The Target 20 core mechanic provides an elegant way to resolve actions in classic
D&D without the need for table lookups, complicated math, or recording of any new
statistics. The idea is to simply check this:
d20 + level + modifiers ≥ 20
For example, attacks can be adjudicated by taking fighting ability (fighter or monster HD)
as "level", and Armor Class as the "modifier" (re: classic descending AC); e.g., fighter level 8 versus
AC 4 rolls d20+8+4, and hits on a total of 20 or more. Similar usage can be made for saving throws,
thief skills, spells known, etc.
A one-page PDF describing the details is to the left (click the picture). An Open Document (ODT)
version is here. Statistical analysis of closeness to OD&D core numbers
are given below (in XLS spreadsheets):
For ongoing discussion, visit my D&D blog, here.