[freeroleplay] Re: Probability Question
- From: James Jensen <cheeb2002@xxxxxxxxxxxxx>
- To: freeroleplay@xxxxxxxxxxxxx
- Date: 20 Nov 2003 11:37:57 -0600
> > >So my question is: on the whole, how drastic of an effect does exploding
> > >the roll like this actually have on the probabilities of a roll? I
> > >figure that the answer is actually somewhere between "an average of 21"
> > >and "all over the place", but where?
>
> > 10.5 + .05*10.5 + .05*.05*10.5 + .05*.05*.05*10.25, etc.
>
> Just to help reduce this:
>
> 10.5 * ( SUM(0.05^n, n = 0 .. infinity) )
>
> However, from there, not even my Dad knows what to do next :).
>
For some reason, I just got this e-mail. Go figure.
Anyway, as I said in a reply to Jerry Stratton, this is actually
geometric series. Put in geometric form, it's:
SUM((10.5)(0.05^n), n = 0 .. infinity)
The solution for a convergent geometric series is a/(1 - r), where a is
the constant part (in this case, 10.5), and r is the base of the
exponential part (0.05 here). As long as the absolute value of the base
is less than 1, the series converges, and you use the formula I just
gave.
In this case, the solution is 210/19.
Now you know.
-J. Jensen
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