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.

Standard notation

---

In most roleplaying games, die rolls required by the system are given in the form AdX, where:

• A is the number of dice to be rolled (1 if omitted).
• d is an abbrieviation for "die" or "dice"; occasionally (e.g., in Stormbringer) a capital "D" is used.
• X is the number of faces of the dice (usually 6 if omitted, although some games assume a different die type); they are usually labelled with consecutive integers beginning at 1.

To this, an additive modifier can be appended, yielding expressions of the form AdX+B

• + denotes addition, and can be replaced by "−" for subtraction.
• B is a modifier which could be a natural number (0 if omitted), or even further die rolls using the same notation (an example of recursion).

For example, if a game would call for a roll of:

• d4 or 1d4 means "roll one 4-sided die."
• 3d6 means "roll three six-sided dice and add them together." 3d means the same thing unless some game-specific convention states otherwise.
• 2d8 means "roll two 8-sided dice and add them together."
• 3d6+2 means "roll three 6-sided dice, add them together and then add 2 to the result."
• 2d10+1d6-3 means "roll two 10-sided dice, add them together, then roll one 6-sided die, add that to the result, and then subtract 3 from the total."

Variations

---

Multipliers

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 with 5."
• 4d6×10+3 means "roll four 6-sided dice, add them together, multiply the result with 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 is occasionally also seen, although it is more common in wargames than role-playing games.

"Keep" notation

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."

Low/high roll

The OpenRoleplaying.org die roller allows the use of L or H instead of the modifier B, to denote the lowest or highest roll on a single die, respectively. So 4d6−L means "Roll four six-sided dice, sum them, and subtract the lowest number rolled", or simply "Roll four six-sided dice, drop the lowest die, and add the rest." 2d+H would be "Roll two six-sided dice and sum them, then add the higher one (again)."

Fudge dice (dF)

The game system Fudge uses customised "Fudge dice", six-sided dice with two plus symbols, two minus symbols, and two blank faces, represented using "F" in place of the variable X. The plus faces count as a roll of +1; the minus faces as −1 and the blank faces as zero. Thus, 4dF+2 would be the total number of plus faces shown, minus the number of minus faces shown, plus two. "1dF" is equivalent to "1d3−2" in standard notation.

d66

Games Workshop's Mordheim uses a "d66" roll, which means rolling two six-sided dice, one representing tens and one units, analoguously to a percentile roll with two ten-sided dice. Note that there are, somewhat confusingly, 36, not 66, different possible results, ranging from 11 to 66.

d666

The game In Nomine uses what it calls the "d666" – in fact this is simply 2d6 which are used to determine whether a player succeeds in a task, with a third die to show degree of success or failure.

Stress dice

In some games, notably Ars Magica and World Tree, dice are rolled differently when determining the outcome of particularly stressful situations. World Tree represents ordinary die rolls with the usual AdX notation, but stress rolls are represented as AsX, where A and X carry the usual meanings.

Some stress dice are also "open-ended." This means that when you roll a value – or within a range of values – on the dice, you roll the dice again and add the previous total to your next roll. If you get the open-ended range, the process is repeated until you stop rolling in the open-ended range, at which point you sum your rolls.

Role-playing game terms