Rollbasis

Rollbasis is a term used in probability and gaming to describe a method of mapping die rolls to outcomes using a predefined basis, typically a weight vector across the faces of the die.

The term is not widely standardized and is found mainly in niche discussions of tabletop mechanics, probabilistic modeling, and game design. In such contexts, rollbasis denotes the rule or function that converts a raw roll into a final score or result.

Mechanically, rollbasis involves selecting a die with N faces and a basis vector B = {w1, w2, ..., wN}. When a face i appears, the rollbasis score is computed by a rule such as s = w_i or s = f(i, B), where the weights encode difficulty, skill, or situational modifiers. If weights are proportional to a target distribution, the rollbasis effectively biases outcomes toward that distribution without changing the die itself.

Applications include adjusting success thresholds in games, modeling nonuniform randomness in simulations, and exploring alternative outcome distributions in design work. Rollbasis shares concepts with weighted randomness and basis-based transformations in probability theory.