[HOE] Math question

[Robert Holland <robert@macauley.com>]

Is there a simple formula for calculating the average of a damage (not skill)
roll? I *think* the average of xdy damage (x rolls of a die with y sides) could
be expressed as 

x * (the sum for i = 0 to infinity of ( (1 / (y^i) ) * ( (y + 1) / 2 ) ) )

Where ( (y + 1) / 2 ) is the average of a single, non-open-ending die of y
sides, and (1 / (y^i) ) is the probability of the die open-ending i times.

I don't remember enough calculus to find a simple formula for that infinite
series, though.

Of course, for values of i greater than 2 the term is less than 1/20th of a
point in all cases (assuming standard die types), so just finding the formula
for i = 0 to 2 would yield sufficiently accurate results for any purpose I can
think of.

--Robert Holland