---
title: "Dice Pool Calculator: Success Odds | Dice Parlor"
description: "Roll a pool of dice and count the hits: the exact chance of at least k successes, with exploding dice and rerolled ones, as a table and a chart."
url: https://diceparlor.me/dice-pool-calculator/
---

# Dice pool calculator

Roll a handful of dice and count every die that reaches the target. Find the chance of scoring at least as many successes as you need, with exploding dice and rerolled ones.

## How to use it

Set how many dice you roll, how many sides they have and the lowest face that counts as a success; 5 on a six-sided die means a 5 or a 6. Then set how many successes you need. The brass plate shows the chance of reaching it, and the table lists every count: **exactly** is the chance of that many and no more, **at least** adds up that many or more.

## Exploding dice and rerolled ones

With **exploding dice**, a die that shows the explode face or higher scores as usual and you roll one bonus die, which can explode again, so a pool can beat its own size. **Reroll once** rolls any 1 again, bonus dice included, and the second result stands.

Each die's chances are worked out exactly, with a short series for the explosions, then combined for the whole pool by convolution. Nothing is simulated.

## Sources

- Charles M. Grinstead and J. Laurie Snell, *Introduction to Probability*, 2nd edition (American Mathematical Society): §7.1 “Sums of Discrete Random Variables” for combining the dice by convolution, and §10.1 “Generating Functions for Discrete Distributions” for the explosion series. Free GNU FDL edition on [Dartmouth's site](https://math.dartmouth.edu/~prob/prob/prob.pdf).

## Questions

**Does a bonus die from an explosion count as a success?**

Only if it reaches the target, like any other die. If dice explode on a face below the target, say on 6 with success on 8, that roll adds a bonus die but scores nothing itself.

**Why does the table stop with exploding dice?**

Explosions can go on and on, so there is no highest count. The table stops once the chance of going further drops below 1 in 100,000, and the at-least column still includes that last sliver.

**Why is my chance 0% when I need more successes than dice?**

Without explosions every die scores at most one success, so a pool of six dice can never reach seven. Turn on exploding dice if your game allows it.