Odds of a roll
See what a roll usually comes to before you make it. Nothing is rolled for real, and nothing is saved.
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Advantage and disadvantage on a d20
Advantage rolls two d20 and keeps the higher, 2d20kh1; disadvantage keeps the lower, 2d20kl1. Advantage helps most in the middle of the die: when you need an 11, it is worth a +5 bonus. Near 2 or 20 it adds much less.
| At least | Normal | Advantage | Disadvantage |
|---|---|---|---|
| 2 | 95% | 99.75% | 90.25% |
| 3 | 90% | 99% | 81% |
| 4 | 85% | 97.75% | 72.25% |
| 5 | 80% | 96% | 64% |
| 6 | 75% | 93.75% | 56.25% |
| 7 | 70% | 91% | 49% |
| 8 | 65% | 87.75% | 42.25% |
| 9 | 60% | 84% | 36% |
| 10 | 55% | 79.75% | 30.25% |
| 11 | 50% | 75% | 25% |
| 12 | 45% | 69.75% | 20.25% |
| 13 | 40% | 64% | 16% |
| 14 | 35% | 57.75% | 12.25% |
| 15 | 30% | 51% | 9% |
| 16 | 25% | 43.75% | 6.25% |
| 17 | 20% | 36% | 4% |
| 18 | 15% | 27.75% | 2.25% |
| 19 | 10% | 19% | 1% |
| 20 | 5% | 9.75% | 0.25% |
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The average of the common dice
A single die averages halfway between 1 and its highest face. Add dice and the averages add up, but the results also bunch together: a d12 lands on 1 as often as on 6, while 2d6 lands on 7 six times as often as on 2.
| Roll | Average | Range |
|---|---|---|
| 2.5 | 1 – 4 | |
| 3.5 | 1 – 6 | |
| 4.5 | 1 – 8 | |
| 5.5 | 1 – 10 | |
| 6.5 | 1 – 12 | |
| 7 | 2 – 12 | |
| 14 | 4 – 24 | |
| 28 | 8 – 48 |
Click a roll to see its curve.
Why 4d6 drop lowest averages 12.24
Rolling 4d6 and dropping the lowest die, 4d6kh3, is the usual way to roll ability scores. Three dice alone, 3d6, average 10.5. The fourth die can only replace the worst of the three: it raises a score or leaves it as it was, and never lowers it. That lifts the average to 12.24 and makes 13 the most common result. An 18 comes up about once in 62 rolls, three and a half times as often as with 3d6.
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