OK Bilbo, you landed me in this thread to answer this question (free will being an aside), and I think the thread itself, rather than my arguments against the existence of randomness, speak to it. Of those whose whose comments were relevant to the matter. In any case the software has been reminding me not to hog the conversation.
George Brooks, Unitarian, seemed to hedge his bets on the existence of ontological randomness (OR), but I think he believes God has directed evolution, rather than a hands-off process. That seems to me to say that he doesn’t believe randomness is compatible with divine sovereignty, but if not he didn’t pursue an explanation.
T_Aquaticus, atheist, though not really clear on the philosophical difference between OR and epistemological randomness, was clearly using the existence of randomness as evidence against the need for God. Clearly, for him, randomness is the antithesis of divine sovereignty.
Jonathan Burke, Christadelphian, pulled the “Calvinist” card to discredit any arguments I might subsequently make. But since it seems to be divine sovereignty he objects to by this, he too would not seem to support its compatibility with OR.
Beaglelady, Episcopalian (I believe) picked up on T_Aquaticus’s theodicy track to say that given the bad state of the world, God is not sovereign (and presumably OR is to blame for unpleasant realities instead).
Merv Bitkofer (Mennonite) supported my view on OR, ie that it does not exist from God’s viewpoint.
GJDS (Orthodox) pointed out that OR is, in effect, a God-shaped gap in the atheist’s worldview.
Now note that, on the world’s leading theistic evolution site, no Christians have come forward to argue a case for the compatibility of ontological randomness with divine sovereignty: all commenters who presented arguments at all in effect made randomness and divine will mutually exclusive alternatives. And that, I think, tends to answer your question, if perhaps casting a little doubt on whether “most Christians believe in God’s sovereignty over all Creation.”
That is consistent with my findings over the last 8 years - although people may talk about God using (ontological) randomness to fulfil his purposes, they have never, ever, given coherent arguments as to how that could be so, or even for how and why such randomness can exist in a created universe. Either randomness is quietly shifted to the epistemological type (eg Brownian motion in cell function, the function of the immune system, etc or here, roulette wheels, until the common reversion to quantum events, which certainly don’t affect roulette and, according to current science, cannot be held to govern most chance events in nature at the macro scale). Or else God’s sovereignty is denied in favour of “spontaneity” or “freedom” or some other buzz-word that has little to do with the irrational happenstance that is actually represented by ontological randomness, as Merv cogently points out.
I have work to do elsewhere now, so will leave this thread to any Christians up for the challenge of saying that God can make a square circle, ie bring about his creative will using events that he has put beyond his own wisdom, power, knowledge - and will.