About

In high-stakes tabletop gaming, the integrity of the random number generator (RNG) is the difference between a heroic victory and a statistical anomaly. This tool is engineered for Game Masters, data analysts, and players who require more than a simple random integer. It addresses the limitations of physical dice - which are often unbalanced due to manufacturing defects - by utilizing the browser's cryptographic entropy (window.crypto).

Unlike basic rollers, this engine supports complex syntax used in systems like D&D 5e (Advantage/Disadvantage), Shadowrun (Exploding Dice), and Pathfinder. It provides immediate statistical foresight, calculating the Mean (x) and Standard Deviation (σ) for your specific formula before you even roll. This ensures you understand the probability curve of your action.

Formulas

To ensure fairness, we calculate the standard deviation σ of a complex dice pool using the variance summation property for independent random variables. For a single die of size n:

Var(d) = n² - 112

For a pool of k dice, the standard deviation is:

σ_total = √k × Var(d)

When using "Drop Lowest" logic (e.g., 4d6dl1), the probability density function shifts significantly, pushing the mean higher. The expected value is calculated by iterating over all n^k permutations.

Reference Data

Mechanic / Operator	Syntax Example	Logic Description	Math Expectation (E)
Standard Sum	`2d6 + 5`	Roll two 6-sided dice, sum them, add 5.	E = 2(3.5) + 5 = 12
Keep Highest (Advantage)	`2d20kh1`	Roll two d20s, keep the single highest value.	E ≈ 13.82 (vs 10.5 flat)
Keep Lowest (Disadvantage)	`2d20kl1`	Roll two d20s, keep the single lowest value.	E ≈ 7.17
Drop Lowest (Stats)	`4d6dl1`	Roll four d6s, remove the lowest die, sum the rest.	E ≈ 12.24 (Range 3-18)
Exploding Dice	`3d6!`	If a die rolls max (6), roll it again and add.	E = n(n+1)2(n-1) for 1 die
Target Success	`10d10>7`	Count how many dice rolled 8, 9, or 10.	P(success) = 0.3 per die
Fudge/Fate	`4dF`	Roll 4 dice with faces [-1, 0, +1].	E = 0 (Bell curve centered on 0)

Frequently Asked Questions

Physical dice often have manufacturing imperfections (air bubbles, rounded edges) that bias the roll. This tool uses a cryptographically secure pseudo-random number generator (CSPRNG), ensuring that every face has a mathematically equal probability of occurring, regardless of previous outcomes.

Yes. Use the specialized buttons "Adv" (Advantage) and "Dis" (Disadvantage) on the interface, or type "2d20kh1" (Keep Highest 1) manually. The system automatically handles the logic and shows you the discarded die in gray.

Common in systems like Shadowrun or Savage Worlds, "Exploding" (syntax: '!') means if you roll the maximum number on a die, you roll again and add the new result to the total. This allows for potentially infinite open-ended rolls.

The system is optimized to render up to 500 simultaneous dice animations without significant lag. However, for extreme cases (e.g., Warhammer 40k Orks), you can use the "Quick Calc" mode which bypasses 3D physics for instant numeric results on thousands of dice.

Yes. The tool is fully WCAG 2.1 compliant. You can Tab through all controls, use Enter/Space to roll, and screen readers will announce the total result and individual die faces.