Probability Distributions

Rolling dice to determine the outcome of an action is the most important mechanic of a table top role playing game. Different systems use various combinations of dice to make decisions. The "Adventure Game Engine" system uses three six-sided dice while more traditional systems like "Pathfinder" and "Dungeons and Dragons" use a single twenty sided die. In the study the dice mechanics the cumulative probability distribution is the most useful.

Cumulative Probability Distributions $P(x\geq X)$

x	1d20	3d6
1	100%	100%
2	95%	100%
3	90%	100%
4	85%	99.54%
5	80%	98.15%
6	75%	95.37%
7	70%	90.74%
8	65%	83.80%
9	60%	74.07%
10	55%	62.50%
11	50%	50.00%
12	45%	37.50%
13	40%	25.93%
14	35%	16.20%
15	30%	9.26 %
16	25%	4.63%
17	20%	1.85%
18	15%	0.46%
19	10%	0.00%
20	5%	0.00%

Each row represents the chance that a dice roll will have a value greater than or equal to the target number. For example, under both dice systems a roll has a 50% chance of being equal or greater than a target number of 11.