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Dice Notation Exact Probability Distribution
x402
Dice Notation Exact Probability Distribution is a paid API for AI agents from dice.openverbs.com, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-14).
Computes the exact probability distribution (mean, variance, standard deviation, min/max, full PMF) of any dice notation string without sampling.
Price / call$0.002
Success—
StatusUnknown
How this service works
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.
Output
Returns a JSON object containing the mean, variance, standard deviation, minimum, maximum, and optionally the full probability mass function (a mapping from each possible outcome integer to its exact probability) for the given dice notation. If the outcome range is too large for exact computation, returns a 400 error.
Example use cases
Tabletop RPG character stat fairness check
“I'm designing a D&D character creation system and want to know the exact mean, variance, and full probability mass function for 4d6kh3 — is it significantly better than a straight 3d6 roll?”
Board game balance analysis
“We're designing a board game where players roll 2d6+1d4 for movement — can you give me the exact probability distribution including every possible outcome and its probability so we can check if it's balanced?”
Craps odds deep dive
“What are the exact probabilities for every possible total when rolling 2d6? I want the complete PMF with mean and standard deviation, not a simulation.”
Technical details
Endpoint
POSThttps://dice.openverbs.com/v1/statsWhen to prefer
Choose this endpoint when you need mathematically exact probabilities rather than sampled approximations — ideal for game balance analysis, academic study, or any context where precision matters. Prefer it over simulation-based approaches when the outcome space is manageable. Use the sibling roll endpoint if you need actual random dice rolls, and the sibling parse endpoint if you only need to decompose the notation structure.
Side effects
- Dice notation produces an outcome range too large for exact computation — returns a clean 400 error
- Invalid or unparseable dice notation string — returns a 400 validation error
- Missing required 'notation' field — returns a 400 schema error
- Network or service timeout — returns a 5xx error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object |
Tags
x402
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