Exploding dice

At the table

Exploding (or “open-ended”) dice add another roll when you hit the die’s maximum face, and keep adding until you stop exploding. Savage Worlds uses this on raising and damage; many house rules explode d4s or d6s on max.

Try it

In the playground, open this recipe in the playground and click Run. Output shows the distribution of one d4 exploding up to two extra rolls on max.

The script

↗output("exploded", explode(d(4), 2))

• explode(die, max_depth) sums the initial roll plus rerolls while the face equals the die’s maximum.
• Increase max_depth for longer tails; very high depths widen the support quickly.

For multiple exploding dice, build a pool of exploded dice (e.g. sum independent explode(d(6), 2) via convolution) or roll pools with per-die rules via pool_map.

exploded · DieRoll · mean 3.281