But at this point I think we're wasting time wringing our hands around the category of things that count as "accidents" into a reductionist vortex. You can really do this with anything if you try. The point is, that most of what you think of as your self-directed subjective experience, is a product of things completely beyond your control.
Whether we live in a deterministic or stochastic universe is really completely orthogonal to that point.