On Exploding Dice
Return to Savage Worlds
Return to Universal Resources
Exploding dice (that is, where if you roll the highest value you roll again and add, and so on) are tricky. Fortunately, the formula for calculating their expected average value isn't too complicated:
x² + x———
2x - 2
Or an easier way when doing it by hand on a calculator: "x times x+1 divide by x-1 divide by 2"
For convenience, here are the most common dice:
- d3 = 3.00
- d4 = 3.33
- d6 = 4.20
- d8 = 5.14
- d10 = 6.11
- d12 = 7.09
- d20 = 11.05
Weird enough, an exploding d2 (a coin, basically) sums to 3.00 as well! Thanks to Bill Stoddard for pointing that out.
Q: But AnyDice shows something slightly different!
A: Yeah, AnyDice is wrong. It only factors in a single explosion, not the possibility of endless explosions.
Savage Worlds Success Chart
Where the above applies to any exploding dice, this table is specifically a useful resource for Savage Worlds. It shows the odds of basic success and a single raise, with no modifiers, for the various possible die types.
| Extra | Success | Raise |
|---|---|---|
| d4 | 25% | 6% |
| d6 | 50% | 14% |
| d8 | 63% | 13% |
| d10 | 70% | 30% |
| d12 | 75% | 42% |
| Wildcard | Success | Raise |
| d4 | 62% | 19% |
| d6 | 75% | 26% |
| d8 | 81% | 25% |
| d10 | 85% | 40% |
| d12 | 88% | 50% |
Return to Savage Worlds
Return to Universal Resources