Quantum indermenency?

No, we believe the cause is fully defined. It is the effect we believe to be underdefined, i.e. probabilistic.

I think I understand to a degree-
But now I'm confused as to what probability really means....
Can 'chance' even make sense?

For example: I role die, we say there is a 1/6 chance of 3, but in reality my role of a 3 is determined by where, how and on what I roll the die.
Again; I use a randon number generator on the calculater: I find 0.773. But this was also determined, by the computer programme in the calculater --- it may be so complex and sporadic that the numbers it picks SEEM random, but they're not really random at all.

Do you see what I mean?

Yep. First off, I said 'we' earlier, suggesting I "believe" in the probabilistic interpretation of QM. Actually I don't, but I accept that, at present, it's the best we've got.

Sure, the role of a die is completely determined... quantum effects aren't going to make any macroscopic difference. Likewise for RNGs.

The difference with QM is that things can actually be in one state or another. For instance, an electron may be an extended wave, however if I examine part of that extended region, I will either find that the electron is absent altogether or entirely within that part.

All other states (position can be a state) are the same and behave the same way. An electron may have a range of wave 'components' (not 'parts') each with a different momentum, however if I measure the momentum I find the entire electron to have the same momentum.

These are two of the postulates of QM:

1. Any system may be described as being in a linear combination of basis states.
2. If I measure with respect to that basis (for instance the basis of position states), I measure the system to be in a single state.

What happens in between is open to interpretation, but the idea that the particle wave represents the probability of the particle's position (and the magnitude of other states in the wavefunction represent the probability of being in that state) has been extenstively tested and found 100% accurate.

There are other interpretations, though, such as many-worlds interpretation.

Well I'm still unconvinced that it makes sense for anything - even microsize - to behaviour in a particular way for no particular cause. I can't see that 'chance' exists at all.

Be sure, the cause is most particular. The effect is uncertain. The causal link is unknown. We know that initial state X is the cause of one of these final states {Y}. Cause is fine. What we can't predict except statistically is, given initial state X, which possible final state Y will be measured. Further, we don't know how the particle gets from its initial to final state other than that the final state was already in the initial state.

But as for it being unconvincing, you're in great company. Einstein rejected it, and Schrodinger, who formulated the wave mechanics in the first place, cited this very thing as a reason why QM must be incomplete.

Hmm; ok.
As always I'm not going to make any firm conclusions here though lol

I think that quantum indeterminacy is a term used to describe the epistemic limitations of quantum mechanics. It is explained by the measurement problem in the uncertainty principle, which says that you can't know, at an equal rate, the position of an object and its momentum.