Dice Pool Calculator
The whole distribution, not just the average.
Work out Dice Pool. The whole distribution, not just the average. Free, with no account and nothing to install.
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
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
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/dice-pool-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Dice Pool Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/dice-pool-calculator" style="color:#64748b">Dice Pool Calculator</a> from The Calc Library</p>The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.