Nice paradox. Your caused to believe free will is an illusion but use the illusion to seemingly cause things yourself. I doubt someone who believed in hard determinism would just live life by letting the chips fall wherever without attempting an active decisions. Why make a decision if I'm not the cause of the decision?
Well, let's be clear. A strict determinist doesn't
exist, because strict determinism necessarily denies the existential predicate of language => to say "free will" is an illusion is to say "I am" is an illusion.
The paradox is rather simply resolved by eliminating the habit in thought of equating "random" with "uncaused." My behavior in a given situation is the product of an infinitely or likely almost infinitely complex web of causal predicates, the most immediate of which are the activities of my neurology occurring completely outside the perception of conscious thought - the subconscious. This makes them unpredictable and uncertain
before they have occurred. That does not make my behavior uncaused. In a given "choice" the entirety of the causal universe of which I am a part was such that the behaviors I manifest were always going to be what they were determined to be - and how I would view and determine them would, in turn, be a product of an infinite web of causes.
As an information system trying to make predictions from incomplete information, thought cannot account for enough of that web of causes to eliminate this appearance of "randomness." Once the mistake is made of severing "randomness" from
uncertainty and projecting randomness as an attribute of reality rather than an attribute of information about reality, it necessarily follows that uncaused phantoms arise - i.e. the will, intelligent design, an implicate order to the Universe.
An information system that has a place in reality for free will as a thing in itself is fundamentally theistic.