What does it mean to be probable, to have a chance? What is Chance? How do you explain probability on a classical scale (e.g. dice, coins, number generators) and on a a quantum scale?

Is chance an illusion? 

One way to describe it is as the amount of variability of unknown factors in a system. I do not know if a coin will land heads or tails, but I do know there is a head and a tail to the coin, and so there is a probability of the coin landing either heads or tails. It is observed that upon analyzing past data that aprox. half of coin tosses result in heads and aprox. half result in tails. Probability can be viewed as a prediction of future outcomes based on past results, but this does not satisfy me on a quantum scale. The coin toss can be analyzed through physics and is ultimately drawn down to a deterministic quantum system. If it is ultimately deterministic, I am puzzled why the results are so evenly distributed. Why is the system one such that out of the uncountable factors involved, the possible products occur with the same frequency? Or, isn't it correct to say that, in a deterministic universe, there is, by definition, never more than one possible outcome, and the proposition of possibility indicates ignorance? 

What are your thoughts or opinions on any of this?