Decision Guide
Use the total when a game or rule calls for a single outcome. Use the sum to compare against difficulty checks, and use the average to estimate long-run expectations before committing to a strategy.
Scenario Pack
RPG Attack Check
1d20 + 5
Range 6–25. Beat the target number to succeed.
Board Game Movement
2d6
Average 7, range 2–12. Use average to plan safe routes.
Percentile Roll
1d100
Treat the result as a percentage check (success if ≤ threshold).
Assumptions and Limits
- Fair roll distribution: each die is independent and uniformly distributed.
- Each roll is an independent trial with no memory of prior outcomes.
- Randomness uses Math.random and is not cryptographic-grade.
- Dice count is capped at 100 per roll.
- Sides are capped at 1000 per die.
- Modifier range is limited to +/- 1000.
- Average is the expected value, not a guaranteed outcome.
Edge and Stress Tests
- 1d2 with modifier 0 should only output 1 or 2.
- 100d1000 verifies upper-bound performance and range.
- Negative modifiers can push totals below zero.
Sources and Review
ECMAScript Math.random() — Pseudorandom uniform source
Discrete uniform distribution — Probability model
Fair die (uniform distribution) — Model assumption
Last reviewed: 2026-03-17
Who / How / Why
Who: Data Analyst Expert Team
How: Independent uniform rolls with a modifier applied last.
Why: Fast, reliable tabletop probability checks.