by **Rayhawk** » Wed Jul 09, 2008 1:52 am

I actually calculated out all the die roll probabilities, including the critical-success possibility of bonus dice earning bonus dice ad infinitum; in all cases they round to half the number of sides, plus one.

avg die roll (once) = (d+1)/2

avg die roll (exploding) = (d+d^2)/(2d-2)

avg d6 roll (exploding) = (6+36)/(12-2) = (42/10) = 4.2

avg die roll (exploding d6es) = (d+1)/2 + 4.2/d

avg d4 (no bonus dice): (4+1)/2 = 2.5 ~ 3

avg d6: (6+1)/2 + 4.2/6 = 3.5 + .7 = 4.2 ~ 4

avg d8: (8+1)/2 + 4.2/8 = 4.5 + .525 = 5.025 ~ 5

avg d10: (10+1)/2 + 4.2/10 = 5.5 + .42 = 5.92 ~ 6

avg d12: (12+1)/2 + 4.2/12 = 6.5 + .35 = 6.85 ~ 7

avg d20: (20+1)/2 + 4.2/20 = 10.5 + .21 = 10.71 ~ 11

So there you go, for every die you can use the value (d/2)+1.