Well yeah, by rationality and observation we can always predict a certain chance of something happening in some way. For example, the coin you flip seems random to you - and indeed, with enough coin-flips you'll usually see something close to an ideal statistical spread of heads and tails, which is usually assumed to be a sign of good randomness. But really, is the coin flip random? The moment your muscles have finished having an effect on the coin, it will follow a predetermined path, obeying the laws of physics. To the average person, those laws mean nothing and the flip is random. To the educated quantum physicist, there are no underlying principles and the quantum behavior is random. To the universe, I suspect it's just another law in effect.
How do you know that a coin flip isn't random? We do know it, because we can do elaborate tests that create a certain bias in the flip and by extrapolating that we can come to the conclusion that a coin flip is determined by a set amount of parameters that normally vary so much as to create a random effect.
But that only works with things like coin flips and die rolls. Other simulations can be done in some cases. But in many other cases, the idea that it is predetermined is just an assumption. Take for example the weather. You would expect that it's predetermined, but how can you tell? Nobody knows all parameters that influence the weather and nobody can prove conclusively that not one of those parameters is truly random.
Let's put things in a slightly larger scope. If we look at the movement of planets, we cans afely say that they are completely determined. One could draw the conclusion that this is because the physics behind it is fully determined. But there are zillions upon sillions of interactions working upon such a planet all the time, stemming from gravity, particles that hit it, space dust, radiation pressure et cetera. All of thses things can slightly influence the planet. Now there are 2 possibilities: these are fully determined, in which case they would have a calculatable effect upon the planet when measured over a very long period of time. But it is also possible that they are fully random, in which case the shear amount of interactions would cause a certain average, which in turn would look like a determined effect to us. You can't tell the difference.
Unless you start looking at single interactions on the smallest scale possible. As far as we currently know, the smallest scale is that of quantummechanics. At this scale interactions are seperated enough to be quantified individualy. And if we do that, we see (or actualy measure) a random distribution. Now there are several explenations possible: Either there is even a smaller level of interaction, or we have arived at the smalest possible scale, and things on that scale are truley random. I won't deny that the first option is possible. But since our current understanding calls for moddels build upon the second assumption, the first one is, in my oppinion, little more then a believe. To reiterate what I have already said, there is no reason to assume that god doesn't role dice, other then our own idea that things should be perfectly determined.
I don't want to say that it is completely impossible, but quantum mechanics is pretty much self-contained, and any currently vaiable theories for explaining the schism between quantum mechanics and general relativity do not do away with the basic concept of random distributions of wave functions. To me this means that any claim that the universe is fundamentaly determined calls for a bit more then just gut feeling and coin analogies