What a success pool measures
A dice pool is not a total. Each die is a separate yes-or-no trial: it succeeds when its face is at least the target. With eight d6 and a target of 5, faces 5 and 6 succeed, so one die has probability 2/6 = 1/3. The useful output is the count of successes, not the sum of all faces. That makes the tool fit tabletop checks such as “how many clues were found?” or “how much progress was made?” where several successes matter.
Formula and distribution
For n dice, success chance p, and threshold t on an s-sided die, p = (s − t + 1) / s. The expected successes are n × p. The exact chance of k successes is C(n,k)p^k(1−p)^(n−k). The browser does a real roll rather than merely showing that expectation. The formula is still useful for judging difficulty before a session: changing a d6 target from 5+ to 4+ raises p from one third to one half.
Worked numbers
Take 8d6 at 5+. Suppose the visible faces are 1, 5, 6, 3, 5, 2, 4, 6. Four faces meet or exceed 5, so the result is four successes. The expected value was 8 × 1/3 = 2.67, thus four is above average but ordinary. The probability of at least one success is 1 − (2/3)^8, about 96.1%. That number answers a different question from the displayed count: reliability, rather than how well this particular attempt went.
Targets, bonuses, and limits
A bonus die changes n; a target adjustment changes p. They are not interchangeable. Adding one die to 8d6 at 5+ adds one third of an expected success. Lowering the target from 5+ to 4+ adds 8 × (1/2−1/3) = 1.33 expected successes. This page deliberately does not implement exploding dice, rerolls, botches, or mixed dice sizes, because those alter the event model. Apply those rulebook steps after the base pool or use a system-specific roller.
Common table errors
Do not count a 4 as a success on a 5+ test, and do not treat the target as a number of successes required. “Target 5” describes a die face; “need 3 successes” is a later pass/fail rule. Check that the pool uses the die size shown in the rules: a 5+ on d10 succeeds 60% of the time, while 5+ on d6 succeeds 33.3%. The page accepts up to 100 dice to keep output readable and avoid turning a table check into an accidental bulk simulation.
How it differs
A standard dice roller adds faces, which is appropriate for 2d6 or damage totals. This counter classifies each face against a threshold and retains the roll list so the count can be audited. It also differs from a probability calculator: it produces one fresh outcome, not an analytic likelihood table. Use it when the game calls for an actual pool roll and the group needs a transparent success count.
Reading a pool at the table
Read the individual faces before announcing the count. That habit catches a mistyped target and makes shared rolls auditable. If a rule says sixes count twice, first count ordinary successes, then add the extra success for every six; do not replace the threshold formula with a different die. If a rule says a one cancels a success, record both quantities, because cancellation is a game rule layered over the independent successes. For example, 1, 5, 6, 1, 5 at 5+ has three base successes; a “ones cancel” rule would reduce it to one. This tool intentionally exposes the faces so those variants can be resolved openly. For planning, compare the chance of meeting a required total with the expected count: an average of 2.67 does not guarantee two successes in one roll. Variance is n p (1−p), so 8d6 at 5+ has variance about 1.78 and results around two or three are especially common.
Set the pass rule after counting
A pool result becomes a game outcome only when the table states the required number of successes. If a lock needs two successes, faces 5, 2, 6, 1, 4 on d6 at 5+ produce two and open it; the same faces fail a three-success requirement. Keep that pass rule separate from the face threshold. The counter classifies dice, but cannot infer whether a game spends extra successes on speed, damage, information, or nothing.