6d3

6d3 is a dice notation used in tabletop gaming and probability problems, indicating that six three-sided dice should be rolled and the results summed. In NdX notation, N denotes the number of dice and X the number of faces on each die. A standard d3 die exists, typically in the form of a tetrahedron marked with values 1 through 3.

Each d3 is independent and uniformly distributed over {1, 2, 3}. Therefore the sum of six such dice has a range from 6 to 18, with an average (expected value) of 12. The variance of a single d3 is 2/3, so the variance of the sum of six is 4, giving a standard deviation of 2. The total number of equally likely outcomes is 3^6 = 729. The probabilities for particular sums can be computed as the coefficient of the corresponding power of x in the generating function (x + x^2 + x^3)^6, or by other combinatorial methods.

In practice, 6d3 is used for games or puzzles where a moderate, compact spread is desired, though it is less common than standard dice like d6 or d20. It may appear in homebrew RPG rules or probability demonstrations. A common way to simulate a d3 with more readily available dice is to roll a six-sided die and map outcomes in pairs to 1, 2, or 3 (for example, 1–2 → 1, 3–4 → 2, 5–6 → 3).

See also NdX notation and other dice types such as d4 and d6.