Math: Formulas

There are several different formulas that rule the rolling of the dice, between the probability that dictates value chances, to finding out reasonable averages to expect during gameplay.

For starters, there are a few terms that need to be defined:

Event: A certain condition that is, or is to be, made true.
Probability: The odds of an event occuring.

For starters, we can begin at how the dice system works, here. Power Advantage runs off of a system of 'x'd'y'+'z', or . For example:

Players start with a 1d4 Kick:
x = 1
y = 4
z = 0

Most attacks that deal damage will follow this formula, which can be converted, into the AIM chats, as:

//roll-dicex-sidesy

And then you add z to the final roll.

Now, with these rolls, there must obviously be maximum possible rolls, and averages of the max and minimum values.

To figure out the max value, one could use the formula of xy+z, or . In this case, you multiply the x and y values together, then add z to the result, yielding the maximum possible value.
Let's give this a test:

A player has a 10d3+5 Flaming Rapid Cut, and wishes to find the maximum possible damage.
So, if the player wanted the maximum damage, he would need to roll perfectly on every d3, thus getting ten values of three. Using the formula, it can be much easier than counting these all up.
xy+z, so (10)(3) + (5) = 35, max.

Now, it would be great to always roll these perfect values, but, alas, it is rarely so. So rare, in fact, that it usually isn't worth hoping for, when you need it. What is more important, however, is the fact that every roll has an average value it can be, which can usually be attained, more often than not.
The formula for this is somewhat more complicated. It follows the standard ((Max)+(Min))/2 formula, but it is suited to fit the values we use, here.
The formulas is ((xy+x)/2)+z, or . For example, in the 10d3+5, we could replace the values with:

(((y-v)/2)/y)^x, or