#### Keklas Rekobah

##### SOC-14 1K

Dice.

Let's say you have charted 'r' number of possible random results to your player's actions. You want to figure out how many of what kind of dice to roll. For our example, we'll say that there are 16 possible devices to be found in "Honest Eddie's Pawn & Bail Bond Emporium." Applying the following formulae...

c = (s ^ n) = Total number of Dice Combinations

n = (r - 1) / (s - 1) = Number of Dice

r = ((s - 1) * n) + 1 = Range of Results

s = ((r - 1) / n) + 1 = Size of Dice

r = 16 {1 ... 16}

We come up with...

n = 1, s = 16 ::

**1d16**(c = 16)

n = 3, s = 6 ::

**3d6-2**(c = 216)

n = 5, s = 4 ::

**5d4-4**(c = 1024)

n = 15, s = 2 ::

**15d2-14**(c = 32,768)

Using only one die (1D or 1d6) yields a completely flat probability for each dice combination. If more dice are used, and their throws are summed, the less linear the probable outcome will be. Thus, 15d2-14 yields a range of results from 1 to 16, but has the most non-linear curve of probable outcomes (a 'Bell' curve) of the other dice combinations.

Pythagorean dice are 4, 6, 8, 12, and 20-sided. A coin is 2-sided. 10-sided dice are common. I generally stick to these values IMTU.

If r = 10 {1 ... 10}, then possible dice combinations are 1d10, 3d4-2, and 9d2-8.

If r = 100 {1 ... 100}, then 1d100 (percentile dice), 9d12-8, 33d4-32, and 99d2-98 could be used.

Programmers, of course, could used any size of 'dice' in their programs, but the principle still stands.

The only thing I haven't figured out yet is how to determine (for example) how many times I'll roll "11" on 5d4-2 {3 ... 18} using only a mathematical formula. A little help, please?

Thanx!