Dice Notation

Dice notation is written NdM. N is how many dice you roll, M is how many sides each one has, so 3d6 means roll three six-sided dice and add them up. Anything after that adjusts the result: +5 adds five, kh1 keeps only the highest die, d1 drops the lowest.

Reading NdM

The letter d stands for die. The number in front says how many, the number after says what kind.

2d10 is two ten-sided dice. 1d4 is a single four-sider. When N is 1 people often drop it and just write d20, which means the same thing as 1d20.

Modifiers hang off the end with a plus or minus sign, and they apply once to the total, not to each die. So 1d20+5 rolls one twenty-sider and adds five, giving a range of 6 to 25 with an average of 15.5.

Keep and drop

Two more letters show up constantly, mostly in role-playing games.

kh keeps the highest dice and kl keeps the lowest, with a number saying how many to keep. 2d20kh1 rolls two twenty-siders and uses only the better one. That’s what D&D 5th edition calls advantage, and it’s the single most common non-basic roll in the game. 2d20kl1 is disadvantage, using the worse die.

d after the dice, confusingly, means drop. 4d6d1 rolls four six-sided dice and throws away the lowest one, keeping the sum of the other three. Context tells you which d is which: the first d always sits between two numbers, the drop d comes after a complete NdM.

Four examples worth knowing

The 4d6d1 line is how most tables generate ability scores. Rolling straight 3d6 averages 10.5, while dropping the lowest of four pushes that up to 12.24, which is why it became the standard.

Advantage is easier to feel in the odds than the average. A flat d20 hits a natural 20 5% of the time. With advantage that becomes 9.75%.

Where the notation came from

It grew out of early tabletop role-playing, specifically the community around Dungeons & Dragons in the 1970s. The 1974 first edition didn’t use it. Rules there spelled rolls out in words, telling you to “roll two eight-sided dice.” The shorthand appeared in D&D fanzines instead, starting with Alarums & Excursions in 1975, where writers proposed calling the dice D4, D6, D8, D10, and D12 and compounding them as 2D6. By the time the Advanced Dungeons & Dragons Players Handbook arrived in 1978 the notation was used throughout without explanation, because everyone already knew it.

Once you can read notation, the next questions are usually about the dice themselves and the odds behind them. The pages below cover the dice shapes that notation refers to, the math that turns 3d6 into a bell-shaped spread, and the character-building rolls that use 4d6d1. You can type any of these strings straight into the roller or use the D&D stat roller for a full set of six scores.

FAQ

What does 3d6 mean?

Roll three six-sided dice and add the results together. The total runs from 3 to 18, averaging 10.5. Middle totals are far more common than the ends, since there are many ways to make 10 or 11 and only one way to make 3.

What does 4d6d1 mean?

Roll four six-sided dice, drop the single lowest, and add the remaining three. It’s the classic method for generating D&D ability scores. The average result is 12.24, noticeably higher than the 10.5 you get rolling three dice straight.

What is the difference between kh and kl?

Both keep a set number of dice out of a larger roll. kh keeps the highest, kl keeps the lowest. In D&D, 2d20kh1 is advantage and 2d20kl1 is disadvantage. The number after the letters says how many dice survive, so 4d6kh3 keeps the best three.

Does the modifier apply to each die or the total?

The total, once. In 3d6+2 you roll three dice, add them, then add two to that sum. If a game wants a bonus on every die it says so in words, and that’s rare enough that notation has no shorthand for it.

Is d20 the same as 1d20?

Yes. Writing d20 without a number in front assumes one die. Game text uses both forms interchangeably, and dice rollers accept either.