🎯

Dice Pool Success Probability Calculator

For dice-pool RPGs, find the chance of scoring at least one success and the expected number of successes when rolling a handful of dice.

Number of dice

Die type

Success on a roll of at least

Successes needed

Loading calculator…

How it works

Per-die p = (sides − target + 1) ÷ sides · P(≥1) = 1 − (1 − p)^dice · Expected = dice × p

Dice-pool systems like World of Darkness roll a handful of dice and count how many beat a target number, so each die is an independent Bernoulli trial with success probability (sides − target + 1) ÷ sides. The chance of at least one success is one minus the chance every die fails, while the number of successes follows a binomial distribution — which is how this tool computes the odds of clearing a required threshold. Expected successes, simply dice × per-die chance, is the fastest sanity check on whether a pool is big enough.

Worked example

Six d10s needing a 7 or higher: each die succeeds on 4 of 10 faces (7,8,9,10), so p = 0.4 and expected successes are 6 × 0.4 = 2.4. The chance of at least one success is 1 − 0.6^6 = 95.3%, and with one success needed that is the headline number.

Sources: Binomial distribution (Wikipedia)

Frequently asked questions

What is a dice pool?

A mechanic where you roll several dice at once and count how many meet or beat a target number, rather than summing them. Systems like World of Darkness and Shadowrun use pools of d10s or d6s.

How is the chance of enough successes found?

Each die is an independent success-or-fail trial, so the count of successes follows the binomial distribution. This calculator sums the probability of falling short and subtracts it from one to get the chance of meeting the requirement.

Does this handle exploding dice or botches?

No. It assumes plain dice with a fixed success threshold. Exploding dice (rerolling max faces) raise the effective per-die chance, and botch rules subtract successes — both need system-specific adjustments.

Related calculators

Gacha Pull Probability Calculator

Chance of pulling a featured unit (or several copies) in N gacha pulls at a flat rate, with an optional spark or exchange: pulls for 50%, 90%, 99% or your own target, expected pulls and copies, the guarantee point, premium currency and cash still needed, and the full copy-count distribution.

Loot Box Expected Value Calculator

Expected value of a loot box, case, pack or crate from its drop chances and item values — three quick tiers or your own full drop table — compared with the price plus any key cost, after marketplace fees. Shows the house edge, the spread per box, what N boxes cost and return, the chance of at least one rare and of breaking even, boxes and money per rare, a pity guarantee and the rare value needed to break even.

Dice Roll Odds Calculator

Find the odds of any dice total — the chance of rolling exactly a sum, at least it, or at most it, plus the most likely roll and the average.

Binomial Probability Calculator

Find the probability of exactly, at most, or at least k successes in n independent trials, each with the same success probability p.

This calculator is for educational purposes. Double-check important results before acting on them.