It might be a really stupid question and I think I am trivializing it. I am not able the understand the big issue with collapse of wave function. So we have set of probabilities and when you measure you find say an electron somewhere. Wave function collapses everywhere else. How is this different from a throw a pair of dice? You have bunch of probabilities for the sum before the throw. When you throw and measure it you have some sum.
The big issue with wavefunction collapse isn't with the reasoning that when we make a measurement we are essentially sampling the probability distribution given by the wavefunction before measurement. The issue is how or even if this collapse occurs. Additionally, before measurement the system is not in a definite state, but at measurement we find it in a definite state, and then the state is not definite after measurement as the state vector evolves via the Schrodinger equation (unless we measure the system to be in a stationary state).
In other words, the act of measurement changed the system in a way we cannot currently account for. This is what leads to the multitude of QM interpretations.
One difference I can think of with the throwing of dice is that the probability of an outcome is just due to our limited knowledge of the system. If we knew exactly how the dice are thrown, how they will bounce off the table, etc. we could exactly predict the result, and we would not need probability. However, with QM measurements we can know everything about the state vector, but the outcome of the measurements cannot be known. (I'm not an expert in QM, so there might be more recent developments/alternative interpretations that could be discussed here).