How much is advantage worth in D&D 5e?

About +3.3 on average, but it varies enormously with what you need to roll. It is worth roughly +25 percentage points when you need an 11, and under +5 points when you need a 2 or a 20. Advantage is strongest exactly when the outcome is most uncertain.

What is the average of 2d6?

7 — the same as 1d12, but distributed very differently. 2d6 rolls a 7 about 16.7% of the time and a 2 or 12 only 2.8% each, whereas every result on a d12 is equally likely at about 8.3%.

Are these numbers simulated or exact?

Exact. The distribution is computed by convolution rather than by rolling dice in a loop, so the answers are the true probabilities and identical every time you load the page.

Does it handle drop-lowest rolls like 4d6 keep 3?

Not currently. Keep-highest and drop-lowest change the shape of the distribution rather than shifting it, so they need a separate calculation. Straight NdX+M pools and d20 checks are covered.

Why does my attack roll chance look slightly different?

The d20 section models a flat check. Attack rolls also auto-hit on a natural 20 and auto-miss on a natural 1, so for an attack add about 5% at each end of what this reports.

Dice probability calculator

Type a dice pool and get the exact odds: the full distribution of totals, the average, and the chance of hitting or beating any target. Below that, the same for a d20 check against a DC, with advantage and disadvantage.

These are computed exactly rather than simulated, so the answers are the real probabilities and do not wobble between page loads.

Dice pool

e.g. 2d6+3, 8d6, d20, 4d8-2

Target total

Average

10.00

Chance of 10 or more

58.3%

Exactly 10

16.7%

Range 5 to 15. Chance of 10 or less: 58.3%.

Full distribution

52.8%
65.6%
78.3%
811.1%
913.9%
1016.7%
1113.9%
1211.1%
138.3%
145.6%
152.8%

d20 check against a DC

DC or AC

Your modifier

Roll type

Chance to succeed

55.0%

Advantage

What advantage is actually worth

Advantage is worth about +3.3 on average, but that average hides the interesting part: its value depends entirely on what you needed to roll. It does almost nothing when you needed a 2, and almost nothing when you needed a 20 — in both cases the outcome was nearly settled already.

It peaks in the middle. When you need an 11, advantage takes you from 50% to 75%, a swing of 25 percentage points, which is the single largest bonus in the game at that point. That is why "can I get advantage on this?" is usually a better question than "can I get +2?".

Disadvantage is the mirror image, and it is why stacking a source of disadvantage onto an enemy is often stronger than an equivalent penalty to their roll. The maths below is exact: advantage is one minus the chance both dice fail, disadvantage is the chance one die succeeds, squared.

Reference

Advantage by target number

Chance of success on a d20, before modifiers. The gain is largest in the middle of the range.
Need	Normal	Advantage	Disadvantage	Advantage gain
2+	95%	99.8%	90.3%	+4.8
5+	80%	96%	64%	+16
8+	65%	87.8%	42.3%	+22.8
11+	50%	75%	25%	+25
14+	35%	57.8%	12.3%	+22.8
17+	20%	36%	4%	+16
20	5%	9.8%	0.3%	+4.8

Distributions

Why 2d6 is not the same as 1d12

Both average 7, and there the similarity stops. A d12 is flat — every result from 1 to 12 is equally likely, at about 8.3% each. Rolling 2d6 produces a bell: a 7 comes up 16.7% of the time and a 2 or a 12 only 2.8% each.

That is why weapon damage feels different at the same average. A greatsword (2d6) is consistent; a greataxe (1d12) is swingy. Over a long fight they converge, but in the one round that matters, the greataxe is the one that can roll a 2.

The more dice in a pool, the tighter the bell. 8d6 fireball damage averages 28 and lands between 20 and 36 about three-quarters of the time — it almost never rolls badly enough to matter, which is part of why area damage is reliable in a way that single big dice are not.

Limits

What this does not model

Rerolls, exploding dice, drop-lowest pools like 4d6 keep 3, and critical hits are not covered here — those change the shape of the distribution rather than shifting it, and each needs its own calculation.

The d20 section assumes a flat check: no natural-1 auto-fail and no natural-20 auto-success, because those rules apply to attack rolls and death saves rather than to ability checks. For an attack roll, add 5% of auto-hit and 5% of auto-miss to what it tells you.

Pools are capped at 50 dice of up to 100 sides, which is well beyond anything 5e asks for and keeps the exact calculation instant.

Common questions

How much is advantage worth in D&D 5e?: About +3.3 on average, but it varies enormously with what you need to roll. It is worth roughly +25 percentage points when you need an 11, and under +5 points when you need a 2 or a 20. Advantage is strongest exactly when the outcome is most uncertain.
What is the average of 2d6?: 7 — the same as 1d12, but distributed very differently. 2d6 rolls a 7 about 16.7% of the time and a 2 or 12 only 2.8% each, whereas every result on a d12 is equally likely at about 8.3%.
Are these numbers simulated or exact?: Exact. The distribution is computed by convolution rather than by rolling dice in a loop, so the answers are the true probabilities and identical every time you load the page.
Does it handle drop-lowest rolls like 4d6 keep 3?: Not currently. Keep-highest and drop-lowest change the shape of the distribution rather than shifting it, so they need a separate calculation. Straight NdX+M pools and d20 checks are covered.
Why does my attack roll chance look slightly different?: The d20 section models a flat check. Attack rolls also auto-hit on a natural 20 and auto-miss on a natural 1, so for an attack add about 5% at each end of what this reports.

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