[MUD-Dev] Re: let's call it a spellcraft

[James Wilson]

On Thu, 24 Sep 1998, Michael.Willey at abnamro.com wrote:

>The two systems I'm considering both use natural logarithms
>to reduce insane numbers into reasonable values - one
>option allows the numbers on a player's "sheet" to escalate
>rapidly, but takes the LN of that number to get an
>effective value (I'm using a multiple dice vs. target #
>system ala Shadowrun, Vampire, et al.  The effective value
>would become the number of chances to hit the target).
>The other option is to use the effective values as
>statistics, and the difficulty of advancement is based
>on e^(current stat value).  (Of course, if players can't
>see actual numbers on their "sheet", this doesn't matter.)

Perhaps the following is obvious to you, but I had to do
a bit of math to see how different these are:

if the cost of moving from p pips to p+1 pips is about e^p 
experience points, then if you define
p (x) := attribute pips when experience is x
you can get a good simulation of the derivative with
p' (x) = e^(-x)
so 
p (x) = C - e^(-x)
(where C is some constant). As x->infinity, e^(-x)->0, so
p(x)->C. Thus p(x) is asymptotic to the horizontal line C.

Translation: difficulty proportional to e^(current stat) implies
that there is an upper bound on the stat value.

The logarithm approach, on the other hand, does not place
an upper bound on stats, or their effective value (log of the stat).
It simply makes it very hard to advance once one reaches high
levels. (Rather than taking logs to find the 'effective stat',
you could make the cost of advancement proportional to the 
current stat; this makes p (x) logarithmic.) This gives you a bit
more room for super-high stats than taking the logs does:
it's the difference between having log(MAX_INT) possible
effective values and having MAX_INT possible effective values.

James