[MUD-Dev] Expected value and standard deviation.

[Eamonn O'Brien]

Kwon J. Ekstrom wrote:

> Most muds I know of (including my own) optimize this by generating
> a range.

> Give the format: xDy+z

>     min = x+z
>     max = (x*y)+z

> At the very least:

>     min = x
>     max = (x*y)

> This guaruntees a single random number.  Additionally it allows
> the ever so popular dice format.

I sincerely doubt many muds do that. An optimization is a faster
means of achieving the same results, your method will change
completely the type of results you get. 2d6 is not the same as
1d11+1 (assuming you could find an 11 sided dice that is). The odds
of getting a 12 on 2d6 is 1 in 36, the odds of getting a 12 on
1d11+1 is 1 in 11. The whole point of having a dice range is that
the more dice you roll, the more your results will tend towards an
average roll. If you make a sword with a 2d4 damage bonus, then you
will end up with 1 sword in 16 getting the +8 maximum, and 1 sword
in 16 getting the 2 minimum, with 1 in 4 getting an average 5. if
you switch that to d7+1 then there is a 1 in 7 chance of any of the
values getting rolled which makes it a lot easier to get the
best/worst items. The best versions end up as common as the average
versions, which is not the desired affect. The best should be rarer
than the average.

It is possible to achieve the same results with 1 random number, but
I doubt it would be worthwhile unless you were rolling very large
numbers of dice at once. If you are happy to work that way that is
fine, but be aware that your optimization has totally changed the
odds of getting every single result, making all dice rolls give a
linear distribution and not the bell curve distribution that you get
with normal dice.

Eamonn
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