Gacha expected pulls API

Computes expected gacha/loot pulls to obtain a target via the geometric distribution, with optional hard-pity truncation and per-copy/total expectations. Answers 'How many pulls on average for a 0.6% rate with 90 pity?', 'Expected loot drops to get N copies?'.

Price$0.06per request

MethodPOST

Route/v1/gametheory/gacha-expected-pulls

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

probabilitygachageometriclootpityexpectationgamingdrops

API URLhttps://x402.hexl.dev/v1/gametheory/gacha-expected-pulls

Integration docs

Example request

{
  "p": 0.006,
  "pity": 90,
  "copies": 1
}

Example response

{
  "p": 0.006,
  "pity": 90,
  "copies": 1,
  "expectedPullsPerCopy": 69.699804,
  "expectedPullsTotal": 69.699804,
  "pullsFor50pct": null,
  "pullsFor90pct": null,
  "probSuccessWithinExpectedPulls": 0.343784,
  "model": "hard pity at pull 90",
  "interpretation": "Expected pulls to obtain 1 copy/copies at rate 0.600% (hard pity at pull 90) ≈ 69.7."
}

Input schema

{
  "type": "object",
  "required": [
    "p"
  ],
  "properties": {
    "p": {
      "type": "number",
      "exclusiveMinimum": 0,
      "maximum": 1,
      "examples": [
        0.006
      ]
    },
    "pity": {
      "type": "integer",
      "minimum": 1,
      "examples": [
        90
      ]
    },
    "copies": {
      "type": "integer",
      "minimum": 1,
      "examples": [
        1
      ]
    }
  }
}

Output schema

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