2d12 Dice Probability — Full Distribution and Odds
Two greataxes: a very wide 23-value range where the extremes are 144 times rarer than the peak. The sum runs from 2 to 24, the average is 13, and the most likely total is 13. 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 |
|---|---|---|---|---|---|
| 2 | 1 | 0.694% | 0.694% | 100.0% | 1 in 144 |
| 3 | 2 | 1.39% | 2.08% | 99.3% | 1 in 72 |
| 4 | 3 | 2.08% | 4.17% | 97.9% | 1 in 48 |
| 5 | 4 | 2.78% | 6.94% | 95.8% | 1 in 36 |
| 6 | 5 | 3.47% | 10.4% | 93.1% | 1 in 28.8 |
| 7 | 6 | 4.17% | 14.6% | 89.6% | 1 in 24 |
| 8 | 7 | 4.86% | 19.4% | 85.4% | 1 in 20.6 |
| 9 | 8 | 5.56% | 25.0% | 80.6% | 1 in 18 |
| 10 | 9 | 6.25% | 31.3% | 75.0% | 1 in 16 |
| 11 | 10 | 6.94% | 38.2% | 68.8% | 1 in 14.4 |
| 12 | 11 | 7.64% | 45.8% | 61.8% | 1 in 13.1 |
| 13 | 12 | 8.33% | 54.2% | 54.2% | 1 in 12 |
| 14 | 11 | 7.64% | 61.8% | 45.8% | 1 in 13.1 |
| 15 | 10 | 6.94% | 68.8% | 38.2% | 1 in 14.4 |
| 16 | 9 | 6.25% | 75.0% | 31.3% | 1 in 16 |
| 17 | 8 | 5.56% | 80.6% | 25.0% | 1 in 18 |
| 18 | 7 | 4.86% | 85.4% | 19.4% | 1 in 20.6 |
| 19 | 6 | 4.17% | 89.6% | 14.6% | 1 in 24 |
| 20 | 5 | 3.47% | 93.1% | 10.4% | 1 in 28.8 |
| 21 | 4 | 2.78% | 95.8% | 6.94% | 1 in 36 |
| 22 | 3 | 2.08% | 97.9% | 4.17% | 1 in 48 |
| 23 | 2 | 1.39% | 99.3% | 2.08% | 1 in 72 |
| 24 | 1 | 0.694% | 100.0% | 0.694% | 1 in 144 |
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 |
|---|---|---|
| ≥ 7 | 89.6% | 1 in 1.12 |
| ≥ 10 | 75.0% | 1 in 1.33 |
| ≥ 14 | 45.8% | 1 in 2.18 |
| ≥ 17 | 25.0% | 1 in 4 |
| ≥ 21 | 6.94% | 1 in 14.4 |
Reading the shape
Each die is uniform, but the sum is not. 2d12 has 144 ordered outcomes spread over 23 totals, and the counts rise toward the middle because a middle total can be assembled from more orderings. The curve is symmetric around 13 — for every way to roll 12 there is a mirrored way to roll 14 — which is why the standard deviation of 4.88 describes the spread on both sides equally.
Compare that with a single die: 1d12 is a flat line at 8.33% 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 2d12?
13. The formula is dice × (faces + 1) / 2 — 2 × (12 + 1) / 2 — which works for any fair die. The standard deviation is 4.88, so most rolls land between 8 and 18.
What is the most likely total on 2d12?
Exactly 13, at 8.33% — 12 of the 144 equally likely outcomes. The extremes (2 and 24) take 1 way each, or 0.694%.
How many possible outcomes does 2d12 have?
144 ordered outcomes — 122 — collapsing into 23 possible sums from 2 to 24. 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 2d12 has a single peak at 13 and why adding dice makes the distribution tighter rather than wider.