D notation
From Wikihack
D notation, or Dice notation is a system to represent different combinations of dice in role-playing games. The system is borrowed from Dungeons & Dragons. Throughout articles in this Wiki, the D notation is used to show the chances of something.
[edit] Notation
The notation has the form of AdX, where A and X are variables:
- A is the number of dice rolled
- X is the number of faces on each die
For example, if an article states that a weapon has a damage of 1d24 (roll one die with 24 sides), it can do a damage between 1 and 24. If an article states that a weapon does a damage of 2d24 (roll two dice with 24 sides each), it can do a damage of (1..24) + (1..24).
If A is omitted, it is taken to be 1.
[edit] Probabilities
Rolling a single die gives any possible roll with equal probability, but multiple dice will tend to give many rolls in the middle of the range and few at the ends. Therefore, rolling 3d6 is not the same as rolling 1d16 and adding 2, even though both give a range from 3 to 18 and a mean (average) of 10.5.
A roll of many dice approximates a normal distribution or "bell curve".
This table gives the probabilities of each possible roll of 3d6:
| d(n,x) | |
|---|---|
 | |
| Distribution | uniform (n=1) triangular (n=2) approx. normal (n>2) |
| Mean | 
|
| Standard deviation | 
|
| Roll | Number of Rolls | Probability |
|---|---|---|
| 3 | 1 | 0.00463 |
| 4 | 3 | 0.0139 |
| 5 | 6 | 0.0278 |
| 6 | 10 | 0.0463 |
| 7 | 15 | 0.0694 |
| 8 | 21 | 0.0972 |
| 9 | 25 | 0.116 |
| 10 | 27 | 0.125 |
| 11 | 27 | 0.125 |
| 12 | 25 | 0.116 |
| 13 | 21 | 0.0972 |
| 14 | 15 | 0.0694 |
| 15 | 10 | 0.0463 |
| 16 | 6 | 0.0278 |
| 17 | 3 | 0.0139 |
| 18 | 1 | 0.00463 |
