Roll The Bones

One thing that makes Hero System different that most other RPGs is the dice. Champions players don't habitually carry around a bunch of dice that make you think of Kepler trying to align the planets within Platonian solids. We use six-sided dice (abbreviated 'd6'), the kind you used as a kid to play Monopoly, Risk, or Yahtzee. We use d6 and only d6. We're pretty exclusive that way. We only use the fancy dice to indicate on the map where the bad guys are—if we use them at all.

So, where D&D might call on a player to roll a d20 (read as 'a twenty-sided die', a geometric shape called an icosahedron), Hero System calls for the player to roll 3d6 (read as 'three six-sided dice'). Why would anyone prefer rolling three dice when you could only roll one? The answer is simple. It's called "The Bell Curve."

Let's say that in order for your character to perform a certain skill, you have to roll ten or less (abbreviated '10-') on the dice. With either a single d20 or with 3d6, the probability of doing so is 50%. So far, so good. Now, let's say that with experience, you character's roll changes so that now you have to roll eleven or less (11-). The probability of doing so on a d20 is 55%, which is not bad. But on 3d6, the probability jumps to 62.5%. The net effect that the mid-range is opened up substantially with 3d6, while the extremes remain highly improbable. (One effect of this is that a person rolling a d20 is ten times as likely to roll a critical failure and get his/her character killed at an inopportune moment.)

The table below, which I constructed based on my own study and knowledge of probabilities back in the mid-90's, shows how likely each outcome is when 3d6 are rolled. There are 216 possibilities that can arise when rolling 3d6: each of the three dice can achieve six different results, which leads to 6³ (6x6x6=216) different total outcomes. Only one of these outcomes produces a result of 3: a '1' on all three dice (abbreviated, for our purposes, as '111'). There are three different ways a 4 can result: each of the three dice could produce a 2, while the others show 1, i.e., 112, 121, and 211. There are six different ways that a 5 can be produced: 113, 131, 311, 122, 212, and 221. And so on.

The table below is organized as follows. The first column shows each possible value from rolling 3d6, 3-18. The second column shows how many different ways (out of 216) that value can be obtained. The third column shows the probability or that value coming up [P_(x)]. And the final column—the really useful one—shows the cumulative probability of all values equal to or less than the current value turning up [P_(x-)]. So, as can be seen from the table, the chance of rolling 8- is about one in four, while the probability of rolling 14- is about nine in ten.

Value	Occurrences	P(x)%	P(x-)%
3	1	0.46	0.46
4	3	1.38	1.85
5	6	2.78	4.63
6	10	4.63	9.26
7	15	6.94	16.2
8	21	9.72	25.9
9	25	11.57	37.5
10	27	12.50	50.0
11	27	12.50	62.5
12	25	11.57	74.1
13	21	9.72	83.8
14	15	6.94	90.7
15	10	4.63	95.4
16	6	2.78	98.1
17	3	1.38	99.5
18	1	0.46	100

All hail the Hero System!