Reality is either governed by rules, or it isn’t.
If all events transpire according to some rule or law, this is nomologicalism.
If there is no reason behind why events unfold as they do, this is accidentalism.
There are two variants of nomologicalism: deterministic and probabilistic. The laws that govern the unfolding of events are either deterministic or probabilistic in nature.
Note, however, that deterministic nomologicalism could be seen as just a special case of probabilistic nomologicalism - the case where all conceivable outcomes of any particular event are assigned a probability of either 0% or 100%. This is analogous to a Turing Machine just being a special kind of Probabilistic Automaton, one with transition probabilities of 0% or 100%.
But if nomologicalism is true then the question is: why is it true? Why do these governing laws exist and how are they enforced?
If there is no reason that we have the laws that we do, or there is no reason that they continue to hold, then this itself amounts to a kind of accidentalism. If there is no reason that the laws are as they are, then they could have been and may yet be otherwise. And if there is no reason that they continue to hold, then they may very well cease to hold at any instant.
In this case, the current state of things is accidental...there’s no reason it couldn’t have been otherwise, there’s no reason it won’t become otherwise.
But, if there is a reason that nomologicalism is true, and thus a reason for why our particular governing laws exist and a reason for why they are consistently enforced, then what is the reason for that reason?
If there is no reason for the reason, then this again amounts to a kind of accidentalism.
The only way to avoid accidentalism is to posit an infinite hierarchy of reasons for reasons for reasons for reasons...and so on. An infinity of reasons.