1d100 Dice Probability — Full Distribution and Odds
Percentile rolls and loot tables. One hundred faces flatten the distribution completely — every result is 1%. The sum runs from 1 to 100, the average is 50.5, and the most likely total is 1. 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 |
|---|---|---|---|---|---|
| 1 | 1 | 1.00% | 1.00% | 100.0% | 1 in 100 |
| 4 | 1 | 1.00% | 4.00% | 97.0% | 1 in 100 |
| 6 | 1 | 1.00% | 6.00% | 95.0% | 1 in 100 |
| 9 | 1 | 1.00% | 9.00% | 92.0% | 1 in 100 |
| 11 | 1 | 1.00% | 11.0% | 90.0% | 1 in 100 |
| 14 | 1 | 1.00% | 14.0% | 87.0% | 1 in 100 |
| 16 | 1 | 1.00% | 16.0% | 85.0% | 1 in 100 |
| 19 | 1 | 1.00% | 19.0% | 82.0% | 1 in 100 |
| 21 | 1 | 1.00% | 21.0% | 80.0% | 1 in 100 |
| 24 | 1 | 1.00% | 24.0% | 77.0% | 1 in 100 |
| 26 | 1 | 1.00% | 26.0% | 75.0% | 1 in 100 |
| 29 | 1 | 1.00% | 29.0% | 72.0% | 1 in 100 |
| 31 | 1 | 1.00% | 31.0% | 70.0% | 1 in 100 |
| 34 | 1 | 1.00% | 34.0% | 67.0% | 1 in 100 |
| 37 | 1 | 1.00% | 37.0% | 64.0% | 1 in 100 |
| 39 | 1 | 1.00% | 39.0% | 62.0% | 1 in 100 |
| 42 | 1 | 1.00% | 42.0% | 59.0% | 1 in 100 |
| 44 | 1 | 1.00% | 44.0% | 57.0% | 1 in 100 |
| 47 | 1 | 1.00% | 47.0% | 54.0% | 1 in 100 |
| 49 | 1 | 1.00% | 49.0% | 52.0% | 1 in 100 |
| 52 | 1 | 1.00% | 52.0% | 49.0% | 1 in 100 |
| 54 | 1 | 1.00% | 54.0% | 47.0% | 1 in 100 |
| 57 | 1 | 1.00% | 57.0% | 44.0% | 1 in 100 |
| 59 | 1 | 1.00% | 59.0% | 42.0% | 1 in 100 |
| 62 | 1 | 1.00% | 62.0% | 39.0% | 1 in 100 |
| 64 | 1 | 1.00% | 64.0% | 37.0% | 1 in 100 |
| 67 | 1 | 1.00% | 67.0% | 34.0% | 1 in 100 |
| 70 | 1 | 1.00% | 70.0% | 31.0% | 1 in 100 |
| 72 | 1 | 1.00% | 72.0% | 29.0% | 1 in 100 |
| 75 | 1 | 1.00% | 75.0% | 26.0% | 1 in 100 |
| 77 | 1 | 1.00% | 77.0% | 24.0% | 1 in 100 |
| 80 | 1 | 1.00% | 80.0% | 21.0% | 1 in 100 |
| 82 | 1 | 1.00% | 82.0% | 19.0% | 1 in 100 |
| 85 | 1 | 1.00% | 85.0% | 16.0% | 1 in 100 |
| 87 | 1 | 1.00% | 87.0% | 14.0% | 1 in 100 |
| 90 | 1 | 1.00% | 90.0% | 11.0% | 1 in 100 |
| 92 | 1 | 1.00% | 92.0% | 9.00% | 1 in 100 |
| 95 | 1 | 1.00% | 95.0% | 6.00% | 1 in 100 |
| 97 | 1 | 1.00% | 97.0% | 4.00% | 1 in 100 |
| 100 | 1 | 1.00% | 100.0% | 1.00% | 1 in 100 |
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 |
|---|---|---|
| ≥ 11 | 90.0% | 1 in 1.11 |
| ≥ 26 | 75.0% | 1 in 1.33 |
| ≥ 51 | 50.0% | 1 in 2 |
| ≥ 76 | 25.0% | 1 in 4 |
| ≥ 91 | 10.0% | 1 in 10 |
Reading the shape
Each die is uniform, but the sum is not. 1d100 has 100 ordered outcomes spread over 100 totals, and the counts rise toward the middle because a middle total can be assembled from more orderings. The curve is symmetric around 50.5 — for every way to roll 49.5 there is a mirrored way to roll 51.5 — which is why the standard deviation of 28.87 describes the spread on both sides equally.
Compare that with a single die: 1d100 is a flat line at 1.00% 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 1d100?
50.5. The formula is dice × (faces + 1) / 2 — 1 × (100 + 1) / 2 — which works for any fair die. The standard deviation is 28.87, so most rolls land between 21 and 80.
What is the most likely total on 1d100?
1 and 2, at 1.00% — 1 of the 100 equally likely outcomes. The extremes (1 and 100) take 1 way each, or 1.00%.
How many possible outcomes does 1d100 have?
100 ordered outcomes — 1001 — collapsing into 100 possible sums from 1 to 100. 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 1d100 has a plateau at 1 and 2 and 3 and 4 and 5 and 6 and 7 and 8 and 9 and 10 and 11 and 12 and 13 and 14 and 15 and 16 and 17 and 18 and 19 and 20 and 21 and 22 and 23 and 24 and 25 and 26 and 27 and 28 and 29 and 30 and 31 and 32 and 33 and 34 and 35 and 36 and 37 and 38 and 39 and 40 and 41 and 42 and 43 and 44 and 45 and 46 and 47 and 48 and 49 and 50 and 51 and 52 and 53 and 54 and 55 and 56 and 57 and 58 and 59 and 60 and 61 and 62 and 63 and 64 and 65 and 66 and 67 and 68 and 69 and 70 and 71 and 72 and 73 and 74 and 75 and 76 and 77 and 78 and 79 and 80 and 81 and 82 and 83 and 84 and 85 and 86 and 87 and 88 and 89 and 90 and 91 and 92 and 93 and 94 and 95 and 96 and 97 and 98 and 99 and 100 and why adding dice makes the distribution tighter rather than wider.