Free TTRPG dice probability calculator. Build a pool (e.g. 3d6 + 1d4 + 2) and a target difficulty; outputs probability of hitting the target, mean, distribution histogram, and supports advantage / disadvantage and exploding dice mechanics.
Built and maintained by Paul Clark, Redmoon Software · Last verified · Sources
Use when designing custom monsters, homebrew rules, or just sanity-checking your party's odds. Especially valuable for indie game designers balancing core mechanics.
AnyDice is the legacy reference and supports far more — but its UI is intimidating. This tool covers 90% of common cases without learning a scripting language.
Green bars meet or exceed the target.
The probability mass function (PMF) of the sum of N dice is computed by convolution. Modifiers shift the PMF; advantage/disadvantage recomputes from two independent rolls.
Success chance is the cumulative probability of the sum (plus modifier) meeting or exceeding the target.
The distribution chart shows every possible total, with bars above the target highlighted in green.
Yes — roll twice and take highest/lowest. The PMF is recomputed accordingly.
Not yet — it's on the list. Use a standard pool with a slightly larger die size as a rough approximation.
The mean is the long-run average total you would roll, useful for balancing damage or setting target difficulties. For a single fair die it sits halfway between the lowest and highest face, such as 3.5 on a d6.
Adding several dice together makes middle totals far more likely than extreme highs or lows, because many die combinations produce a middling sum but only one produces the maximum. This clustering is why 3d6 feels more consistent than a single d18.
Input
3d6 + 5 vs target 15, standard roll.
Output
78.2% success. Mean total: 15.5.
3d6 has mean 10.5, range 3–18; adding +5 gives mean 15.5, range 8–23. To beat 15 you need a base roll ≥ 10, which the cumulative distribution puts at ~78%.
The probabilities here are computed by convolving the full outcome distribution rather than by rolling dice in software. That means they are exact — there is no sampling error, and running it twice gives the identical answer.
It matters because Monte Carlo estimates of tail probabilities are unreliable at exactly the point people care about them. The chance of a critical outcome or of failing three saves in a row is small, and a simulation needs a very large number of trials before it estimates a small probability well. Enumeration has no such problem.
One d20 is uniform: every face is equally likely, so a +1 modifier is worth a flat 5% across the whole range. Three d6 is not — the sum is a bell, 10 and 11 come up far more often than 3 or 18, and a +1 is worth much more near the middle of the curve than at either end.
That is the practical difference between the two systems and it is why a modifier means something different in each. In a d20 game a bonus is a constant improvement; in a dice-pool or 3d6 game the same bonus swings a marginal roll dramatically and does almost nothing on a roll that was already hopeless.
Target numbers behave the same way. Moving a 3d6 target from 10 to 11 changes the odds far more than moving it from 16 to 17.
The method behind this tool, so you can check it rather than take it on trust.
Exact enumeration, not simulation.
Probabilities are computed by convolving the full outcome distribution, so they are exact rather than sampled — there is no Monte Carlo error in these numbers.
Most GMs choose a target number and hope it feels fair. Reverse the process — decide the success rate you want, then read the target off the curve — and difficulty stops being a guess.
How dice pools really behave — bell curves vs. flat d20s, what advantage actually does to your odds, exploding dice, and how to set fair target numbers.
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