Dice Roller
- Updated
- Formula shown
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How to use the dice roller
- Press a quick button (d4 to d100) to roll one die, or type dice notation such as
3d6+2into the box and press Roll. - Roll several groups at once by separating them with commas, for example an attack and its damage:
1d20+5, 2d6+3. - Read each total and the individual dice. Dice in parentheses were dropped by a keep or drop rule.
- The chart shows the chance of every possible total; with several groups, choose which one to chart. Your recent rolls are listed underneath.
Dice notation
NdS + M = add a modifier M (or − to subtract)
NdSkhK / NdSklK = keep the K highest / lowest dice
NdSdlK / NdSdhK = drop the K lowest / highest dice
So 2d20kh1 rolls two twenty-sided dice and keeps the higher one (advantage in Dungeons & Dragons), 2d20kl1 keeps the lower one
(disadvantage), and 4d6dl1 rolls four d6 and ignores the lowest, the classic way to roll an ability score. You can add several kinds of dice
in one group, such as 1d8+1d6+3. Each group can have up to 100 dice with 2 to 1,000 sides.
How the probabilities are worked out
The chart is exact, not a simulation. One die with S sides gives each face a chance of 1/S. The distribution of a sum is the convolution of the distributions being added: the chance of a total t from two dice is the sum, over every face a of the first die, of P(first = a) × P(second = t − a). The calculator repeats this die by die. Keep and drop rules are counted with a dynamic program that goes through the face values from best to worst and counts how many ways the dice can land so that a given set is kept.
The rolls themselves come from your browser's crypto.getRandomValues, the same secure generator used by the
random number generator, with rejection sampling so every face is equally likely. Results are random: nothing about
an earlier roll makes the next one more or less likely.
Worked example: advantage on a d20
With advantage you roll two d20 and keep the higher. The higher die is at most k when both dice are, which happens with chance (k/20)², so the chance that the higher die is exactly k is (k² − (k − 1)²)/400. A natural 20 comes up 39 times in 400 (9.8%), almost twice as often as on a single die. The average rises from 10.5 to 13.825, and the chance of rolling 11 or more rises from 50% to 75%. With disadvantage it falls to 25%.
Chance of rolling at least a target on a d20
| Target | 1d20 | Advantage (2d20kh1) | Disadvantage (2d20kl1) |
|---|---|---|---|
| 5 or more | 80% | 96% | 64% |
| 8 or more | 65% | 87.8% | 42.3% |
| 10 or more | 55% | 79.8% | 30.3% |
| 12 or more | 45% | 69.8% | 20.3% |
| 15 or more | 30% | 51% | 9% |
| 18 or more | 15% | 27.7% | 2.3% |
| 20 or more | 5% | 9.8% | 0.3% |
Common rolls at a glance
| Roll | Range | Average | Standard deviation | Most likely |
|---|---|---|---|---|
| 1d6 | 1 to 6 | 3.5 | 1.71 | 1 and 2 and 3 and 4 and 5 and 6 |
| 2d6 | 2 to 12 | 7 | 2.42 | 7 |
| 3d6 | 3 to 18 | 10.5 | 2.96 | 10 and 11 |
| 1d20 | 1 to 20 | 10.5 | 5.77 | 1 and 2 and 3 and 4 and 5 and 6 and 7 and 8 and 9 and 10 and 11 and 12 and 13 and 14 and 15 and 16 and 17 and 18 and 19 and 20 |
| 2d20kh1 | 1 to 20 | 13.83 | 4.71 | 20 |
| 2d20kl1 | 1 to 20 | 7.17 | 4.71 | 1 |
| 4d6kh3 | 3 to 18 | 12.24 | 2.85 | 13 |
| 8d6 | 8 to 48 | 28 | 4.83 | 28 |
| 1d100 | 1 to 100 | 50.5 | 28.87 | 1 and 2 and 3 and 4 and 5 and 6 and 7 and 8 and 9 and 10 and 11 and 12 and 13 and 14 and 15 and 16 and 17 and 18 and 19 and 20 and 21 and 22 and 23 and 24 and 25 and 26 and 27 and 28 and 29 and 30 and 31 and 32 and 33 and 34 and 35 and 36 and 37 and 38 and 39 and 40 and 41 and 42 and 43 and 44 and 45 and 46 and 47 and 48 and 49 and 50 and 51 and 52 and 53 and 54 and 55 and 56 and 57 and 58 and 59 and 60 and 61 and 62 and 63 and 64 and 65 and 66 and 67 and 68 and 69 and 70 and 71 and 72 and 73 and 74 and 75 and 76 and 77 and 78 and 79 and 80 and 81 and 82 and 83 and 84 and 85 and 86 and 87 and 88 and 89 and 90 and 91 and 92 and 93 and 94 and 95 and 96 and 97 and 98 and 99 and 100 |
Ability scores rolled with 4d6 drop lowest average 12.24, about 1.7 more than 3d6, and an 18 comes up 21 times in 1,296 (1.6%).
Two dice: why 7 is the most common total
| Total (2d6) | Ways out of 36 | Chance |
|---|---|---|
| 2 | 1 | 2.8% |
| 3 | 2 | 5.6% |
| 4 | 3 | 8.3% |
| 5 | 4 | 11.1% |
| 6 | 5 | 13.9% |
| 7 | 6 | 16.7% |
| 8 | 5 | 13.9% |
| 9 | 4 | 11.1% |
| 10 | 3 | 8.3% |
| 11 | 2 | 5.6% |
| 12 | 1 | 2.8% |
Tips
- Streaks happen. Three 1s in a row on a d20 has a 1 in 8,000 chance, and over many sessions some unlikely streaks are almost certain to turn up.
- More dice, steadier totals. 3d6 and 1d16+2 share a range of 3 to 18, but 3d6 clusters around 10 and 11 while 1d16+2 is flat.
- History stays on this page. Recent rolls are kept only in your browser's memory for this visit. They are not saved, shared or put in the page address.
For odds of other events, try the probability calculator or count arrangements with the permutation and combination calculator.
Frequently asked questions
Are the dice rolls really random?
Yes. Each die is drawn in your browser with crypto.getRandomValues, a cryptographically secure generator, using rejection sampling so that every face is exactly equally likely. Earlier rolls have no effect on later ones, so streaks are just chance.
How do I roll with advantage or disadvantage?
Type 2d20kh1 for advantage (roll two d20 and keep the higher) or 2d20kl1 for disadvantage (keep the lower). Advantage raises the chance of 11 or more from 50% to 75% and the average from 10.5 to 13.825; disadvantage lowers that chance to 25%.
What does 4d6 drop lowest mean?
Roll four six-sided dice and add the highest three, written 4d6dl1 or 4d6kh3. It is a common way to roll ability scores. The totals run from 3 to 18 with an average of about 12.24, and 18 comes up 21 times in 1,296 (about 1.6%).
Why is 7 the most common total with two dice?
Six of the 36 equally likely combinations add up to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), more than any other total, so the chance is 6/36 or about 16.7%. Totals of 2 and 12 each have only one combination, a chance of 1 in 36.
Is my roll history saved?
No. The history is kept only in your browser’s memory while the page is open. It is not stored on a server, saved to an account or added to the page address, and reloading the page clears it. Press Clear history to empty it at any time.