Advantage & Disadvantage Calculator (d20 Probability)

How it works

single-roll chance p = successful faces ÷ 20 (face + modifier ≥ target; attack rolls: natural 20 and the critical range always hit, natural 1 always misses) · advantage = 1 − (1 − p)² · disadvantage = p² · best of 3 = 1 − (1 − p)³ · average of best of n = Σ k × [(k/20)ⁿ − ((k − 1)/20)ⁿ]

With advantage you roll two d20s and keep the higher, so you fail only if both dice fail: 1 − (1 − p)². With disadvantage you keep the lower and need both to succeed: p². The effect is largest in the middle — at a 50% base chance advantage gives 75% and disadvantage 25%, roughly ±5 on the roll — and small at the extremes. Advantage also nearly doubles the critical chance from 5% to 9.75%. These are the standard d20 rules in the System Reference Document 5.1, which work the same in most d20 tabletop games.

Worked example

Attacking AC 15 with +5 you need a natural 10 or higher: 11 of 20 faces, a 55.00% chance. With advantage it rises to 1 − 0.45² = 79.75% (+24.75 points), with disadvantage it falls to 30.25%, and the critical chance with advantage is 9.75%. The average advantage roll is 13.83.

Sources: System Reference Document 5.1 (CC-BY-4.0) · Wikipedia — Order statistic

Frequently asked questions