I'm in the middle of an existential crisis right now. So I look towards the warm bosoms of math to comfort me.
In my current campaign I use a roll under as a resolution mechanic. But roll under is the most over-used method in old school gaming, and for good reason. It works. roll under is square-one of resolution mechanics. It requires no math. It requires no arbitrary decisions. It's binary; you fail or you succeed.
On the other end of the spectrum, roll over is the least-used method, and for good reason. Most roll over methods require math and arbitrary decisions. It is also the flagship mechanic of the mediocrity that is modern elf games.
If I had to pick between the two, I would choose roll under. But that's the easy choice. And this post isn't about doing things easy.
I want to explore the possibility of a roll over mechanic that is simple and intuitive.
The traditional roll under mechanic uses a variable that the player rolls equal to or under in order to succeed. That variable is an Ability Score most of the time. Allow me to introduce Kenned.
Kenned is a first level fighter. He's got dreams and aspirations; and he's got a Strength score of 16. Right now all that matters is Kenned's Strength Score. (Fuck your dreams and aspirations Kenned.)
In the traditional roll under mechanic, Kenned has an 80% success rate for Strength tests. But if we flip to a roll over mechanic, Kenned looks a bit more scrawny. In the roll over mechanic, Kenned only has a 25% success rate. Now most people would abandon the roll over idea here because they think it means restructuring D&D. But this isn't the case.
Both mechanics have two things in common. They both have a dice roll. And they both have a target number. However in the case of the roll under mechanic, this target number is an ability score most of the time. This just doesn't work in a roll over mechanic because the maxim of "high score be good" is broken by the nature of the roll over mechanic. And since we can't change the dice roll, we have to change the target number.
But changing the target number comes with a stipulation. The success rates have to be the same. In other words a score of 16 has to have a success rate of 80% in a roll under mechanic and a roll over mechanic.
After a lot of mad scribbling I've come to a target number of 21.
In order to keep the maxim "high score be good" we have to invert the roll under mechanic. One would think this would result in a target number of 20, but this proves to not be the case. This is the result of adding the score to the roll. In a roll under mechanic there's no math. So by introducing a modifier the target number increases by one. But the success rates check out. A score of 16 has an 80% success rate in both systems.
So the basic mechanic in this roll over system would look like this:
d20 + modifier ≥ 21 = Success
The modifier varies depending on what is tested. Ability Scores modify ability checks; skills modify skill checks; etc; etc.
The key to this mechanic is to modify the target number instead of the roll. Instead of applying a -4 penalty to the roll, add 4 to the target number.
Let's go back to Kenned. He's got some leather armor. Leather armor has an AC of 2. So we add that to any attack rolls' target numbers. So Kenned would have an "AC" of 23 (or 25 if he's got good DEX.)
This method means players don't have to do multi-step math. It's roll and add. That's it. Only the target number fluctuates, and it's easy for the DM to communicate the target number.
I'm no math-man, but I think this works out. Regardless it's a basic start and I'll explore it further later after I've accepted nihilism.