Dice are honest in a very particular way: every face has the same chance, but the totals don't. That is why 7 shows up so often in board games, why a 20 feels rare in a role-playing session, and why you sometimes wait forever for a six. This guide explains the math with real counts, no formulas required beyond a little division. Every number here comes from counting all the combinations, the same tables you can see on our dice roller.
One die: every face has the same chance
A fair die with n sides gives each face a 1 in n chance. On a regular six-sided die (a d6), each face comes up 1 time in 6, about 16.67%. The average roll is the middle of the faces: (n + 1) / 2.
| Die | Chance of each face | Average roll |
|---|---|---|
| d4 | 1 in 4 (25%) | 2.5 |
| d6 | 1 in 6 (16.67%) | 3.5 |
| d8 | 1 in 8 (12.5%) | 4.5 |
| d10 | 1 in 10 (10%) | 5.5 |
| d12 | 1 in 12 (8.33%) | 6.5 |
| d20 | 1 in 20 (5%) | 10.5 |
| d100 | 1 in 100 (1%) | 50.5 |
How long until a six? On average 6 rolls, but that is only an average. Long droughts are normal, and so are two sixes in a row.
Two dice: why 7 is the most common total
Roll two dice and there are 6 × 6 = 36 equally likely combinations, counting which die shows what. The totals are not equally likely, because some totals can be made in more ways. A 2 needs a 1 and a 1, only one way. A 7 can be 1+6, 2+5, 3+4, 4+3, 5+2 or 6+1: six ways.
| Total | Ways (of 36) | Chance |
|---|---|---|
| 2 | 1 | 2.78% |
| 3 | 2 | 5.56% |
| 4 | 3 | 8.33% |
| 5 | 4 | 11.11% |
| 6 | 5 | 13.89% |
| 7 | 6 | 16.67% |
| 8 | 5 | 13.89% |
| 9 | 4 | 11.11% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 1 | 2.78% |
So a 7 comes up 1 time in 6, six times more often than a 2 or a 12. The average total is 7 as well. Game designers lean on this: in many board games, the spaces or numbers around 7 pay off most often. You can see it live on our 2 dice page.
Three dice: the bell takes shape
With three dice there are 6 × 6 × 6 = 216 combinations, and the middle totals pull further ahead. The most likely totals are 10 and 11, with 27 ways each, which is 12.5% apiece. The extremes are rare: a 3 or an 18 has only 1 way in 216, under half a percent.
| Total | Ways (of 216) | Total | Ways (of 216) |
|---|---|---|---|
| 3 | 1 | 11 | 27 |
| 4 | 3 | 12 | 25 |
| 5 | 6 | 13 | 21 |
| 6 | 10 | 14 | 15 |
| 7 | 15 | 15 | 10 |
| 8 | 21 | 16 | 6 |
| 9 | 25 | 17 | 3 |
| 10 | 27 | 18 | 1 |
The average is 10.5. The more dice you add, the more the totals bunch up around the middle. Full tables are on the 3 dice page.
At least one six, double sixes, and a famous bet
“At least one” questions are easiest to answer backward: find the chance of no six and subtract it from 1. One die misses a six 5 times in 6, so four rolls in a row all miss with probability 5/6 multiplied by itself four times. That gives a chance of at least one six in 4 rolls of 1 - (5/6)^4 = 51.77%. Just better than a coin flip.
A double six with two dice is a 1 in 36 shot. In 24 rolls of two dice, the chance of at least one double six is 49.14%; in 25 rolls, 50.55%. These two bets puzzled a 17th-century French gambler, the Chevalier de Méré, who won on the first and lost on the second. His question was part of the 1654 letters between Blaise Pascal and Pierre de Fermat that laid the groundwork for probability theory.
One more for dice-game fans: five of a kind in a single roll of five dice happens 6 times in 7,776 combinations, or 1 chance in 1,296. Try it on our 5 dice page, and use the keep feature (tap a die to keep it) to re-roll the rest.
Role-playing dice: the d20, advantage and ability scores
In tabletop role-playing games, the d20 decides most actions. Each number has a flat 5% chance, so “roll 15 or higher” is 6 faces out of 20, a 30% chance. Advantage means rolling two d20 and keeping the higher one. You only fail if both dice fail, which changes the picture a lot:
| Target | One d20 | With advantage |
|---|---|---|
| 10 or higher | 55% | 79.75% |
| 15 or higher | 30% | 51% |
| Natural 20 | 5% | 9.75% |
| Average roll | 10.5 | 13.825 |
For ability scores, a common method is to roll 4d6 and drop the lowest die. The average comes out at 12.24, a bit above the 10.5 you would get from a plain 3d6. Our 4d6 drop lowest page lists the chance of every score, and the d20 page has the full advantage table.
What the averages really tell you
An average is what you get over many rolls, not what the next roll will be. A d6 averages 3.5, a face it can never show. Two dice average 7, but a 7 still only lands 1 time in 6. Over a few rolls, anything can happen; over hundreds, the counts settle close to the tables above. And dice have no memory: after three 2s in a row, the next roll is exactly as random as the first.
Updated November 3, 2026