# D notation

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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.

## Notation Edit

The notation has the form of ndx, where n and x are variables:

• n 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 dice 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 n is omitted, it is taken to be 1.

## Probabilities Edit

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)
Distributionuniform (n=1)
triangular (n=2)
approx. normal (n>2)
Mean$n(x+1)/2$
Standard deviation$\sqrt{n(x^2-1)/12}$
RollNumber of RollsProbability
310.00463
430.0139
560.0278
6100.0463
7150.0694
8210.0972
9250.116
10270.125
11270.125
12250.116
13210.0972
14150.0694
15100.0463
1660.0278
1730.0139
1810.00463