D&D Advantage and Disadvantage: The Math Behind It
Advantage and disadvantage are the simplest, most elegant mechanics in D&D 5e. Roll two d20s, take the higher (advantage) or lower (disadvantage). One sentence — but the probability shift it produces is bigger than you'd guess, and it's not the same at every target number.
The basic mechanic
You're rolling against a Difficulty Class (DC) — a number you need to meet or beat on a d20 (plus modifiers). With advantage, you roll two d20s and use the higher result. With disadvantage, you roll two and use the lower. Modifiers, proficiency, crits — all that still applies as normal, just to whichever die you ended up using.
Why it's not "+5 to your roll"
The most common shorthand for advantage is "it's like +5 to your roll." That's approximately right at the middle DCs — but it's wildly wrong at the extremes.
The rule has its biggest effect when you have a 50/50 chance to succeed. It barely moves the needle when you almost always succeed or almost always fail. To see why, imagine you need a 2 or higher to succeed (95% chance on a single roll). Rolling twice and taking the higher only fails if both dice come up 1 — that's 1/400, or 0.25%. So your success rate goes from 95% to 99.75%. A real boost, but only +4.75%.
Now imagine you need an 11 or higher (50%). Both dice missing means both rolled 10 or lower — that's 50% × 50% = 25%. So success goes from 50% to 75%. That's +25 percentage points, or roughly the equivalent of +5 to your roll at that DC.
The full table
Here's how often you'll succeed at each target number, with and without advantage. The "swing" column is how many percentage points advantage adds. Disadvantage is the same table reversed.
| Need to roll | Single d20 | With advantage | Swing | With disadvantage |
|---|---|---|---|---|
| 2+ | 95% | 99.75% | +4.75 | 90.25% |
| 5+ | 80% | 96% | +16 | 64% |
| 8+ | 65% | 87.75% | +22.75 | 42.25% |
| 10+ | 55% | 79.75% | +24.75 | 30.25% |
| 11+ | 50% | 75% | +25 | 25% |
| 13+ | 40% | 64% | +24 | 16% |
| 15+ | 30% | 51% | +21 | 9% |
| 17+ | 20% | 36% | +16 | 4% |
| 20+ | 5% | 9.75% | +4.75 | 0.25% |
When to spend a resource for advantage
Many character abilities give you advantage on a single roll — Bardic Inspiration synergies, Reckless Attack, the Help action. These are valuable in proportion to where the roll lands on the curve.
If a teammate is making a 50/50 roll on something important — disarming a trap, hitting a critical foe, persuading the duke — burning a Help action is a +25 percentage-point swing. Huge. If they need a 2 to succeed (basically already succeeding), don't bother; the swing is only +4.75 and the resource is wasted.
The corollary: when the DM imposes disadvantage on you for a marginal roll, fight for anything that cancels it. The same +25 swing now works against you.
Critical hits with advantage
A natural 20 is a critical hit (5% per die). With advantage, your chance of rolling at least one nat 20 across two dice is 1 − (19/20)² = 9.75%. Roughly double. This is why paladins love advantage with smites — a crit doubles the smite damage dice on top of the weapon dice.
Disadvantage works in reverse: you only crit if both dice show a nat 20, which is 0.25% — 1 in 400 attacks.
Critical fumbles, by the same logic
A natural 1 has the same kind of asymmetry. Plain d20: 5% chance. With disadvantage, you fumble if either die comes up 1, which is 9.75%. With advantage, both dice would need to roll a 1 — 0.25%. Helpful when you've got something dangerous on the line.
Common myths, sorted
- "Advantage and disadvantage cancel out." Rules-as-written, yes — if you have both, you roll a single die. They don't stack or compound. Many tables house-rule otherwise; check with your DM.
- "It's the same as +5." Only at middle DCs. Worth far less at the extremes.
- "Three sources of advantage = roll three dice." No — advantage is binary. You either have it or you don't.
Practical play tips
- Rate "give me advantage" effects by where they land on the d20: roughly +5 at DC 11, declining toward +0 at the edges.
- Stacking attack bonuses past the +5 point of diminishing returns? You're better off seeking sources of advantage instead.
- If your build can flip enemy attacks into disadvantage (Cloak of Displacement, certain spells), you're cutting their crit chance from 5% to 0.25% — a major defensive boost most players underrate.
Want to feel the math? Open the roller, pick the D&D attack preset (d20 + d6), and roll a few dozen times with and without re-rolling for the higher.
Related
For the broader picture, see Dice Probability Basics for Board Gamers.