10d6 Dice Probability — Full Distribution and Odds
Ten dice for high-level damage. The spread is narrow relative to the mean, which is exactly why designers cap dice pools. The sum runs from 10 to 60, the average is 35, and the most likely total is 35. Below is every sum with its exact number of ways, its probability, the cumulative odds and the "at least" thresholds worth memorising.
Every possible sum
| Sum | Ways | Exactly | At most | At least | Odds of exactly |
|---|---|---|---|---|---|
| 10 | 1 | 0.000% | 0.000% | 100.0% | 1 in 60466176 |
| 11 | 10 | 0.000% | 0.000% | 100.0% | 1 in 6046618 |
| 13 | 220 | 0.000% | 0.000% | 100.0% | 1 in 274846 |
| 14 | 715 | 0.001% | 0.002% | 100.0% | 1 in 84568 |
| 15 | 2,002 | 0.003% | 0.005% | 100.0% | 1 in 30203 |
| 16 | 4,995 | 0.008% | 0.013% | 100.0% | 1 in 12105 |
| 18 | 23,760 | 0.039% | 0.071% | 100.0% | 1 in 2545 |
| 19 | 46,420 | 0.077% | 0.148% | 99.9% | 1 in 1303 |
| 20 | 85,228 | 0.141% | 0.289% | 99.9% | 1 in 709 |
| 22 | 243,925 | 0.403% | 0.937% | 99.5% | 1 in 248 |
| 23 | 383,470 | 0.634% | 1.57% | 99.1% | 1 in 158 |
| 24 | 576,565 | 0.954% | 2.52% | 98.4% | 1 in 105 |
| 25 | 831,204 | 1.37% | 3.90% | 97.5% | 1 in 72.7 |
| 27 | 1,535,040 | 2.54% | 8.34% | 94.2% | 1 in 39.4 |
| 28 | 1,972,630 | 3.26% | 11.6% | 91.7% | 1 in 30.7 |
| 29 | 2,446,300 | 4.05% | 15.7% | 88.4% | 1 in 24.7 |
| 31 | 3,393,610 | 5.61% | 26.1% | 79.5% | 1 in 17.8 |
| 32 | 3,801,535 | 6.29% | 32.4% | 73.9% | 1 in 15.9 |
| 33 | 4,121,260 | 6.82% | 39.2% | 67.6% | 1 in 14.7 |
| 34 | 4,325,310 | 7.15% | 46.4% | 60.8% | 1 in 14 |
| 36 | 4,325,310 | 7.15% | 60.8% | 46.4% | 1 in 14 |
| 37 | 4,121,260 | 6.82% | 67.6% | 39.2% | 1 in 14.7 |
| 38 | 3,801,535 | 6.29% | 73.9% | 32.4% | 1 in 15.9 |
| 39 | 3,393,610 | 5.61% | 79.5% | 26.1% | 1 in 17.8 |
| 41 | 2,446,300 | 4.05% | 88.4% | 15.7% | 1 in 24.7 |
| 42 | 1,972,630 | 3.26% | 91.7% | 11.6% | 1 in 30.7 |
| 43 | 1,535,040 | 2.54% | 94.2% | 8.34% | 1 in 39.4 |
| 45 | 831,204 | 1.37% | 97.5% | 3.90% | 1 in 72.7 |
| 46 | 576,565 | 0.954% | 98.4% | 2.52% | 1 in 105 |
| 47 | 383,470 | 0.634% | 99.1% | 1.57% | 1 in 158 |
| 48 | 243,925 | 0.403% | 99.5% | 0.937% | 1 in 248 |
| 50 | 85,228 | 0.141% | 99.9% | 0.289% | 1 in 709 |
| 51 | 46,420 | 0.077% | 99.9% | 0.148% | 1 in 1303 |
| 52 | 23,760 | 0.039% | 100.0% | 0.071% | 1 in 2545 |
| 54 | 4,995 | 0.008% | 100.0% | 0.013% | 1 in 12105 |
| 55 | 2,002 | 0.003% | 100.0% | 0.005% | 1 in 30203 |
| 56 | 715 | 0.001% | 100.0% | 0.002% | 1 in 84568 |
| 57 | 220 | 0.000% | 100.0% | 0.000% | 1 in 274846 |
| 59 | 10 | 0.000% | 100.0% | 0.000% | 1 in 6046618 |
| 60 | 1 | 0.000% | 100.0% | 0.000% | 1 in 60466176 |
Large pools are sampled to 40 rows so the table stays readable; the page numbers are still exact, not interpolated.
Rolling a target or higher
This is the form most checks actually use — "did I beat 12?" rather than "did I roll exactly 12".
| Target | Chance of meeting it | Odds |
|---|---|---|
| ≥ 29 | 88.4% | 1 in 1.13 |
| ≥ 32 | 73.9% | 1 in 1.35 |
| ≥ 36 | 46.4% | 1 in 2.16 |
| ≥ 40 | 20.5% | 1 in 4.88 |
| ≥ 43 | 8.34% | 1 in 12 |
Reading the shape
Each die is uniform, but the sum is not. 10d6 has 60,466,176 ordered outcomes spread over 51 totals, and the counts rise toward the middle because a middle total can be assembled from more orderings. The curve is symmetric around 35 — for every way to roll 34 there is a mirrored way to roll 36 — which is why the standard deviation of 5.40 describes the spread on both sides equally.
Compare that with a single die: 1d6 is a flat line at 16.7% per face. Adding dice does not widen the range proportionally — it makes extreme results rarer. That is the whole reason systems that want predictable outcomes roll pools, and systems that want drama roll one big die.
Frequently asked
What is the average roll of 10d6?
35. The formula is dice × (faces + 1) / 2 — 10 × (6 + 1) / 2 — which works for any fair die. The standard deviation is 5.40, so most rolls land between 29 and 41.
What is the most likely total on 10d6?
Exactly 35, at 7.27% — 4,395,456 of the 60,466,176 equally likely outcomes. The extremes (10 and 60) take 1 way each, or 0.000%.
How many possible outcomes does 10d6 have?
60,466,176 ordered outcomes — 610 — collapsing into 51 possible sums from 10 to 60. The counts here are exact integers from a convolution, not a normal approximation, so the tails are right: a normal curve would misstate the odds of the extreme rolls.
Why is the middle so much more likely than the ends?
Because sums have more ways to happen than faces do. There is exactly one way to roll all ones, but a middle total can be assembled from many orderings, and each ordering is a distinct outcome. That is why 10d6 has a single peak at 35 and why adding dice makes the distribution tighter rather than wider.