How much higher is the average with exploding dice?

It depends on the die size: a d6 averages 4.2 per die instead of 3.5 (about 20% more), because a 1-in-6 chance of exploding is relatively large. A d20 only averages about 11.05 instead of 10.5 (about 5% more), since its maximum face is rarer.

Exploding Dice Roller

Rolls a set of dice using the common tabletop-RPG 'exploding dice' house rule: any die that lands on its maximum face is rerolled and added again, chaining for as long as maximum faces keep appearing (capped so it can never run forever). Described in system-neutral terms and not tied to any specific published game.

Sides per die

Number of dice

Your roll will appear here.

What this generator does

Rolls dice where the maximum result triggers another roll that adds to the total, so a lucky die can keep going. It is why some systems have no upper limit on a roll despite using ordinary dice.

How to use this tool

Set the number of sides and dice.
Press roll.
See every individual roll plus the running total.

Worked examples

A single d6 that keeps going: Roll shows 6, then 6 again, then 4 — the chain stops at the first non-maximum face, and the total for that one die is 6 + 6 + 4 = 16.

Common use cases

Tabletop RPGs using an exploding-dice house rule
Adding extra swing to a dice game
Teaching probability with a fun twist

How this generator works

Each die is rolled from your browser's Web Crypto generator, and any die landing on its maximum face is immediately rolled again, with the new result added on and the check repeated — a chain that continues for as long as maximum faces keep appearing. The expected total per die works out to s(s+1) / (2(s-1)) for an s-sided die: for a d6, that's 4.2 rather than the flat 3.5 a normal d6 averages, a 20% boost from the chance of chaining. Each die's chain is capped at 100 extra rolls so a vanishingly unlikely unbroken run of maximums can never hang the page.

Limitations and good to know

Because a maximum result rolls again, there is no theoretical ceiling on the total — very high results are rare but not impossible. The average is higher than the same dice rolled without the rule (about 20% higher for a d6, less for a larger die, since a bigger die's maximum face comes up less often).
Each die's own chain is capped at 100 additional rolls, purely so an astronomically unlikely unbroken run of maximums cannot hang the page — you will never see this limit reached.

Frequently asked questions

How much higher is the average with exploding dice?: It depends on the die size: a d6 averages 4.2 per die instead of 3.5 (about 20% more), because a 1-in-6 chance of exploding is relatively large. A d20 only averages about 11.05 instead of 10.5 (about 5% more), since its maximum face is rarer.