I think that the dice in this scenario would have to be considered a purely reactionary mechanism. They aren't comparing options - there's no decision being made by the dice. They're just reacting to externalities. Same thing as a river flowing around obstacles. The river isn't selecting its path, it's only reacting to externalities. I think I'd end up leaning a little more toward saying that dice have no mechanism for comparing possible outcomes and deciding on a course of action.
The way I see it is.........we are, ultimately, in the final analysis, 'just' much, much more sophisticated reactionary mechanisms. If we agree that it's all 'happening automatically' then I think it's hard to avoid saying what I just said, when you dig down into it. We may never fully understand the processes in detail, but it seems to be very, very difficult to explain, even in principle, how it could be otherwise (than that we are very sophisticated reactionary mechanisms). That some of the responses are 'machine learned', or stochastic, or due to random effects, wouldn't change this, nor would the fact that the system runs forward/backward (in 'time') simulations, since those would appear to run automatically too.
For example, yesterday, 'I' ('me') did not with any personal control 'call up' the options about whether to work or not to work, or 'call up' the 'simulations' for different scenarios. They all just happened in my system automatically and I reacted, and no matter how sophisticated it felt, or the complexity of the various external and internal factors affecting my system, it's hard to even suggest that I reacted any other way than automatically at any given moment, no matter what I did.
I get what you say about determinism, indeterminism and predictability and without taking anything at all away from what you said about them, I think they are slightly separate issues to the above. In a nutshell, randomness (if it plays a part) wouldn't essentially change what I said above. Everything would still be happening automatically and we would be part of the amazing unfolding of the universe while having the mental sensation of both 'watching ourselves' and the sensation that our 'self' can voluntarily initiate control.
To paraphrase Einstein (I think it was him), if, hypothetically, the weather (or equally the universe) were for any set of reasons or permutations to become self-conscious, it might readily think that it was steering itself around. But that would be a wonderful illusion. Possibly one that the weather or the universe in that scenario would be (or us in our actual scenario are) almost compelled to experience, even if at certain intellectual moments we find ourselves catching a mind-blowing and humbling glimpse of what is (probably) really happening. In some ways (only some) it seems akin to intellectually realising certain other things, such as that we are almost certainly apes descended from apes or that there's probably no god, two things which although relatively easy to accept today for many people, have been (were) for many people more profoundly difficult to accept when first put forward. One could make a case that not having the capacities and abilities that we think we have is the biggest bogeyman of all, the hardest to accept and possibly the one with the most worrying day-to-day implications. Though to be fair, that has been said about the other two as well.