How to use it
- Type a dice expression in Dice expression, or press one of the Examples. Notation: 2d6 is two six-sided dice; add or subtract a number or another roll.
- Press Roll to roll. The result shows each term, with dropped dice in brackets, and the Total.
- Read the Every total and its chance table or the chart to see how likely each total is for this expression.
- Roll as often as you like. Clear the list empties the rolls on this page.
The dice notation
The notation follows the common roleplaying form: a number of dice, a d, and the number of sides. Terms are joined with a plus or a minus. The page reads these forms, in any capitals and spacing.
- 2d6+3: two six-sided dice plus 3. d20: one twenty-sided die.
- 4d6 drop lowest (or 4d6dl1): roll four dice and drop the lowest. 4d6 kh3 keeps the highest three; keep lowest 2 and drop highest 1 work too.
- d20 advantage rolls two d20 and keeps the higher; d20 disadvantage keeps the lower.
- d6!: an exploding die. A six rolls again and its face is added, so the total has no upper limit.
How the chance of each total is found
Each term is counted on its own, as a number of ways for every total, and the terms are then combined. A keep or drop is counted by the multisets of faces, so no roll is missed. Every chance is a fraction of exact whole numbers, shown as a percentage and as one in N.
- Up to six exploding dice are counted exactly; the rest of the chance, above the last exact total, is shown as a remainder.
- A table is shown for up to 400 totals. A roll of 100d6 has more than that, so the page gives its lowest, highest and average instead.
Worked example: 4d6 drop lowest
Four six-sided dice make 1,296 equally likely rolls. Dropping the lowest die leaves the three highest. The lowest total, 3, needs four 1s, which is 1 roll. The highest total, 18, needs at least three sixes, which is 21 rolls: four sixes, or exactly three sixes with a lower fourth die. So 18 comes up 21 times in 1,296, about 1.62%. Averaged over every roll, the total is about 12.24, the usual stat roll.
| Total | Rolls out of 1,296 | Chance |
|---|---|---|
| 3 | 1 | 0.077% |
| 18 | 21 | 1.620% |
Frequently asked questions
What does drop lowest mean?
The dice are all rolled, the lowest is removed and the rest are added. For 4d6 drop lowest, a roll of 6, 1, 5 and 3 gives 6 + 5 + 3 = 14, with the 1 dropped.
How is advantage different from rolling twice?
Advantage rolls the die twice and keeps the higher result, so the chance of a 20 is 1 minus (19/20) squared, which is 39 in 400 or 9.75%. The page counts that exactly.
What is an exploding die?
An exploding die rolls again each time it shows its top face and adds the new face. Its total can be as high as you like, so the page lists the exact chances up to a limit and reports the rest as more than that total.
Are the rolls fair?
Each face comes from the browser's cryptographic random generator. A random number that would favour some faces is drawn again, so every face has the same chance, and the list of rolls is not stored.
Can I subtract a roll from a total?
Yes, with a minus sign, as in 2d6 - 1d4. An exploding die cannot be subtracted, because its total has no upper limit.
Why is there no table for some large rolls?
A table lists every possible total. A roll such as 100d6 has more totals than the table holds, so the page gives the lowest, the highest and the average, and the roll still works.
Sources
- Wikipedia: Dice notation (keep and drop, exploding dice, the 4d6 drop lowest example)
- MDN: Crypto.getRandomValues() (cryptographically strong random values)
Figures and text last checked on Tuesday, November 10, 2026.