Dice Roller

How dice notation works

Tabletop games write rolls in a short code called dice notation. The roller understands the common forms, so you can copy a roll straight from a rulebook or character sheet.

• NdS means roll N dice with S sides each and add them. 3d6 is three six-sided dice. Leave out N for one die: d20.
• +M or −M adds or subtracts a fixed number, the modifier: 1d20+5.
• Groups can be mixed: 1d8+1d6+3 rolls a d8 and a d6, then adds 3. You can subtract dice too: 1d20-1d4.
• khK / klK keep only the highest or lowest K dice: 4d6kh3 keeps the best three of four.
• dlK / dhK drop the lowest or highest K dice, which is the same thing said the other way round: 4d6dl1 equals 4d6kh3.

The roller shows the range and the exact average for whatever you type, before you roll.

The average of a roll

A fair die with S sides averages the middle of its faces. Add one average per die, then the modifier:

Worked example: 3d6+2. One d6 averages (6 + 1) ÷ 2 = 3.5, so three of them average 10.5. Add 2 and the average is 12.5. The lowest total is 1 + 1 + 1 + 2 = 5 and the highest is 6 + 6 + 6 + 2 = 20.

Middle totals turn up far more often than the extremes. Three d6 can land in 6 × 6 × 6 = 216 equally likely ways. A total of 10 can be made 27 different ways, so it comes up 12.5% of the time. A total of 3 needs three 1s, which is 1 way in 216, or about 0.46%.

Advantage, disadvantage and keeping dice

Keeping the best die changes the odds a lot. Say you need 15 or more on a d20.

• Normal roll: 6 of the 20 faces are 15 or higher, so the chance is 6 ÷ 20 = 30%.
• Advantage (2d20kh1): you fail only if both dice are 14 or lower: (14 ÷ 20)² = 0.49. So the chance is 1 − 0.49 = 51%.
• Disadvantage (2d20kl1): both dice must be 15 or higher: (6 ÷ 20)² = 9%.

For keep and drop rules, the average shown is calculated exactly from the probabilities of every possible order of the dice, not estimated from practice rolls. That is how the tool knows that 4d6kh3 averages about 12.24, almost two points more than plain 3d6.

Is the roller fair?

Each die gets its own number from your browser’s cryptographic random number generator, crypto.getRandomValues. Turning a random number into a die face needs care. If you took a random byte (0 to 255) and used the remainder after dividing by 6, four faces would come up 43 times in 256 and two faces only 42 times, because 256 does not divide evenly by 6. The roller avoids this “modulo bias” by throwing away the few values at the top of the range and drawing again. Every face is exactly equally likely.

The results are decided before the short animation starts. The flicker is only for show, and it switches off if your device asks for reduced motion.

Tips

• Percentile rolls: d100 gives 1 to 100 in one go, so you do not need two d10s.
• Coin flips: d2 works as heads or tails.
• Odd dice for real life: a custom die can have up to 1,000 sides. 1d350 picks a random page from a 350-page book.
• Limits: up to 20 dice in one group and 100 dice in one roll, which covers even big fireball damage like 8d6 many times over.
• History: your last 20 rolls stay listed under the tool until you clear them or leave the page.

Choosing between people rather than numbers? The wheel spinner picks a name fairly. Dice are also the classic way to make a diceware passphrase, five rolls per word; the password generator builds strong passphrases with the same kind of secure randomness.