Dice Roller
Roll 1 to 10 dice, any type from d4 to d100, and see the exact odds for every possible sum of your current selection.
Press Roll.
Exact probability of every sum, 2d6
| Sum | Ways | Probability |
|---|---|---|
| 2 | 1 / 36 | 2.78% |
| 3 | 2 / 36 | 5.56% |
| 4 | 3 / 36 | 8.33% |
| 5 | 4 / 36 | 11.11% |
| 6 | 5 / 36 | 13.89% |
| 7 | 6 / 36 | 16.67% |
| 8 | 5 / 36 | 13.89% |
| 9 | 4 / 36 | 11.11% |
| 10 | 3 / 36 | 8.33% |
| 11 | 2 / 36 | 5.56% |
| 12 | 1 / 36 | 2.78% |
Rolls so far this session: 0. Every die is drawn independently with crypto.getRandomValues and unbiased rejection sampling.
Worked example
The tool's own default, 2d6, rolled with a fixed illustrative seed (your real rolls above use live randomness): 4 + 1 = 5.
2d6: the classic bell curve
Two six-sided dice produce 36 equally likely combinations, but only 11 distinct sums (2-12) -- so the sums in the middle are far more common than the extremes. 7 is the single most likely total, at exactly 6 out of 36 (16.67%).
| Sum | Ways | Probability |
|---|---|---|
| 2 | 1 / 36 | 2.78% |
| 3 | 2 / 36 | 5.56% |
| 4 | 3 / 36 | 8.33% |
| 5 | 4 / 36 | 11.11% |
| 6 | 5 / 36 | 13.89% |
| 7 | 6 / 36 | 16.67% |
| 8 | 5 / 36 | 13.89% |
| 9 | 4 / 36 | 11.11% |
| 10 | 3 / 36 | 8.33% |
| 11 | 2 / 36 | 5.56% |
| 12 | 1 / 36 | 2.78% |
Add a third die and the curve sharpens
3d6 spans sums 3-18 across 216 combinations, and the peak at 10-11 (27/216, 12.5% each) is proportionally taller than 2d6's peak -- more dice concentrates probability more tightly around the middle, the same reason a tabletop game might use 3d6 instead of a flat d20 for a bell-curve mechanic instead of a uniform one.
| Sum | Ways | Probability |
|---|---|---|
| 8 | 21 / 216 | 9.72% |
| 9 | 25 / 216 | 11.57% |
| 10 | 27 / 216 | 12.50% |
| 11 | 27 / 216 | 12.50% |
| 12 | 25 / 216 | 11.57% |
| 13 | 21 / 216 | 9.72% |
Showing the middle of the range (8-13); the full 3-18 range is in the tool above.
Frequently Asked Questions
Are the dice actually fair?
Yes -- each die is an independent draw from randomInt(1, sides) via crypto.getRandomValues and rejection sampling, so every face on every die has an exactly equal chance, and one die's result never influences another's.
Why isn't the sum of two dice evenly spread across all possible totals?
Because there's only one way to roll a 2 (1+1) but six ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) on two six-sided dice -- more combinations land on the middle sums than the extremes. The table below shows this exactly, computed by convolution rather than simulation.
What does "computed by convolution" mean?
It means the distribution is built by combining each die's 1-through-sides possibilities with the running total from the dice already accounted for, rather than by rolling millions of times and counting -- so the table is exact, not an approximation that happens to look close.
Why does the table sometimes show a summary instead of every row?
With many dice or a d100, the number of possible sums can run past a hundred rows, which stops being a readable table -- the summary shows the range and the single most likely sum instead, computed from the exact same math.
Does it work offline?
Yes, once loaded -- every roll happens in your browser.
Every result here is drawn live in your browser with cryptographically-secure randomness -- nothing is predetermined, saved, or replayable. See the Terms.