Skill checks. We know them, right. You roll a check to see if a character succeeds at something. So there are at least two options. They succeed or they do not.
1. Success and fail are very different
While the one option is usually well defined, the other isn’t. We can roll if they succeed to climb a mountain. If they, do, great, mountain is climbed. What happens when they don’t? Do they find they lack the stamina, half way up? Is the weather bad? Have authorities blocked the path, because the weather is supposed be bad? Did the local guide have a heart-attack? In short, while the success is usually done, the fail requires explication.
That’s where approaches like Fail Forward or Rule of Kirk come from. Fail Forward is the idea that the game should not stop from a bad roll. So the chraracters still get some success, but maybe use up some resources or alert the guards while doing so or whatever.
Rule of Kirk is less known nowadays. It was more prominent early this millenium. It works like that: Sometimes, when Kirk and Spock are ambushed, they overcome the attackers easily. Whereas other times they just get captured without offering resistance. Why? Because James T. doesn’t even try, when he won’t succeed.
Both these strategies and probably more exist, because Fail on its own is underdefined.
No we could make it explicit before we roll, which leads us to…
2. Skill checks and random tables are the same thing
What’s a random table? A list of events and you pick one by rolling dice. Which is neatly fits what we do with skill checks. Or maybe skill checks are a way to use a random table, because we tend to factor some character stat in, when we check a skill. Now, our skill check tables are clearly ordered, from bad to good result. But what if that isn’t the case?
I got this idea from a friend’s game, now only available wayback, specifically from the herbalist’s table. So if you want to find some herbs, you roll that table and find whatever it says. If you have the Herbalism skill, you can turn the result up and down with your skill ranks, adjusting what you find. We can in the same way factor stats into any other random table, provided the scales are comparable.
Now, those options are not always well defined. We have already seen this with fail above. Someone has to do that explication. They get some general guidelines and are then to make something up. There are degrees to that. When the random treasure table denotes a sword +1, we might still want to know what that thing looks like. And when a young hero “takes something from them” on a Direct Engage in Masks, they must tell what that something is.
In fact PbtA moves are a place to see this correlation of skill checks and random tables rather clearly. This has consequences though.
3. Typical studies of probability in RPGs fall short
You know, those nice bar diagrams you can get from anydice.

And then people discuss the advantages and disadvantages of bell curves vs. flat distribution. But that is not what we ultimately use while playing the game. It’s about the entries of that random table. That is the resulting fictional events and/or changes in the game’s mechanical currencies.
It doesn’t help much to know that you can hit a “normal” difficulty sixty percent of the time, when there is no notion on what normal is. Discussions on expected damage output per turn among optimizing D&D players are in fact more sensible.