When a die rolls its maximum, it "explodes" — roll again and add. Pick a die and a count; the chain continues until a non-max result.
An exploding die is a single die that, on its maximum face, triggers another roll of the same die which is added to the total. If the new die also shows max, it explodes again — and so on. There's no upper bound on a single chain, though the probability of long chains drops geometrically (1/6 chance per d6 step, 1/10 per d10, etc.).
An exploding d6 has an average of 4.2 instead of 3.5 — about a 20% bump. The expected value of an exploding dN is N/(N–1) × (N+1)/2. Critically, the variance grows: an exploding d6 has a standard deviation of roughly 2.4 vs 1.7 for a flat d6, so outcomes are more swingy.
Like exploding, but each subsequent die after the first has 1 subtracted from it. Caps the runaway potential.
Some systems explode on more than just the maximum — e.g. d10!>=8 explodes on 8, 9 or 10. Useful for dice pools where you want frequent re-rolls.
The main app handles standard formulas — 1d20+5, 3d6+2, advantage, keep-highest, modifiers — with history and saved formulas. (Heads up: the main app does not yet parse the ! exploding-notation; this page is a focused tool for that case.)