Dice OutcomesHow the odds are calculated
The calculator counts every equally likely combination of the dice exactly — it does not simulate rolls. Counts are kept as whole numbers, even when there are more combinations than a normal number can hold, and only converted to a percentage for display. That's why results are shown as an exact fraction too.
Worked examples
- Rolling 15 or higher on 1d20: 6 of the 20 faces qualify, so the chance is 6/20 = 30%.
- Rolling exactly 7 on 2d6: 6 of the 36 combinations add up to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), about 16.67%.
- Rolling 10 or more on 2d6: also 6 of 36, about 16.67%.
- Rolling 7 or more on 2d6: 21 of 36 combinations, exactly 21/36 (7/12) — about 58.33%.
- Rolling 15 or more on 1d20+5: the die needs 10 or higher, 11 of 20 faces, exactly 11/20 = 55%.
- The average total of 2d6 is 7; for 2d6+3 the whole distribution shifts up by 3, so the average is 10.
Supported pools and limits
You can use any pool the dice roller accepts — dice added together plus one modifier, up to 100 dice with 2–100 sides each. Each calculation also has a work budget; pools beyond it are declined with an explanation instead of slowing your browser down. Rules like exploding dice, rerolls or keeping the highest few dice aren't supported yet.
A high probability isn't a guarantee: any single roll can still land on an unlikely result.