How are these probabilities computed?

By exact enumeration, not random simulation. The tool builds the full probability distribution of each die and combines them with convolution or by enumerating outcomes, so the results are precise rather than approximate sampled estimates.

How do exploding dice work?

When a die rolls its maximum face, it explodes — you roll it again and add the result, repeating on each new maximum. This calculator caps the explosion depth to keep the math finite, which captures virtually all of the probability mass since deep chains are vanishingly rare.

What is a dice pool success count?

In pool systems you roll many dice and count how many meet or beat a target number. Games like Shadowrun and World of Darkness use this. The tool computes the chance of getting at least a given number of successes using the binomial distribution per die.

How does keep-highest or keep-lowest work?

You roll several dice and keep only the best or worst one — the classic advantage and disadvantage mechanic. The calculator enumerates every combination of dice, applies the keep rule, and tallies the resulting distribution exactly.

Why does the expected value matter?

The expected value is the long-run average result, which helps designers balance mechanics and helps players judge a roll. Combined with the full distribution, it tells you not just the average but how spread out and how swingy a mechanic is.

Dice Tower & Anydice Probability Calculator

Designing or playing a system with unusual dice mechanics means knowing the real odds, not guessing. This calculator computes exact probabilities for exploding dice, keep-highest or keep-lowest rolls, and dice-pool success counting, using enumeration and closed-form distributions rather than random simulation.

How it works

Each mechanic uses a precise method:

exploding   : a die at max face rerolls and adds, recursively (depth-capped)
keep N of M : enumerate all M-die outcomes, keep best/worst N, tally the sum
pool success: per die P(hit) = (faces ≥ target)/faces; combine via binomial
expected    : Σ outcome × probability over the full distribution

For exploding and keep mechanics the tool builds the complete probability distribution and reports it as a table. For pool systems it returns the chance of reaching at least your target number of successes, the most common question at the table.

Example and tips

Rolling 4d6 and keeping the highest 3 — the classic ability-score method — has an expected value of about 12.24, not 10.5, because dropping the lowest die shifts the average up. Exploding a d6 raises its mean from 3.5 to 4.2 once chained explosions are included. Use the distribution table to spot swingy mechanics: a high expected value with a wide spread feels very different at the table from a tight one.