Either our decison-making process is a strictly deterministic process or some element of chance is at play.
I don't get the feeling that a nuanced approach to probability, randomness, likelihood, and chance is going to help here. So I'll try a different tact. Consider a deterministic universe in which we define "determinism" to be that which is determined by anything (not just a collection of laws of physics). Thus, for example, a system's state can be determined through self-organization or top-down causation. Put simply, a system can be determined by itself (such as through coherent emergent functional processes), such that e.g., brain functions (the "mind" being one set or kind of said function) can determine future brain states through mechanisms like "choice". Then, since we are limited to your simplistic conception of determinism and chance, we have both determinism and free will. Even more simply, we can consider nonlinear or circular causality, wherein the brain state at time
t is both caused by and determined by the brain state at time
t. This addresses the overly simplistic "for every effect, there must be a cause" argument.
This is not intellectually difficult to grasp
Indeed, it is extremely simplistic. That's the problem. As decades of research have shown, things like probability, logic, and so forth are highly counter-intuitive. They have to be taught or learned by possibly everyone and certainly almost everyone. So if you are combining an argument that concerns both probability and logic AND is meant to characterize the entire cosmos AND FURTHER is simple, then we have
a priori reason to doubt your description. This is born out by the incompatibility between your descriptions and of those whose expertise is relevant here.