On Exploding Dice

Return to Savage Worlds


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.


Return to Savage Worlds