Coupon collector API

Computes the expected number of random draws (with replacement) to collect all (or k of n) distinct coupon types, plus variance and standard deviation. Answers 'How many cereal boxes to get all 6 toys?', 'Expected draws to complete a collectible set?'.

Price$0.04per request

MethodPOST

Route/v1/gametheory/coupon-collector

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

probabilitycoupon-collectorexpectationharmoniccollectiblesgachadiscretedraws

API URLhttps://x402.hexl.dev/v1/gametheory/coupon-collector

Integration docs

Example request

{
  "n": 6
}

Example response

{
  "n": 6,
  "collect": 6,
  "expectedDraws": 14.7,
  "expectedDrawsRounded": 15,
  "variance": 38.99,
  "stdDev": 6.244197,
  "interpretation": "Expected number of random draws (with replacement) to collect 6 distinct of 6 item types is ≈ 14.7 (≈ 15 draws)."
}

Input schema

{
  "type": "object",
  "required": [
    "n"
  ],
  "properties": {
    "n": {
      "type": "integer",
      "minimum": 1,
      "maximum": 1000000,
      "examples": [
        6
      ]
    },
    "collect": {
      "type": "integer",
      "minimum": 1,
      "examples": [
        6
      ]
    }
  }
}

Output schema

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