Dice Pool Success Calculator
Many games roll a handful of dice and count how many beat a target rather than adding them up, and that behaves quite differently from a single roll: the average rises steadily with the pool while extreme results get rarer, so a big pool is reliable rather than lucky. This computes the exact distribution of successes, the chance of at least one, and the average — all counted rather than simulated.
What this generator does
Each die succeeds independently with a fixed chance, so the number of successes follows the binomial distribution. The tool computes the chance of every possible count, the cumulative chance of at least each, and the average — checking the whole distribution sums to one.
How to use this tool
- Enter how many dice, how many sides, and the target number.
- Read the average and the chance of at least one success.
- Look down the table for the chance of exactly a given number.
- Lower the target by one and see how much it changes.
Understanding the controls
- How many dice
- The pool size. Doubling it doubles the average but makes an unusually good or bad result much less likely.
- Sides per die
- Ten in many systems, six in others. Every die in the pool is assumed the same.
- Success on
- The target number: this face or higher counts. Lowering it by one changes the odds far more than adding a die does at typical pool sizes.
Common use cases
- Working out the odds in a success-counting dice system
- Balancing a game where difficulty is a target number
- Comparing a bigger pool against an easier target
- Checking whether a house rule makes a task too easy
- Explaining why large pools produce consistent results
How this generator works
Every die is an independent trial that succeeds when it rolls the target or higher, so the chance of a single success is the number of qualifying faces over the total. The count of successes is then binomial: the ways of choosing which dice succeeded, times the chance of that pattern. Before display the whole distribution is confirmed to sum to exactly one, every entry is recomputed from the binomial coefficients, and the average is calculated from the distribution itself and compared against the closed form.
Randomness and fairness
Nothing here is random. This computes the odds exactly rather than rolling anything — a roller is a different tool.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Exploding dice, where a maximum roll grants another die, are not modelled and change the distribution substantially.
- Every die in the pool is identical, so mixed pools need a different calculation.
- Botches and critical failures, which many systems layer on top, are outside the plain success count.
- Rerolls of any kind change the odds and are not accounted for.
Privacy and your data
The odds are computed in your browser and your pool settings are never transmitted, stored or included in analytics.
Related generators
- Dice Pool RollerRoll a pool of same-sided dice and count how many meet a success threshold.
- Dice Probability CalculatorThe exact distribution of any dice total — every outcome counted, not simulated, with the odds of rolling at least a given number.
- Card Draw Probability CalculatorExact odds of drawing what you need from a deck, bag or pool — without replacement, which is the part people get wrong.
- Ability Score Odds CalculatorGives the exact distribution for rolling dice and dropping the lowest, and the real chance of a maximum somewhere in a set.
- Multiple Custom Dice RollerRoll a mixed pool of differently-sided dice at once, like 2d6 + 1d8, plus a modifier.