Househack part 1 (dice)

For character skill and combat rolls:

[Highest of] XdY versus Target Number, Difficulty Class, Magic Score, etc.

Where X = skill rating (maximum of three, for now), Y = tool quality (d4 up to d12). 

(I might save the d20 for some special rolls, like saving throws.)

Hopefully, compatibility won't be too much of an issue. I can see fighters with multiple attacks roll, say, 3d8 with their longsword against an adjusted AC. Since everything is compressed to a 1-12 range, smaller dice will not have as good of a probabilistic gradation as I might like. The d4s increment in leaps of 25%, which might be a bit much. Besides, they don't roll very well. Anyhow, I think this system is intuitive enough. A tiebreaker stat for contested rolls will probably be required, though. Actually, character level is a good fit. This is open-source roleplaying (OSR) material, by the way.

Inspiration: MESBG