To preface, I have no logical or syllogistic arguments against determinism. Many arguments are sophistic or simply ahistorical and undialectical.
Also, I take it that you're assuming "free-will = indeterminism" and "no free-will = determinism"? I'll roll with this for now.
Hard (Laplacian) determinism presupposes that you can fully predict the future once you know all the initial conditions. This means all events must necessarily have one-to-one connections between their cause and effect, granted we know the initial conditions and the functions to evolve it. Thus, "knowing what's likely" is, in my opinion, not convincing enough to believe in metaphysical determinism.
Notice the connection between knowledge and reality here:
The universe could be deterministic for all we know, but we cannot know all the initial conditions to evolve it deterministically for ourselves. Here, if we subscribe to some kind of technical limits to our knowledge acquisition, then we have "seemingly" random or stochastic processes, but governed by completely deterministic processes. Our physical theories have mathematical equations we can solve to connect cause and effects. Sounds too good and simple to be real? From the text I linked above:
Nature, however, is much more clever than this. Towards the end of the 1800's, mathematicians and scientists began encountering some very difficult equations to solve — some in fact were completely unsolvable. A particularly troublesome set of mathematical equations were non-linear differential equations. Much in the same vein, there existed the horribly difficult and outstanding problem of three mutually gravitationally attracted bodies — the so called "three-body problem" (or its generalization to "n-bodies").
At first, problems such as these were cast-off as special cases and largely ignored. It would turn out that these so-called "special cases" would bring the birth of a new way of thinking. When these equations were finally studied in detail a fundamental change, which would ultimately overthrow the ideas of determinism, began to occur in mathematics and science. Inklings of the science that would be come to be known as "chaos" began to appear.
So are our theories just incomplete? That there is a deterministic fabric but we are not clever enough to figure it out? If we can't figure that out then for all we know we do recognize a psychological free-will. One might retort that this free-will is an "illusion" (i.e. not real; doesn't exist in a metaphysical sense). I don't like this because I take phenomenology/experience to be first class, not mathematical equations, the latter is chauvinistic and reductive. The content of people's thoughts and decisions are meaningful to them. One's action could be interpreted by outsiders as both determined and completely unpredictable, depending on who you ask. If you psychoanalyze someone to "get down to the bottom" of their desires to explain how they are currently, then it functions as therapy, not necessarily something logically right or wrong.
If you say to your coworkers and fellow working class people that their lives are ultimately governed by mathematics and physics, then you either depress a potential comrade from future actions or set the ball rolling for their revolutionary escape (through negating what you've just said).
Either way, free-will in the sense of phenomenology versus free-will in the sense of indeterminism are really separate concepts in my eyes.
But then, by accepting the former free-will and being on the fence about the latter free-will, am I conceding that nature-in-itself is truly deterministic and that we're too dumb to figure it out?
To have a nature-in-itself being deterministic while everyone believes they have free-will, you might subscribe to the existence of a Kantian unknowable thing-in-itself. This, I presume, refers to the ultimate in what you mean by "ultimately no freedom". In other words, if this nature-in-itself is actually governed by deterministic principles, then we ultimately have no free-will.
But why do we have this assumption of determinism (and scientific reductionism; if we believe from the Big Bang, everything was determined)? Just because our 19th century mathematics and mechanistic physics worked out well then? Why is this determinism a fallback epistemological assumption? Are we just influenced by the way mathematical and physical sciences are taught in schools? That we can know these bits of proofs and derivations once we grasp these abstractions of nature taught by our teachers?
On the other hand, the universe might be infinitely complex and constantly changing. Let's take this assumption à la Engels: The ebbs and flows of our scientific development is a dialectical grapple with this dialectical nature. The dialetheistic structure of {abstraction}, {negation}, {concrete; production of new knowledge} is not a static method, but manifests itself in how we might choose to best move forward and develop new ways to understand the world.
This means not projecting our assumptions and dogma. Events that have no one-to-one connections between their cause and effect, but rather one-to-many, or many-to-many, are still caused, but they are indeterministic. Quantum physics can be interpreted to be completely indeterministic, but still caused. This is acceptable if one accepts the infinite nature of the universe that allows itself to be captured and abstracted by humans (inb4 occam's razor). We are to understand it at some certain levels and parts, but not the whole all at once. If we understand this, the "necessity" of one-to-one cause and effect seems like a dogmatic belief that only function to hinder further development. It can be a limiting case of certain physical theories (classical physics), but that is where it ends.