Dice Roll Generator

Purpose & User Intent: The Dice Roll Generator computes outcomes from standard dice notation (NdS ± M) to support tabletop RPG design, probability analysis, and scenario planning. It is used by game masters planning encounters, players validating skill checks, and developers prototyping game aids. The tool converts expressions like 3d6+2 into simulated rolls, aggregates results, and exposes distribution summaries, enabling quick sanity checks, balance testing, and exploration of unlikely or extreme outcomes without manual arithmetic. Core Logic & Features: The engine parses NdS (+/- M) strings, validates dice count (N ≥ 1), number of sides (S ≥ 2), and an optional modifier (M may be negative). It performs N independent rolls of S-sided dice per trial and adds M. It supports single-roll mode and batch mode, where results are collected across trials. Optional features include reproducible seeding, per-trial logging, and descriptive statistics (mean, median, min, max, standard deviation) plus a simple distribution histogram of sums. Differentiators include robust notation parsing, strict input validation, and rapid bulk simulations. Inputs & Outputs: Required inputs are dice_notation (string, e.g., 3d6+2) and trials (integer > 0). Optional: seed for reproducibility. Outputs include an array of per-trial totals, a summary object (min, max, mean, median, stdev, count), and a distribution map (sum -> frequency). Formatting rules ensure integer sums, consistent decimal handling for statistics, and exporting compatibility with JSON or CSV downstream pipelines. Algorithms & Calculations: Parsing uses a regular expression to extract N, S, and M; a loop executes N random rolls per trial using a uniform 1..S distribution, then adds M. After all trials, statistics are computed using standard moment calculations and median. Reproducibility relies on a seedable RNG when a seed is provided. Error & Edge Cases: Invalid notation or incompatible values produce validation errors without UI messages. The tool validates N and S ranges and ensures trials is positive. Seed=None yields non-deterministic results. Extremely large trials or dice counts may trigger performance constraints. Negative modifiers are supported; non-integer inputs are rejected. Industry/Region & Localization: Uses en-US numeric formatting; supports standard gaming dice (d4, d6, d8, d10, d12, d20, d100). Localization considerations focus on decimal separators and thousands separators; can be extended to other locales without changing core logic. Assumptions & Exclusions: Assumes fair dice and independence between rolls; excludes cryptographic RNG or network data; not tied to specific game rules beyond arithmetic; no UI or front-end behavior is described here.