Determinism and Randomness
An event is fully determined when every facet of the final state is determined by the initial state. The undetermined facets of the final state are random (a logical complement of determined).
There's a difference between apparent randomness and true or fundamental randomness. Apparent randomness arises when we simply have not found the elements of the initial state that determine the final state. True randomness arises when those undetermined facets of the final state are not determined by anything at all.
(Note: whether or not these distinctions are meaningful is questionable, but I'll get to that in my post on Meaning.)
Theists object that a random event would by uncaused, and that a thing that is not caused by anything else can only be caused by itself. This "self-causation" is absurd, they claim. This argument hinges on the principle that everything has a cause (The Principle of Sufficient Reason or PSR). Yet, this principle is invalid and unjustifiable vis-a-vis causality. There have been attempts to justify it, but the PSR is generally considered to be unpersuasive by modern philosophers.
The reason that it is defunct with respect to causality is that, if some truly random events occur, nothing breaks. Sacrifice the PSR and you won't notice.
The foundational problem with the PSR is that, for it to make sense, you have to stretch the terms 'exist' or 'cause' well beyond their limits. I write about this on my blog here.
A fine illustration of the futility of the PSR comes from Quantum Mechanics. If radioactive decays have a truly random element to them, life (and physics) goes on. As far as I can tell, the only things threatened by abandonment of the PSR are a bunch of untestable philosophical claims.
Conceiving of true randomness (if it exists) is quite a psychic shock. I remember that I rejected it at one time, though I rejected it for aesthetic reasons. However, the shock value of fundamental randomness now makes it a rather beautiful thing to my mind: a harmless idea upon which so few can look without fear.
Either Christians won't dare consider that the PSR might not hold in every case, or they have considered it and don't like the consequences.
If the PSR breaks down, if determinism and randomness are truly complementary, then there can be no justice as theists perceive it. Persons do not metaphysically deserve punishment or reward because their decisions were either fixed when God created the universe, or were mistakes beyond their control.
A breakdown of the PSR represents a threat to moral reality for theists.