And either way, most troll systems don’t have any more math than roll under, and you do most of it before/between sessions, on the character sheet.
In practice, however, I'm not sure that is always the case, hence why many people here complain about how their players forget all the different bonuses or which number they are using: e.g., ability attribute, attribute modifier, proficiency, spells, items, etc. There is a lot of math that happens at the table. While that may be an issue mostly with D&D, D&D and its kin are the 800 lb. gorilla in the room, and most (but not all) roll over systems are d20 D&D-based. There is a reason, for example, that Pathfinder 1 was referred to as "Mathfinder."
And it’s very awkward and trips up a lot of people. I’ve seen it many times over 20 years or so playing different games.
I disagree with the first sentence. I do not doubt that you have "seen it many times over 20 years or so playing different games." However, you may be exaggerating things about how "very awkward" that this is or how often it trips people up. Because most roll under games are not trying to say, "you want to roll as low as possible" or that "the lower the number, the better." Most roll under systems just amount to trying to roll under a given value, usually either the character's Attribute value or Skill Rating value. So the whole "the lower, the better" doesn't really apply.
In my experience, people get tripped up all the time with roll over systems as well. You know how many times I've seen people get tripped up about that over my 20 years or so of playing different games? How long do you have to listen to my stories or read through the threads here? Sure, people understand roll high but there is usually more math involved in roll over than just rolling a high number.
If you were to go back in time on this forum, I would be where you are. I would be complaining about roll under or talking about how much better roll over is. You will find many of the threads here on ENWorld where I have done so, and I will still complain about how horrible THAC0 is. But actually running many of these roll under games has been something of a harsh lesson for me about my own assumptions about what is or isn't intuitive.
Much to my own surprise even, I have found the learning curve for many new players much quicker with roll under systems, at least comparatively with roll over. In some cases, it's been watching long time players who consistently struggled with remembering what they had to roll over or add to their rolls have
a much easier time when they play roll under games like Black Hack, Dragonbane, or Mausritter. There is no, "hey did you remember to add this, this, this, and this to your roll?" It's usually just, "did you roll under your ability score?" or "did you roll under your skill score?"
You can tell me that roll high is more intuitive, and while that may be true, I can tell you that these roll under games have often been quicker and easier for many of my players who really only had prior experience with roll over games. So the question for me is not "which is more intuitive: roll high or roll low?" Instead, for me the question is, "why are my players having an easier time with roll under than roll over?" I would like to believe that there is an explanation for the phenomenon with an answer that amounts to more than repeating variations of the mantra that "higher is better" or assuming that my intuitions about roll high is what's at stake here.
That is an issue with D&D, not with roll high systems universally.
Just like there are particular issues with some roll under games and not roll under systems universally.
I often introduce people to gaming via games other than D&D. They don’t have to think about roll high, they just roll and add the modifier. Better games make target numbers more transparent than D&D 5e, but 5e rarely trips newbies up in this regard.
I also introduce people to gaming via games other than D&D. They don't have problems with roll under. You often don't even have to add the modifier. You roll and compare with the number on your sheet. You know as soon as you roll. No arithmetic required. It's not hard.
Neither is a problem, but it’s silly to pretend that roll high isn’t more intuitive than roll low. Hell, it doesn’t even matter why, just that it is.
Roll high is more intuitive than roll low. However, what is being contrasted is NOT roll high and roll low, but, rather,
roll over and
roll under. It is similar to but not the same as the aforementioned. A roll over game is not just about rolling as high as you can. It's about rolling a value
over some other value. That is where the complexities often lie.
Again, IME, I have personally found roll under to be easier and quicker for people to learn because the player knows when they roll if they succeeded or fail. In terms of the psychology present, there is often instant gratification. Players will generally have the number they need to beat on their character sheet, whether that is a skill or attribute. In roll over systems, the number they have to beat is very often in the GM's head.
This is why I have come to increasingly value tabletop games that make it super quick and easy to read success when the roll happens: e.g., many roll under games, PbtA, FitD, Free League's Year Zero Engine, etc. I know that there are roll over games where that's the case too - e.g., Cypher System - but roll over more often then not puts the math after the roll and the TN may or may not be known.
