Birthday paradox API

Computes the shared-birthday collision probability for k people over D days, or inverts to find the people needed for a target probability. Answers 'What is the chance two of 23 people share a birthday?', 'How many people for a 50% collision?'.

Price$0.04per request

MethodPOST

Route/v1/gametheory/birthday-paradox

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

probabilitybirthday-paradoxcollisionhashingcombinatoricspuzzlediscretepigeonhole

API URLhttps://x402.hexl.dev/v1/gametheory/birthday-paradox

Integration docs

Example request

{
  "people": 23
}

Example response

{
  "people": 23,
  "days": 365,
  "probabilityOfSharedMatch": 0.5072972343,
  "probabilityNoMatch": 0.4927027657,
  "interpretation": "With 23 people and 365 equally likely birthdays, the chance at least two share a day is 50.7297%."
}

Input schema

{
  "type": "object",
  "properties": {
    "people": {
      "type": "integer",
      "minimum": 0,
      "examples": [
        23
      ]
    },
    "days": {
      "type": "integer",
      "minimum": 1,
      "examples": [
        365
      ]
    },
    "probability": {
      "type": "number",
      "minimum": 0,
      "maximum": 1,
      "examples": [
        0.5
      ]
    }
  }
}

Output schema

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