"I never said "reality is probabilistic". Seemingly you must consider that there are only 2 possible options for the nature of reality: probabilistic or 100% deterministic."
At its foundation, nature is one or the other, or your belief is logically inconsistent. The problem is one of cosmology; the initial condition either had 100% potential for every observed physical outcome, or a probabilistic structure of which the slightest interference predicts 'no determinism.' Classical probability (binary outcomes) only answers the question of existence/nonexistence, and existence implies the continuous function of binary probabilities from the initial condition.
"I might as well ask you : 'And your belief that reality is 100% deterministic is objectively based on' what experimental evidence?"
An expanding universe. Self limiting chaotic phenomena. Strong quantum correlations (and if Joy Christian is right, strong quantum correlations at every scale). Want more?
"Do you have anything to say about, or any ideas about, what it is that NUMBERS represent about the nature of physical reality, or are you a platonist?"
I think you don't understand what a Platonist is. The best two modern examples are Kurt Godel and Roger Penrose. A Platonist avers that mathematical structures live objectively in a world of their own, even if they have no relation to the physical world.
My personal view is closer to Max Tegmark's -- that coherent mathematical structures always describe some physical phenomenon, even if we do not recognize the utility; there are numerous examples, the most dramatic of which is Einstein's adoption of Riemannian geometry for general relativity.
In the science of physics, mathematics is the language that compactly symbolizes the phenomenon it corresponds to. We may get the description wrong, just as we do in natural language, in a statement whose syntax is correct while its meaning is wrong. For example, we can say "The moon shines black" is syntactically correct though the phenomenon is not witnessed in physical reality. That doesn't imply that the alphabet and the rules for making sense of its combinations are not objective. Same with our mathematical tools -- meaning precedes construction, if the construction describes something physical. Meaning is the product of a coherent mathematical theory.