How does advantage and disadvantage work in D&D?

With advantage, roll 2d20 and take the higher result. With disadvantage, roll 2d20 and take the lower. Advantage raises the average d20 roll from 10.5 to about 13.8. Disadvantage lowers it to about 7.2. The probability of rolling a natural 20 with advantage is 9.75% (up from 5%), while with disadvantage it drops to 0.25%.

Are digital dice rolls truly random?

Digital dice use pseudorandom number generators (PRNGs) which are deterministic but statistically indistinguishable from true randomness for gaming purposes. Cryptographically secure PRNGs (like those in modern browsers) pass all statistical randomness tests. Physical dice, ironically, are often less fair — manufacturing imperfections and rolling technique can introduce bias.

FunApril 12, 2026

Dice Roller Guide: Probability, D&D Dice & Fair Rolling

Q: What dice are in a standard D&D set?

A standard D&D polyhedral dice set contains 7 dice: d4 (tetrahedron), d6 (cube), d8 (octahedron), d10 (pentagonal trapezohedron), d00 (percentile, numbered 00-90), d12 (dodecahedron), and d20 (icosahedron). The d20 is the most iconic — used for attack rolls, ability checks, and saving throws.

Q: What is the probability of rolling a specific number on a d20?

Each face of a d20 has an equal 1/20 chance, or 5%. The probability of rolling at or above a number: rolling 10+ is 55% (11 out of 20), rolling 15+ is 30%, rolling a natural 20 is 5%. For rolls with modifiers, add the modifier to the die result and compare to the target number (DC or AC).

Q: How do I calculate the average of a dice roll?

The average of a single die is (max + 1) / 2. For a d6: (6+1)/2 = 3.5. For a d20: (20+1)/2 = 10.5. For multiple dice, multiply by the number of dice: 2d6 averages 7, 3d8 averages 13.5. Add any fixed modifier: 2d6+3 averages 10.

By The hakaru Team·Last updated March 2026

Quick Answer

*Standard D&D set: d4, d6, d8, d10, d00, d12, d20 (7 dice).
*Average of any die: (max + 1) / 2. d20 average = 10.5.
*Advantage raises d20 average from 10.5 to ~13.8.
*Each d20 face has exactly 5% probability (1 in 20).

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The Standard Polyhedral Dice Set

Tabletop RPGs use dice named by their number of faces. A “d” followed by the face count: d4, d6, d8, d10, d12, d20. The notation “2d6+3” means roll two six-sided dice and add 3 to the total.

Die	Shape	Range	Average	Common Use
d4	Tetrahedron	1–4	2.5	Dagger damage, minor healing
d6	Cube	1–6	3.5	Fireball, ability scores, board games
d8	Octahedron	1–8	4.5	Longsword damage, hit dice
d10	Pentagonal trapezohedron	1–10	5.5	Damage rolls, percentages
d12	Dodecahedron	1–12	6.5	Greataxe damage, barbarian hit dice
d20	Icosahedron	1–20	10.5	Attack rolls, ability checks, saves

Basic Probability

A fair die gives each face equal probability. For a d6, each face has a 1/6 chance (16.67%). The probability of rolling at or above a target on a d20: subtract the target from 21 and divide by 20. Need a 15 or higher? (21 − 15) / 20 = 6/20 = 30%.

For multiple dice, the distribution is no longer flat. Rolling 2d6 produces a bell curve centered on 7. The probability of rolling exactly 7 on 2d6 is 6/36 (16.67%), while rolling a 2 or 12 is only 1/36 (2.78%). More dice = more concentrated results around the average.

Advantage and Disadvantage

D&D 5th Edition’s advantage/disadvantage system is elegant math. With advantage, you roll 2d20 and keep the highest. The probability distribution shifts dramatically:

Average roll: 10.5 → 13.82 (advantage) or 7.18 (disadvantage)
Rolling 20: 5% → 9.75% (advantage) or 0.25% (disadvantage)
Rolling 1: 5% → 0.25% (advantage) or 9.75% (disadvantage)

Advantage is roughly equivalent to a +3.3 bonus, but it’s not linear. It’s most impactful when you need a middling number (around 10–12) and least impactful at the extremes.

Damage Dice Math

When comparing weapons, average damage matters more than maximum. A greatsword (2d6, avg 7) deals more consistent damage than a greataxe (1d12, avg 6.5). The greatsword can’t roll a 1, while the greataxe can. But the greataxe has a chance at 12 damage that the greatsword can’t reach.

For critical hits (double the dice), the greatsword advantage grows: 4d6 averages 14 versus 2d12 averaging 13. More dice = more reliable results near the average.

Digital vs. Physical Dice

Modern pseudorandom number generators pass every statistical test for fairness. Browser-based crypto.getRandomValues() is cryptographically secure. Physical dice, meanwhile, have manufacturing tolerances. Cheap dice with hollow pips or air bubbles show measurable bias over thousands of rolls. Casino dice (precision-machined, transparent) are the most fair physical dice.

For online play, digital dice are faster and provably fair. For in-person games, the ritual of rolling physical dice is part of the experience. Some players swear their lucky dice roll better. Statistics disagree, but superstition is half the fun.

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Frequently Asked Questions

What dice are in a standard D&D set?

Seven dice: d4, d6, d8, d10, d00 (percentile), d12, and d20. The d20 is the most-used for attack rolls, ability checks, and saving throws.

What is the probability of rolling a specific number on a d20?

Each face has exactly 5% (1/20) probability. Rolling 15+: 30%. Rolling a natural 20: 5%.

How does advantage/disadvantage work?

Advantage: roll 2d20, take the higher (average ~13.8). Disadvantage: roll 2d20, take the lower (average ~7.2). Natural 20 with advantage: 9.75%.

How do I calculate the average of a dice roll?

(max + 1) / 2 per die. d6 = 3.5, d20 = 10.5. Multiply by number of dice and add modifiers: 2d6+3 = 10.

Are digital dice truly random?

Pseudorandom generators are statistically indistinguishable from true randomness for gaming. Physical dice often have more bias from manufacturing imperfections.