I work as a data scientist in Dundee, Scotland. Dundee is a HUGE gaming development community, with the University of Abertay having their own Gaming degrees and colleges. One aspect about gaming and with analysing player behaviour is you want high player retention. Using data, the gaming developers here find the breaking point of players (when they quit and never return) and figure out a way to "reward" the player with an achievement right before that happens. The goal is to hook the player early in the game, where they feel they get value out of the time committed. At any point during a game when the effort far out weighs the invested time, players quit. That's why when you play mobile games, the first levels 1 - x are easy, and then progressively get harder. But then at some point in the harder levels, you have to throw the player a bone or make the next level up attainable.

The way to do this is exactly what you are referring to, and that's the APPEARANCE of randomness. You can still have randomness, but very easily attach a probability to it. Increase the probability of x happening, as y is happening. For example, for every 10 fails at a level, the probability of x happening increases by z% (or some algorithm like that.