Dice Pool Calculator
The whole distribution, not just the average.
The whole distribution, not just the average.
Expected successes
2.4
40% per die · 95.33% chance of at least one
A dice pool is a binomial distribution, and the useful output is the whole shape rather than the average. Six dice needing 7+ on a d10 average 2.4 successes and deliver anything from zero to six — which is the difference between a system that feels swingy and one that feels reliable. The standard deviation says how swingy. It grows with the square root of the pool size while the average grows linearly, so larger pools are proportionally more consistent — a 20-dice pool almost never disappoints, and a 3-dice pool routinely does. The at-least-one figure is usually the one that matters at the table, because most systems care whether you succeeded rather than by how much.
How the Dice Pool Calculator works
Probability of each number of successes when rolling a pool of dice against a target, with the standard deviation. The shape matters more than the average. It is what makes a system feel swingy or reliable.
Also known as: chance of successes in a dice pool · world of darkness odds · how many dice do i need · probability of at least one success
Where to go next
The Dice Pool question rarely arrives on its own. These are the ones that usually come with it:
- Drop Rate Calculator — At the expected number of attempts, you are only 63% there.
- Critical Hit Calculator — Tells you which stat to raise next.
- Gacha Pity Calculator — Pity changes the maths completely.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
How do dice pools work?
Roll several dice and count how many meet or beat a target number. It is a binomial distribution, so the number of successes has a predictable spread around the average.
Why does the spread matter?
Because the average alone hides how often you get nothing. Six dice averaging 2.4 successes still fail entirely about 5% of the time, and that failure rate is what players actually feel.
Are larger pools more consistent?
Proportionally, yes. The standard deviation grows with the square root of the pool while the average grows linearly, so a 20-dice pool almost never disappoints and a 3-dice pool routinely does.
What is a botch?
In several systems, every die showing 1 — a critical failure. It is vanishingly rare with a large pool: six d10 all showing 1 is one chance in a million.
Does exploding dice change this?
Substantially, and it is not modelled here. Dice that re-roll on a maximum result produce an unbounded distribution with a longer tail and a higher average.
Put this calculator on your own site
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Related calculators
Drop Rate Calculator
At the expected number of attempts, you are only 63% there.
OpenCritical Hit Calculator
Tells you which stat to raise next.
OpenGacha Pity Calculator
Pity changes the maths completely.
OpenPercentage Calculator
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Open