Dice Probability Charts: 2d6 Sums, d20 Odds and More
Dice look simple, but the odds change quickly once you roll more than one. This page collects the numbers people look up most often, for board games, tabletop RPGs and classroom probability lessons. Every figure is exact, worked out from all possible outcomes, and you can test any of them yourself with the online dice roller.
One die
A fair six-sided die gives each face a 1 in 6 chance, about 16.7%. The average roll is 3.5. For other dice the rule is the same: a d4 gives 25% per face, a d8 12.5%, a d10 10%, a d12 about 8.3% and a d20 5%.
Two dice (2d6): the sum chart
With two dice there are 36 equally likely combinations, but the sums are not equally likely. Seven is the most common because six combinations make it (1+6, 2+5, 3+4 and the reverse). Two and twelve each have only one way.
| Sum | Ways | Chance | This or higher |
|---|---|---|---|
| 2 | 1 / 36 | 2.8% | 100% |
| 3 | 2 / 36 | 5.6% | 97.2% |
| 4 | 3 / 36 | 8.3% | 91.7% |
| 5 | 4 / 36 | 11.1% | 83.3% |
| 6 | 5 / 36 | 13.9% | 72.2% |
| 7 | 6 / 36 | 16.7% | 58.3% |
| 8 | 5 / 36 | 13.9% | 41.7% |
| 9 | 4 / 36 | 11.1% | 27.8% |
| 10 | 3 / 36 | 8.3% | 16.7% |
| 11 | 2 / 36 | 5.6% | 8.3% |
| 12 | 1 / 36 | 2.8% | 2.8% |
This is why 6, 7 and 8 come up so often in games like Monopoly and Catan, and why a 2 or 12 feels rare: each happens about once every 36 rolls.
Doubles
The chance of rolling doubles with two dice is 6 in 36, exactly 1 in 6 or about 16.7%. The chance of rolling doubles three times in a row is 1 in 216, about 0.5%.
Chance of at least one 6
A common mistake is to add the chances: two dice are not "two sixths" likely to show a six. The right way is to work out the chance of no six at all and subtract it from 1.
| Dice rolled | Chance of at least one 6 |
|---|---|
| 1 | 16.7% |
| 2 | 30.6% |
| 3 | 42.1% |
| 4 | 51.8% |
| 5 | 59.8% |
| 6 | 66.5% |
So even with four dice you get a six only a bit more than half the time, and it takes six dice to reach about two in three.
d20 odds, advantage and disadvantage
In tabletop RPGs you often need to roll a target number or higher on a d20. Each number adds 5%. With advantage you roll twice and keep the higher result; with disadvantage you keep the lower.
| Need at least | Normal | Advantage | Disadvantage |
|---|---|---|---|
| 5 | 80% | 96% | 64% |
| 8 | 65% | 87.8% | 42.2% |
| 10 | 55% | 79.8% | 30.2% |
| 12 | 45% | 69.8% | 20.2% |
| 15 | 30% | 51% | 9% |
| 18 | 15% | 27.8% | 2.2% |
| 20 | 5% | 9.8% | 0.2% |
Advantage helps most for middle targets: needing 11 or more goes from 50% to 75%. A natural 20 has a 5% chance normally and 9.75% with advantage.
Average totals
The average of one die is half of (lowest + highest): 3.5 for a d6, 10.5 for a d20. For several dice, multiply: 2d6 averages 7, 3d6 averages 10.5 and 4d6 averages 14.
Common myths
- "A number is due." Each roll is independent. A die that has not shown a 6 for ten rolls is still exactly 1 in 6 on the next one.
- "Rolling harder changes the result." With a fair die and a real tumble, force does not favour any face.
- "Two dice double my chances." They do not add up; use the table above.
FAQ
What is the most common roll with two dice?
Seven. Six of the 36 combinations add up to 7, a chance of about 16.7%.
What are the odds of rolling a 6 on one die?
1 in 6, or about 16.7%.
What are the odds of rolling doubles with two dice?
1 in 6, or about 16.7%: six of the 36 combinations are doubles.
How much does advantage help on a d20?
It depends on the target. Needing 11 or more goes from 50% to 75%, and the chance of a natural 20 nearly doubles from 5% to 9.75%.
Want to check the numbers? Roll a few hundred times with the dice roller and keep an eye on its history, or pick numbers in any range with the random number generator.