[MUD-Dev] Expected value and standard deviation.

[Zach Collins {Siege}]

On Sat, 30 Aug 2003, Ben Chambers wrote:

> I've actually been exploring a system similar to this.  Instead of
> numbers being generated through a formula like 4d6, it would be
> generated by two numbers, one representing the center and the
> other representing the spread (standard deviation).  Different
> skills would affect each in different ways.  For example, a
> thieves backstab would lower the standard deviation and maybe
> raise the center a little.  A barbarian's wild swing would raise
> the center a lot but also increase the standard deviation.

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.

    20d2: floor 20, ceiling 40, median 30
    5d12: floor 5, ceiling 60, median 30

Note that these two rolls have the same median (and mode!), but that
20d2 will tend to roll closer to its median value, providing less
risk for someone who doesn't want to roll low.  Conversely, 5d12
provides a significantly higher reward for its risk.

    20d2-10: floor 10, ceiling 30, median 20
    4d8: floor 4, ceiling 24, median 16

And because computers don't need to use regular solids to offer
'fair' dice...

    3d7+3: floor 6, ceiling 24, median 13.5

To summarize, I think that managing the mean and statistical
deviation of a bell curve is a fine idea, but it's an idea which
many of us have been using all along.

--
Zach Collins
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