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Dice Notation

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Dice Notation is a shorthand leftover from PnP D&D. This notation allows the extremely short representation of complex summations of random numbers.

Dice Notation SyntaxEdit

In dice notation, the lower-case letter 'd' followed by a whole number is used to represent rolling a figurative die with the listed number of sides and then using the result of that die roll in whatever computation the dice notation was present in. The die is rerolled each time the computation is computed, and multiplying a dice roll rolls the coefficient number of dice independently and sums them together, rather than rolling once and multiplying the result. As is standard for the parenthesis grouping operator, any functions, including dice notation, inside the parenthesis are evaluated down to a single number, and then used for the rest of the calculation.


d4: This returns the result of a four-sided die roll. The possible values are 1, 2, 3, and 4. Each possible value is equally probable.

2d6+7: This rolls two six-sided dice and adds their values together, and then adds 7 to that value. The possible values of this expression are 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19. 14 is the most probable result, while 9 and 19 are the least probable.

3(1d8+2d6+10)+d4: This is an example of the damage dealt by a +3 Force Critical Battle Axe on a Critical Strike Sneak Attack made by a 4th-level Rogue with a Strength score of 25. The possible values range from 40 to 94, and are very unevenly distributed. The 1d8+2d6+10 is evaluated first, and then the result of that is multiplied by 3 and then added with the result of d4. In practice, expressions of this complexity are not overly uncommon.

Common Types of DiceEdit

d4: A four-sided die. This is used for the damage of Daggers, Magic Missiles, and several other very weak sources of damage.

d6: A six-sided die. This is used for the damage of Short Swords, Shocking Grasp, and many other weak sources of damage.

d8: An eight-sided die. This is used for the damage of Long Swords, the healing from Cure Light Wounds, and several other average-strength weapons.

d10: A ten-sided die. This is used for the damage of Bastard Swords, Niac's Cold Ray, and a few other strong sources of damage.

d12: A twelve-sided die. This is actually not a common type of die in usage, but it is a common type of die in a PnP D&D player's set of dice. This is used for Greataxe damage.

d20: A twenty-sided die. This is the die used when making checks.

d100: A hundred-sided die, also known as "percentile dice". While very few actual hundred-sided polyhedral dice are produced, it's not altogether uncommon to roll 10(d10-1)+d10 instead and interpreting a roll of zero as a roll of 100 instead. This achieves the same result, a range of equally-probable numbers from 1 to 100, but doesn't require a physical 100-sided die, which would be difficult to manufacture. The d100 is used for rolls for stabilizing.

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