Re: [HOE] Math question

[Jason Young <jason_d_young@yahoo.com>]

Robert,

Your series looks correct to me. I haven't done high-end math in about 12
years, so I'm not going to be any help with the simple formula. I wanted
to do something like that, too, but realized I would spend hours simply
trying to resurrect my math skills and still might end up without an
answer. I chose not to do that.

What I just happen to have, though, is a page I wrote for Savage Worlds.
If you look at the chart for Averages for Extras (the top, left chart on
the page), you'll get the approximate results for 1dy. You can then
multiply for x's larger than that.

http://www.aracnet.com/~jnryoung/j/sw/swdice.html

I'm not good at math, but I'm pretty quick with a spreadsheet. I
calculated each probability for each die out to a result of 40 and took a
weighted average to determine the numbers reported in that chart.

Sometimes, it's faster to be dumb. :-)

Incidentally, a quick check of your series for x=1, y=4, and i=0 to 2
gives an average of 3.3 (actually 3.28). My chart has 3.3 as the average
of 1d4. Hmmm, very suspicious.

--- Robert Holland <robert@macauley.com> wrote:
> 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


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