The secret math behind your favorite tabletop RPG dice rolls

Music · Published 18 October 2026 Swipe more like this →

In short: Rolling a d20 is more than just luck; it is a standardized language of probability. From the Gaussian curves of multiple dice to complex algebraic modifiers, this notation allows players to manipulate mathematical outcomes. It transforms simple random numbers into a sophisticated system for determining success in tabletop games.

Dice notation, also known as dice algebra, is a system used in wargames and tabletop role-playing games to represent combinations of dice using simple algebra-like notation. The standard format is nds, where 'n' is the number of dice, 'd' stands for die, and 's' is the number of faces. For example, 3d6 means rolling three six-sided dice and adding them together.

The notation has evolved significantly since the 1970s. While early Dungeons & Dragons lacked a standardized way to call for rolls, player Ted Johnstone and writer Barry Gold introduced the current notation in 1975. It became so popular that Gary Gygax adopted it for Advanced Dungeons & Dragons in 1977–1979. Today, this legacy is cemented in the 'd20 System' branding.

Advanced systems use modifiers and complex selection rules. Expressions like nds+c add or subtract a constant, while nds-L or nds-H allow players to drop the lowest or highest result, respectively. More complex strings like AdXkhL+B allow for keeping specific numbers of high, low, or chosen dice (S1:p23-S1:p27). Some games even use 'dice pools,' where players count how many dice meet a specific condition rather than summing the faces.

There are also specialized variants for different probability needs. The D66 roll (d6x10+d6) provides 36 possible results from 11 to 66, serving as a base-six alternative to the d100. Other systems use 'Fudge' dice, which feature plus, minus, and blank faces to determine results from -4 to +4, effectively functioning as 4d3-8. Mathematically, rolling three or more dice creates a probability distribution that is approximately Gaussian, following the central limit theorem. This means that as you add more dice, the results tend to cluster toward the middle, creating a more predictable 'bell curve' compared to the flat probability of a single die.

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