What I believe (is obviously true) is that there is interaction between the mental world, where we have free will and the physical world, where the mental act leads us to influence the physical world. Once the physical world starts "moving", then laws of causation apply.
So if I decide to scratch my nose, I send signals to the muscles in my arm which raise my hand to my nose. If my hand then brushes a fly away, it's flight path is subject to the laws of cause and effect.
My free decision to scratch my nose was not pre-determined, it is not random, and it is the result of a free choice which is the origin of a string of cause and effect.
Hard determinists must find it impossible to discipline their children. If they have no free will then how can they blame them for bad behaviour?
The truth is that no-one really believes in hard determinism, they can't. That I think is why Peter Strawson starts his essay with the admission that he does not really understand what determinism is.
Philosophers who defend determinism often resort to a fallacious argument along the lines of "everything must have a physical cause" and then use a regress argument to show that free will cannot be the original cause. They come across like Berkeley did arguing for idealism, using rules they make up themselves (B.'s ideas must resemble their cause) to justify their chain of reasoning and ending up with a result which is contrary to common sense and denies the very nature of humanity.