[koryk]

I am not a physicist, but the "no probabilities" problem could just be solved with a constant offset right? Or just say that whichever direction the marble rolls is the zero degree mark.

I don't see how "no cause" problem is fully true either. The system has potential energy due to the marble being places at the top of the dome, so that was the cause.

[romwell]

To see "no probabilities" easier: there's no probability distribution for when that ball starts rolling.