When playing classic D&D, I like having some mechanics that don’t reduce the 3–18 range for ability scores to ±3. I’ve been using “roll score or less on nd6” for ability checks. (The n depends upon the difficulty of the check.) It’s unfortunate that this doesn’t take the character’s level into account.
So, here’s what I’m considering:
Roll a d20 for each character level. Pass if any are less than or equal to the ability score.
Although, unlike nd6, this has no provision to factor in a difficulty.
One possibility is to use different dice. For an easier task, roll d12s instead of d20s. For a harder task, roll d30s instead of d20s.
Another possibility is to have the difficulty modify the character’s level. But what do we do when modified level is less than one?
Maybe require rolling score or less on multiple d20s. e.g. If the effective character level were zero, success requires rolling the ability score or less on two d20s.
Here is an Anydice program showing the odds.