Tool
Dice Pool Roller
Roll a pool, count successes against a target number, and let dice explode.
Dice Pool Roller
Each die succeeds 40.0% of the time, so 6 dice average 2.40 successes.
Roll a handful of dice and count how many beat a target number, rather than adding them up. Set the pool size, the die type and the target, and optionally let maximum rolls explode into extra dice.
This is a fundamentally different question from the one the standard dice roller answers. Summing dice produces a bell curve around a middle value; counting successes produces a binomial distribution whose shape depends on the target, and the two behave nothing alike as you add dice.
The expected number of successes is shown before you roll, which is the number that actually tells you whether the pool is the right size.
How the Dice Pool Roller works — and why it's fair
Every die in the pool is rolled independently with an unbiased draw over its faces, using rejection sampling so that a d10 or a d20 is genuinely uniform rather than skewed low by a remainder. Each die is then compared against your target and counted as a success or not — no addition happens anywhere.
That makes the result a binomial variable: n independent trials, each succeeding with probability p, where p is the number of faces at or above the target divided by the total faces. A d10 with a target of 7 succeeds on 7, 8, 9 or 10, so p is 0.4 exactly, and a pool of six such dice averages 2.4 successes.
The shape is the interesting part. Summing 6d10 gives a tight bell curve around 33 — extreme totals are vanishingly rare. Counting successes on 6d10 at target 7 gives a spread where zero successes happens about 4.7% of the time and all six happens about 0.4%, and the whole range is regularly visited. Pool systems feel swingy because they genuinely are, in a way a summed roll is not.
Exploding dice change the model in a way worth stating precisely. When a die shows its maximum face it is rolled again and the extra die is added to the pool, and that extra die can itself explode. The number of dice is therefore no longer fixed, which is why a pool of six can return seven successes — the successes are counted over the original dice plus every explosion they generated.
Explosions add a decreasing tail rather than a fixed bonus. A d10 explodes on a 10, so one in ten dice generates an extra die, one in a hundred generates two, one in a thousand generates three. The expected pool size is n divided by (1 − 1/sides), which for six d10s is 6.67 dice rather than 6 — a real but modest increase that people consistently overestimate.
The tool marks exploded dice with a dashed border so the distinction between the original pool and its explosions stays visible in the result rather than being collapsed into a single count.
When the Dice Pool Roller is fair — and when it is not
What it does guarantee
- Every die in the pool is independent and uniform over its faces, with rejection sampling removing any remainder skew.
- The success probability per die is computed exactly from your target and die type, and shown before you roll.
- Explosions are recursive and unbounded in principle, so a genuinely hot pool is not artificially capped.
What it does not
- Successes are counted, not summed. A pool result carries no information about how high the individual dice rolled.
- The distribution is much wider than a summed roll of the same dice, so a zero-success result on a good pool is ordinary.
- Explosions are capped at a hundred recursions as a safety limit. That threshold is effectively unreachable but it is a limit.
Two worked examples
6d10, success on 7+
- Four faces of ten succeed, so p = 0.4 and the expected count is 2.4 successes.
- Zero successes happens about 4.7% of the time — roughly one roll in twenty-one.
- All six succeeding happens about 0.4%, or one roll in 244.
6d10, success on 7+, exploding on 10
- Each 10 adds another die, and that die can explode again.
- Expected pool size becomes 6 ÷ (1 − 0.1) = 6.67 dice rather than 6.
- Expected successes rise from 2.4 to about 2.67 — real, but far smaller than the drama of an explosion suggests.
Systems that count rather than sum
Tabletop systems built on dice pools are the direct case, and the reason the standard dice roller does not serve them: a pool system asks how many dice cleared a threshold, and totalling them produces a number the rules have no use for.
It is also a clean demonstration of the binomial distribution for anyone teaching probability, precisely because the parameters are visible and adjustable. Moving the target from 7 to 6 on a d10 changes p from 0.4 to 0.5 and shifts the whole distribution, which is much more legible than the same change expressed algebraically.
Game designers use it to feel out how a threshold mechanic behaves before committing to it. The gap between the expected count and the frequency of a zero-success result is the number that determines whether a system feels tense or punishing, and it is not obvious from the parameters alone.
For summed rolls with modifiers, the standard dice roller is the tool. For a die whose faces are words rather than numbers, or whose faces are deliberately unequal, the custom dice builder handles that.
Frequently asked questions
Why count successes instead of adding the dice?
Because that is what pool-based systems ask for. A total is a different question with a different distribution, and the standard dice roller answers that one.
How is the success probability calculated?
Faces at or above your target, divided by the number of faces. A d10 at target 7 has four qualifying faces, so p is exactly 0.4.
Why can I get more successes than dice?
Explosions. A maximum face adds another die to the pool, and that die is counted too — so six dice can produce seven successes.
How much do explosions actually add?
Expected pool size becomes n ÷ (1 − 1/sides). For six d10s that is 6.67 dice, a 11% increase — much less than the excitement of an explosion implies.
Can a chain of explosions run forever?
In principle it is unbounded; in practice the tool caps recursion at a hundred, which corresponds to odds so remote it will never be reached in play.
Why do pool results feel so swingy?
Because a binomial spread is genuinely much wider than the bell curve of a summed roll. Zero successes on a decent pool is a normal outcome, not bad luck.
Are the dashed dice different somehow?
Only in origin — they are the explosions. They are rolled and counted identically to the original pool.
Does the target apply to exploded dice too?
Yes. Every die in the pool, original or exploded, is checked against the same target.
What is the largest pool I can roll?
Fifty dice, which is well beyond any system in normal use and enough to see the binomial shape emerge from a single roll.