I disagree that dualism necessitates the creation of a third category. Simply proposing that "mind" is a seperate "substance" does not entail that it's operations cannot be classified as some mixture of chance and determinism.
However there is a legitimate third category that we have not considered - "fated". I do not beleive that it applies to anything but it is not in itself incoherent.
I would say that the classificiations of the operation of a system go like this:
1) Determinism: The system will always give a particular output when starting from a particular internal state and presented with a particular set of inputs. The inputs may or may not have relevance.
2) Chance : There are a range of possible outputs for each initial state and set of inputs. (In actual cases this range and the probability distributions of the results will virtually always be restricted by the deterministic operations of the system so this is better considered as a combination of determinism and chance)
3) Fate : There is one possible output regardless of the state of the system and the inputs.
Since determinism is the only option which allows the internal state to dominate the output I suggest that determinism is the only option compatible with anything worth of the name "will".