Standard notation Dice notation

probability mass function of roll of 3d6 , probability density function of normal distribution same mean , standard deviation.

in role-playing games, die rolls required system given in form adx. , x variables, separated letter d , stands die or dice. letter d commonly lower-case, notation uses upper-case d (non-english texts can use equivalent form of first letter of given language s word dice , use english d ).

a number of dice rolled (usually omitted if 1).
x number of faces of each die.

if final number omitted, typically assumed six, in contexts, other defaults used.

for example, if game call roll of d4 or 1d4 mean, roll 1 4-sided die.

3d6 mean, roll 3 six-sided dice. commonly, these dice added together, systems direct player use them in other way, such choosing best die rolled.

to basic notation, additive modifier can appended, yielding expressions of form, adx+b. plus replaced minus sign ( − ) indicate subtraction. b number added sum of rolls. so, 1d20-10 indicate roll of single 20-sided die 10 being subtracted result. these expressions can chained (e.g. 2d6+1d8), though usage less common. additionally, notation such adx-l not uncommon, l (or h , less commonly) being used represent lowest result (or highest result ). instance, 4d6-l means roll of 4 six-sided dice, dropping lowest result. application skews probability curve towards higher numbers, result roll of 3 can occur when 4 dice come 1 (probability 1/1296), while roll of 18 results if 3 dice 6 (probability 21/1296 = 7/432).

rolling 3 or more dice gives probability distribution approximately gaussian, in accordance central limit theorem.