Dice notation

Dice notation (also known as dice algebra, common dice notation, RPG dice notation, and several other titles) is a system to represent different combinations of dice in role-playing games using simple algebra-like notation such as 2d6+12.

Standard notation

In most role-playing games, die rolls required by the system are given in the form AdX. A and X are variables, separated by the letter "d", which stands for die or dice. The letter "d" is most commonly lower-case, but some notation uses upper-case "D".

  • A is the number of dice to be rolled (1 if omitted).
  • X is the number of faces of the dice

If the final number is omitted, it is typically assumed to be a six, but in some contexts, other defaults are used.

For example, if a game would call for a roll of d4 or 1d4 this would mean, "roll one 4-sided die."

3d6 would mean, "roll three six-sided dice." Commonly, these dice are added together, but some systems could direct the the player to choose the best die rolled.

To this basic notation, an additive modifier can be appended, yielding expressions of the form, AdX+B. The plus is sometimes replaced by a minus sign ("−") for subtraction. B is a number to be subtracted from the final total. So, 1d20+10 would indicate a roll of a single 20-sided die with 10 being added to the result. These expressions can also be chained (e.g. 2d6+1d8), though this usage is less common.

Variations and expansions


In some games, the above notation is expanded to allow for a multiplier, as in AdX×C or C×dX, where:

  • × denotes multiplication, and can be replaced by "/" or "÷" for division.
  • C is a natural number (1 if omitted, and often a multiple of 10).

For example,

  • 1d6×5 or 5×d6 means "roll one 6-sided die, and multiply the result by 5."
  • 4d6×10+3 means "roll four 6-sided dice, add them together, multiply the result by 10, and then add 3."

Percentile dice (d%)

Often, the variable X in the above notation will be "100" or "%". Although a 100-sided die does exist, it is both more common and more uniformly random to use a combination of two ten-sided dice known as percentile dice, where one die represents tens and the other units; depending on the game, a roll of two zeroes can mean 100 or zero.

The d1000 (using 3 10-sided dice) is occasionally also seen, although it is more common in wargames than role-playing games.

Selective results

A number of notational strategies exist for discarding only certain types of results.

Some games extend the standard notation to AdX(kY)+B where, in addition to the above, Y is the number of dice kept from the roll. Whether the dice omitted are the highest, lowest, or the player's choice depends on the game in question. Seventh Sea only uses 10-sided dice, and uses notation of the form 8k6, meaning "Roll eight ten-sided dice, keep the highest six, and sum them."

An alternative notation used by the die roller allows the use of a plus or minus followed by L or H instead of the modifier B, to denote dropping or re-adding the lowest or highest roll on a single die, respectively.

6-sided variations

Various Games Workshop systems use an erroneously named d66 roll, by which they mean d6×10+d6. Note that there are (somewhat confusingly) 36, not 66, different possible results, ranging from 11 to 66.

Blood Bowl, also a Games Workshop product, introduces the block die with special notation Xdb or roll block dice X times, blocker/defender chooses (if more than 1 die) with X being one of 3, 2, 1 (usually omitted), -2, -3. Alternatively words for & against can be used to describe a Xdb (in this case X > 0). As an example 2db against is equal to -2db which are both short ways of saying 2 dice block, defender chooses from the results rolled.

In Nomine, a game about Angels and Demons from Steve Jackson Games, uses a three-dice variation called the d666. However, this is actually a combination of 2d6 (for determining success / failure) and 1d6 (for determining degree of success / failure). The notation of d666 is a reference to The Number of the Beast.

The FUDGE role-playing system uses a die marked with minus signs, plus signs and blank sides, meaning -1, +1 and 0 respectively. The default is one third of each, usually represented by a six-sided die with two of each, known as dF.2 or just dF. Four of these (4dF) are rolled to determine results from -4 to +4, which is equivalent to 4d3-8.Variants include dF.1, which is a six-sided die with four blanks, one plus and one minus.

10-sided variations

The Cyborg Commando role-playing game by Gary Gygax uses a dice mechanic called d10x. This is equivalent to d10×d10 and gives a non-linear distribution, with most results concentrated at the lower end of the range.



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