things to a die roll, but is my die roll random? There is a totally predictable method to my die roll.

Studying psychology gave me a definition of random allocation as being 'everything having an equal chance of being selected' which my die roll would have as each side has a 1/6 chance. Or at least it should, but if I weigh a die to make the 1 face heavier to get more 6s (opposite die faces add up to 7) then my chances aren't equal any more, but surely they're no more or less random than before, just with different odds?

Thus, were radioactive decay to be found to have some way of predicting it, would that also have to be considered no longer random or can I still consider a process random if I can't work out the outcome prior to the event (at that time) even if I could with enough data?

Random:

made, done, or happening without method or conscious decision.

Edit: It is usual for no one to chip into these discussions or have I not typed something right?
Edit2: @Syber (I do suspect replying would infract me because of the bump), thanks, but I actually am subbed to those channels and saw the videos on release, so I guess I had my answer long before you posted. Either way, that does indeed answer everything so I guess that's the end of the debate.

xD No, you didn't mess it up, nice post. I also found this article on how probability is not something you should assign to an object quite interesting and related.

The probability of something can change, and the article had a few good examples with how finding out something changes your probabilities in the same scenario of the same question. Hence the randomness of something is only something we can assign to the object based on what we know.

The chance of rain tomorrow would be 'random' 1000 years ago without all the equipment we now have, because the probability is only based on what we know, not the object/event we talk about. :P

What's it?
You haven't provided a link to the thing you're talking about.