[MUD-Dev] Expected value and standard deviation.

[Ben Chambers]

From: Zach Collins (Siege)
> On Sat, 30 Aug 2003, Ben Chambers wrote:

> The thing is, xDy dice numbers do the same thing, simply
> increasing the floor of the curve.  Lots of dice means a high
> center and floor, while large dice increase the spread.  20d2 is a
> lot; it hasn't got nearly the high-scoring potential of 5d12, but
> still guarantees you'll tend to roll higher on the mean.  Add in
> the +z component of a standard dice roll and you have a means of
> effectively managing the floor (lowest possible score on the
> curve).  20d2-10 seems a whole lot less attractive versus a
> straight 4d8, while still guaranteeing a good average score.

I agree.  But as a developer, it is in my opinion more intuitive to
be able to manipulate the spread and center independently.  That's
the big difference.  I want to maintain the mean but increase the
spread of dice, it is a pain.  Doing it with mean/spread format is
easy, simply increase the number corresponding to the spread.  The
other difference is that a normal distribution produces numbers that
are continuous -- a decimal number with theoretical range from
-infinite to infinite.  Furthermore, if you investigate the amount
of random number generation necessary, using the normal distribution
only requires 1 random number for every generation (actually 2 for
the first, and then none for the second, and then 2 for the
third... but average is 1).  The dice require a number of random
numbers equal to the number of dice.  While not a significant
bottleneck, it is still a potential optimization.
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