Parse dice notation such as "3d6+2", "4d6kh3" (keep highest 3) or "2d20dl1" (drop lowest 1) into structured terms. Malformed notation is a clean 400.

Roll dice notation with a cryptographically secure RNG, optionally repeated. Returns per-die rolls, the kept dice and the total for each roll.

Compute the exact probability distribution of a dice notation — mean, variance, standard deviation, min/max and the full probability mass function — with no sampling. Notations whose outcome range is too large for exact computation are clean 400s.