๐ฒ Dice Probability Calculator
Supports up to 6 dice (the number of combinations grows very quickly beyond that).
Specify the number of dice and the number of sides to calculate the exact probability distribution for every possible sum. Uses precise combinatorial math, useful for evaluating probabilities in board games and tabletop RPGs.
How to use
- Enter the number of dice (1 to 6).
- Select the number of sides (d4, d6, d8, d10, d12, d20).
- The probability of each possible sum is shown as a chart.
How the calculation works
Choose a number of dice and sides to see the exact probability of every total, found by counting all the combinations. The distribution for one die is combined with itself once per die (a convolution), counting the ways to reach each total. The results are exact, not approximations. With more dice, totals cluster around the middle and the chart approaches a bell curve (the normal distribution). Use it in board games or tabletop RPGs to find the chance of rolling a given total or better.
Worked example
Two six-sided dice (2d6) Total 7: 6/36 โ 16.67% (the most likely) Totals 2 and 12: 1/36 โ 2.78% each Three six-sided dice (3d6) Totals 10 and 11: 27/216 = 12.5% each Totals 3 and 18: 1/216 โ 0.46% each
Things to be aware of
- For the chance of a total or more, add up the probabilities of all totals at or above it.
- In Catan, 7 (the robber) is the most common roll, followed by 6 and 8.
- An RPG check of โ8 or more on 2d6โ succeeds 15/36 โ 41.7% of the time.
FAQ
How is the probability calculated?
It performs an exact combinatorial calculation (convolution) considering every possible combination of die faces โ this is an exact probability, not an approximation.
Whatโs the probability of rolling a 7 with 2d6 (two six-sided dice)?
6 out of 36 possible combinations sum to 7, giving a probability of 6/36 โ 16.67% โ the most likely sum for 2d6.
Why is 7 more likely than 2 or 12 with 2d6?
There are 6 combinations that sum to 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), while only 1 combination sums to 2 or 12 (1+1 or 6+6 respectively).