Some one already did it yay!

So what this is say when calculating the values for averages in exploding dice the average value is equal to the Die's average value (one half of the die's highest value + one eg a D6 is 3.5) Multiplied by N/(N-1)

Where N is the Die type:
((N+1)/2) (N/(N-1))

A listing for reference:

D4 = 3.33333333333333
D6 = 4.2
D8 = 5.14285714285714
D10 = 6.11111111111111
D12 = 7.09090909090909

OR

D4 = 3 & 1/3
D6 = 4 & 1/5
D8 = 5 & 1/7
D10 = 6 & 1/9
D12 = 7 & 1/11

edit for formula

I've always just used an approximation of the Average on the Die + .5. Glad to see that it's very close to the actual numbers. I may try to build these in to my Spreadsheet of Calculations.

John

its but more than the averages if you take a second look, its most significant for smaller dice

the average of 3d4 non exploding is 7.5, and the average of exploding 3d4 is 10

Yeah you have a good point for the d4 and to a lesser extent the d6. Most of the rest are approximated by average + .5. I'll try to use one significant digit in my calculations spreadsheet. Though there's probably not a lot of people with d4 stats

John

the average number is off by at least .5 in every die type

D4 = 3 & 1/3 VS 2.5
D6 = 4 & 1/5 VS 3.5
D8 = 5 & 1/7 VS 4.5
D10 = 6 & 1/9 Vs 5.5
D12 = 7 & 1/11 Vs 6.5

but if your going to use the numbers in the first one then you should be fine

I'm pretty sure his averages are using exploding dice (2.5 is the avg for non-exploding d4 but 3.33 is the avg for exploding d4)...

My current spreadsheet uses straight averages. I'll build in the 'exploding averages' for the ability score dice rolls in my sheet. I'll use the calculated values above rounded to 1 significant digit after the decimal point.

Thanks for finding the site for those.

John

oh i cant open his sheet from home, it sounded like he didnt see the difference between avg and explode on higher dice

Nope I do. I was just saying that for a 'ball park' I've always considered the average of an exploding die to be the "regular Average + .5". Which is pretty close for d6 and above.

john

ahh i didnt understand you at all there gotcha now