Rollune
One die gives a flat distribution: every face is equally likely. Adding dice creates a bell curve centred on the average. Average of XdY is X × (Y+1) ÷ 2. So 1d12 (6.5 average, flat) and 2d6 (7 average, clustered) feel very different even though both top out at 12.
Averages for every die
| Die | Average | Each face |
|---|---|---|
| d4 | 2.5 | 25% |
| d6 | 3.5 | 16.7% |
| d8 | 4.5 | 12.5% |
| d10 | 5.5 | 10% |
| d12 | 6.5 | 8.3% |
| d20 | 10.5 | 5% |
| d100 | 50.5 | 1% |
Rule of thumb: the average of XdY is X × (Y + 1) ÷ 2. 8d6 averages 28; 2d8 + 3 averages 12.
One die is flat; several dice make a curve
A single d20 is equally likely to show 1 or 20. Add dice together and the middle totals become more common, because there are more combinations that produce them.
2d6 distribution
| Total | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ways (of 36) | 1 | 2 | 3 | 4 | 5 | 6 | 5 | 4 | 3 | 2 | 1 |
| Chance | 2.8% | 5.6% | 8.3% | 11.1% | 13.9% | 16.7% | 13.9% | 11.1% | 8.3% | 5.6% | 2.8% |
That's why games built on 2d6 (Powered by the Apocalypse, for example: 10+ is a full success, 7–9 a partial one) feel predictable: a 7–9 comes up 41.7% of the time and 10+ 16.7%.
3d6 vs 1d20
Both range widely, but 3d6 (3–18) clusters hard around 10–11 (each 12.5%), while a d20 treats every number the same. Rolling 3d6 for a skill check makes experts reliable and long shots truly rare; a d20 keeps upsets possible. Old-school D&D rolled ability scores with 3d6, averaging 10.5.
Keeping dice shifts the curve
Dropping or keeping dice moves the average:
4d6drop lowest: average 12.24 (vs 10.5 for 3d6), and an 18 happens about 1.6% of the time.2d20keep highest (advantage): average 13.83.2d20keep lowest (disadvantage): average 7.18.
Using odds at the table
- Players: look for advantage or bonuses on rolls where you need around 8–14; that's where each +1 matters most.
- GMs: a DC 15 check for a character with +5 succeeds 55% of the time. Set DCs by how likely you want success to be.
- Damage: roll averages are fine for monsters. Many GMs use listed average damage to speed up combat.
Check the min, average and max of any roll in the online dice roller.
