Dice sum probability API

Computes the exact probability that N dice with S sides sum to (exactly / at least / at most) a target via convolution DP, with favorable/total counts and odds. Answers 'What is P(sum=7) on 2d6?', 'Chance of rolling at least 15 on 4d6?'.

Price$0.04per request

MethodPOST

Route/v1/gametheory/dice-sum-probability

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

probabilitydicerpgsumconvolutiontabletopdiscretegaming

API URLhttps://x402.hexl.dev/v1/gametheory/dice-sum-probability

Integration docs

Example request

{
  "dice": 2,
  "sides": 6,
  "target": 7,
  "mode": "exact"
}

Example response

{
  "dice": 2,
  "sides": 6,
  "target": 7,
  "mode": "exact",
  "minSum": 2,
  "maxSum": 12,
  "expectedSum": 7,
  "favorableOutcomes": 6,
  "totalOutcomes": 36,
  "probability": 0.1666666667,
  "odds": "5 : 1 against",
  "interpretation": "P(sum = 7 with 2d6) = 0.166667 (6/36)."
}

Input schema

{
  "type": "object",
  "required": [
    "dice",
    "sides",
    "target"
  ],
  "properties": {
    "dice": {
      "type": "integer",
      "minimum": 1,
      "maximum": 200,
      "examples": [
        2
      ]
    },
    "sides": {
      "type": "integer",
      "minimum": 2,
      "maximum": 1000,
      "examples": [
        6
      ]
    },
    "target": {
      "type": "integer",
      "examples": [
        7
      ]
    },
    "mode": {
      "type": "string",
      "enum": [
        "exact",
        "atLeast",
        "atMost"
      ],
      "examples": [
        "exact"
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}