I've been using probability theory (, statistics, bayesian inference) for a while - and I find it very useful and mathematically elegant, but I still can't get where is the hidden "randomness" in a formal definition of random variable. I guess, there must be some "God with a Dice" that chooses which $\omega \in \Omega$ like "is going to realize". Or there's no such a thing and we always operate (and think of it as) just with numbers weighted by measure of corresponding (exists due to $\Omega$/$\mathcal B (\mathbb R)$ measurability of random variable) elements of $\Omega$ and no "dice inside"?
Or, in other words: how can something deterministic model something random? And if it can, where in formal definition that "randomness" is?