Clarification of Advantage vs Probability/Success of an Adversary
There is nothing special about advantage versus probability of success, and they should be used where it makes sense and improves readability. When considering distinguishing games (like for encryption, PRG, and the like) advantage has the benefit of simplifying notation. Also, it &quot;behaves nicely&quot; in the sense of being able to add advantages and the like (although this should always be checked formally via the distinguishing probability equations). Note that in distinguishing tasks, it is always possible to succeed with probability 1/2. So, it is only interesting to know how much the adversary can succeed beyond 1/2, and this is the advantage. This makes things nice since we can just talk about a negligible or non-negligible advantage.
When considering computational and not distinguishing tasks, advantage no longer makes sense. Here, if the adversary can succeed with non-negligible probability then it's broken. As such, the success probability is all you need to talk about.