Dice Probability Library — 26 Standard Pools
Exact distributions for the pools that actually come up at a table: single dice from d4 to d100, the 2d6 family, three-die pools, and the big d6 handfuls used for spell damage. Each page lists every sum, the number of ways to reach it, cumulative odds and the thresholds worth remembering.
| Pool | Sum range | Average | Most likely | Peak chance | Outcomes |
|---|---|---|---|---|---|
| 1d4 | 1–4 | 2.5 | 1 | 25.0% | 4 |
| 1d6 | 1–6 | 3.5 | 1 | 16.7% | 6 |
| 1d8 | 1–8 | 4.5 | 1 | 12.5% | 8 |
| 1d10 | 1–10 | 5.5 | 1 | 10.0% | 10 |
| 1d12 | 1–12 | 6.5 | 1 | 8.33% | 12 |
| 1d20 | 1–20 | 10.5 | 1 | 5.00% | 20 |
| 1d100 | 1–100 | 50.5 | 1 | 1.00% | 100 |
| 2d4 | 2–8 | 5 | 5 | 25.0% | 16 |
| 2d6 | 2–12 | 7 | 7 | 16.7% | 36 |
| 2d8 | 2–16 | 9 | 9 | 12.5% | 64 |
| 2d10 | 2–20 | 11 | 11 | 10.0% | 100 |
| 2d12 | 2–24 | 13 | 13 | 8.33% | 144 |
| 2d20 | 2–40 | 21 | 21 | 5.00% | 400 |
| 3d4 | 3–12 | 7.5 | 7 | 18.8% | 64 |
| 3d6 | 3–18 | 10.5 | 10 | 12.5% | 216 |
| 3d8 | 3–24 | 13.5 | 13 | 9.38% | 512 |
| 3d10 | 3–30 | 16.5 | 16 | 7.50% | 1,000 |
| 3d20 | 3–60 | 31.5 | 31 | 3.75% | 8,000 |
| 4d4 | 4–16 | 10 | 10 | 17.2% | 256 |
| 4d6 | 4–24 | 14 | 14 | 11.3% | 1,296 |
| 4d8 | 4–32 | 18 | 18 | 8.40% | 4,096 |
| 4d10 | 4–40 | 22 | 22 | 6.70% | 10,000 |
| 5d6 | 5–30 | 17.5 | 17 | 10.0% | 7,776 |
| 6d6 | 6–36 | 21 | 21 | 9.28% | 46,656 |
| 8d6 | 8–48 | 28 | 28 | 8.09% | 1,679,616 |
| 10d6 | 10–60 | 35 | 35 | 7.27% | 60,466,176 |
Why the numbers are exact
Every count is an integer convolution of the single-die distribution, so nothing is approximated. That matters in the tails: a normal approximation of 3d6 puts an 18 at about 0.90% when the true value is 1 in 216, or 0.463% — nearly double. For balance work the difference between "rare" and "essentially never" is the whole decision.