Dice notation you can use
The notation is the one used by most tabletop games.
NdSrolls N dice with S sides:3d6,2d10,d20(one die is assumed when N is left out).+and-add or subtract numbers and other dice:3d6+2,2d8+1d4+3,2d6-1d4.khNkeeps the highest N dice andklNkeeps the lowest N:4d6kh3. You can also write it out:4d6 drop lowest,5d6 keep highest 3.dlNanddhNdrop the lowest or highest N dice.d20 advantagerolls two d20 and keeps the higher;d20 disadvantagekeeps the lower.advanddisalso work.
Each term takes 1 to 100 dice with 2 to 1,000 sides, and dice times sides may not exceed 20,000 so the chart stays exact and fast. Multiplication (*) is rejected rather than guessed at.
The page shows how it read your expression (for example, 4d6 drop lowest becomes 4d6kh3), so you can check it. Dropped dice appear struck through in the roll history.
Worked example
Suppose a game asks for 15 or more on a d20 with a +3 bonus. The bonus means you need a natural 12 or higher, which is 9 faces out of 20. Enter d20+3 and 15 in the target box:
d20+3, chance of at least 15: 45.0% d20 advantage, at least 15: 51.0% (1 - (14/20)^2) d20 disadvantage, at least 15: 9.0% ((6/20)^2) d20, at least 15: 30.0%
Advantage adds 21 percentage points to the plain 30% and disadvantage takes 21 away. Now compare two ways to roll ability scores, with a target of 15 or more:
3d6, average 10.50: 9.3% at least 15 4d6 drop lowest, average 12.24: 23.1% at least 15
Dropping the lowest of four dice raises the average by about 1.7 and makes a 15 or better roughly two and a half times as likely.
How the probability chart is calculated
The chart is exact, not a simulation. For a plain sum of dice, the tool starts with the distribution of a single die (every face equally likely) and repeatedly combines distributions with a convolution: the chance of a total is the sum, over every way two partial totals could produce it, of the product of their probabilities. Constants shift the whole chart left or right, and subtracted dice mirror it.
Keep-highest and drop-lowest rolls cannot be done by simple convolution because the dice depend on each other, so the tool counts every combination of face values with dynamic programming. For example, rolling four dice and dropping the lowest averages about 12.24, higher than the 10.5 of plain 3d6. The same method gives the familiar result that advantage on a d20 averages 13.825 and disadvantage 7.175.
Hover a bar to see its exact percentage. Very wide ranges are grouped into bins so the chart stays readable; the probability table below lists exact values when the range is small.
Using the numbers
Use Chance of rolling at least to turn a target into a probability. To hit a difficulty of 15 with d20+3, enter 15 and read the percentage. Bars at or above your target are highlighted. The statistics panel gives the average, most likely total, median and standard deviation, which tells you how swingy a roll is: many small dice cluster tightly around the mean, while one large die spreads results evenly.
Individual rolls use your browser's pseudo-random generator. That is fine for games, but it is not certified randomness, and nothing is sent to a server.
Frequently asked questions
What does 4d6 drop lowest mean?
Roll four six-sided dice, discard the lowest one and add the other three. It is a common way to generate character ability scores and averages about 12.24.
How do I roll with advantage?
Type d20 advantage (or d20 adv). It rolls two d20 and keeps the higher. For disadvantage, use d20 disadvantage or d20 dis.
Is the probability chart a simulation?
No. It is calculated exactly by combining the dice distributions, so there is no sampling error.
Why can't I use a huge number of dice?
Exact calculation gets expensive as the number of outcomes grows, so each term is limited to 100 dice, 1,000 sides and 20,000 for dice times sides, with a tighter limit on keep and drop rolls. Typical tabletop expressions are well within the limits.
Can I subtract dice or add several different dice?
Yes. Chain terms with plus and minus, such as 2d6+1d4-1 or 1d20+1d6+4.
Are the rolls truly random?
They come from your browser's pseudo-random generator, which is suitable for games but not for cryptography or regulated gambling.