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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 basic system is this:
d20 + level + modifiers ≥ 20
Some additional information can be found on the one-sheet linked to the left.
(For example, D&D monster to-hit rolls are effectively: d20+HD+AC ≥ 20.)
You can also see spreadsheet analyses of the probabilities in question below.
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