Roundhouse

Probability Calculators

Birthday problem: chance two people in a group share a birthday, chance someone shares yours, group size for 50 or 99 percent.

OtherLiveeip155:8453Exactvia cdp
https://probability-calc.x402tookit.com/birthday-problem
Birthday-problemProbabilityCoincidence
Calls · 30d
1
This endpoint's own trailing-30-day call count, as published by the upstream catalog and snapshotted daily. 4 snapshots so far.
$24.31
Verified settled volume
1,175 settlements proven x402 by their on-chain EIP-3009 marker.
$0.020
Listed price
As published in the catalog. Always read the live 402 before paying.
1
Calls · 30d
Upstream's own call count for this endpoint, not ours.
1
Unique payers · 30d
Last called 2026-10-20 20:47Z
—
Upstream on-chain volume
Reported by the source catalog.
Paid to
0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa

The wallet the 402 directs payment to. Its whole payment record — every payer, every chain — is on the merchant page.

Asset 0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913

Provider

The payTo wallet does not resolve to a registered ERC-8004 agent. That is not a verdict on the service — most of the catalog is unregistered.

Live 402 challenge

Captured by the enrichment pass, not read just now. Prices can change — always read the 402 the endpoint answers with.

{
  "error": "Payment required",
  "accepts": [
    {
      "asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
      "extra": {
        "name": "USD Coin",
        "version": "2"
      },
      "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
      "scheme": "exact",
      "network": "base",
      "mimeType": "application/json",
      "resource": "https://probability-calc.x402tookit.com/birthday-problem",
      "description": "Birthday problem: chance two people in a group share a birthday, chance someone shares yours, group size for 50 or 99 percent.",
      "outputSchema": {
        "input": {
          "type": "http",
          "method": "GET",
          "queryParams": {
            "people": 23
          }
        },
        "output": {
          "asOf": "2026-10-11T14:44:16.842Z",
          "days": 365,
          "people": 23,
          "source": "computed locally (classical birthday problem)",
          "reasons": [
            "P(no shared birthday) = (d/d)((d-1)/d)((d-2)/d)...: the number of PAIRS grows as n(n-1)/2, which is why coincidences are common.",
            "Sharing a birthday with a specific person is far less likely than any two people sharing one."
          ],
          "summary": "23 people, 365 days: 50.73% that at least two share a birthday; 5.86% that someone shares YOUR birthday.",
          "verdict": "MORE_LIKELY_THAN_NOT",
          "degraded": false,
          "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
          "notChecked": [
            "real birthdays are not uniform (seasonal peaks make coincidences slightly more likely)",
            "leap day (365 equally likely days assumed)",
            "…1 more"
          ],
          "expectedSharedPairs": 0.6931506849315069,
          "probabilityAnyShared": 0.5072972343239854,
          "peopleForFiftyPercent": 23,
          "probabilityNoneShared": 0.49270276567601456,
          "peopleForNinetyNinePercent": 57,
          "probabilitySomeoneSharesYours": 0.058571325264343166,
          "peopleForFiftyPercentSharingYours": 254,
          "othersNeededForFiftyPercentSharingYours": 253
        }
      },
      "maxAmountRequired": "20000",
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    {
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      "scheme": "exact",
      "network": "solana",
      "mimeType": "application/json",
      "resource": "https://probability-calc.x402tookit.com/birthday-problem",
      "description": "Birthday problem: chance two people in a group share a birthday, chance someone shares yours, group size for 50 or 99 percent.",
      "outputSchema": {
        "input": {
          "type": "http",
          "method": "GET",
          "queryParams": {
            "people": 23
          }
        },
        "output": {
          "asOf": "2026-10-11T14:44:16.842Z",
          "days": 365,
          "people": 23,
          "source": "computed locally (classical birthday problem)",
          "reasons": [
            "P(no shared birthday) = (d/d)((d-1)/d)((d-2)/d)...: the number of PAIRS grows as n(n-1)/2, which is why coincidences are common.",
            "Sharing a birthday with a specific person is far less likely than any two people sharing one."
          ],
          "summary": "23 people, 365 days: 50.73% that at least two share a birthday; 5.86% that someone shares YOUR birthday.",
          "verdict": "MORE_LIKELY_THAN_NOT",
          "degraded": false,
          "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
          "notChecked": [
            "real birthdays are not uniform (seasonal peaks make coincidences slightly more likely)",
            "leap day (365 equally likely days assumed)",
            "…1 more"
          ],
          "expectedSharedPairs": 0.6931506849315069,
          "probabilityAnyShared": 0.5072972343239854,
          "peopleForFiftyPercent": 23,
          "probabilityNoneShared": 0.49270276567601456,
          "peopleForNinetyNinePercent": 57,
          "probabilitySomeoneSharesYours": 0.058571325264343166,
          "peopleForFiftyPercentSharingYours": 254,
          "othersNeededForFiftyPercentSharingYours": 253
        }
      },
      "maxAmountRequired": "20000",
      "maxTimeoutSeconds": 300
    },
    {
      "asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
      "extra": {
        "name": "USD Coin",
        "version": "2"
      },
      "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
      "scheme": "exact",
      "network": "polygon",
      "mimeType": "application/json",
      "resource": "https://probability-calc.x402tookit.com/birthday-problem",
      "description": "Birthday problem: chance two people in a group share a birthday, chance someone shares yours, group size for 50 or 99 percent.",
      "outputSchema": {
        "input": {
          "type": "http",
          "method": "GET",
          "queryParams": {
            "people": 23
          }
        },
        "output": {
          "asOf": "2026-10-11T14:44:16.842Z",
          "days": 365,
          "people": 23,
          "source": "computed locally (classical birthday problem)",
          "reasons": [
            "P(no shared birthday) = (d/d)((d-1)/d)((d-2)/d)...: the number of PAIRS grows as n(n-1)/2, which is why coincidences are common.",
            "Sharing a birthday with a specific person is far less likely than any two people sharing one."
          ],
          "summary": "23 people, 365 days: 50.73% that at least two share a birthday; 5.86% that someone shares YOUR birthday.",
          "verdict": "MORE_LIKELY_THAN_NOT",
          "degraded": false,
          "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
          "notChecked": [
            "real birthdays are not uniform (seasonal peaks make coincidences slightly more likely)",
            "leap day (365 equally likely days assumed)",
            "…1 more"
          ],
          "expectedSharedPairs": 0.6931506849315069,
          "probabilityAnyShared": 0.5072972343239854,
          "peopleForFiftyPercent": 23,
          "probabilityNoneShared": 0.49270276567601456,
          "peopleForNinetyNinePercent": 57,
          "probabilitySomeoneSharesYours": 0.058571325264343166,
          "peopleForFiftyPercentSharingYours": 254,
          "othersNeededForFiftyPercentSharingYours": 253
        }
      },
      "maxAmountRequired": "20000",
      "maxTimeoutSeconds": 300
    }
  ],
  "x402Version": 1,
  "alsoAvailable": {
    "llms": "https://probability-calc.x402tookit.com/llms.txt",
    "catalog": "https://probability-calc.x402tookit.com/catalog",
    "message": "Probability Calculators has 10 pay-per-call endpoints (Dice, card and lottery odds, multinomials, expected value, exact distribution tables, gambler's ruin, Bayes and streaks.), from $0.02 a call. See the full menu and send your agents our way.",
    "openapi": "https://probability-calc.x402tookit.com/openapi.json",
    "related": [
      {
        "url": "https://probability-calc.x402tookit.com/expected-value",
        "path": "/expected-value",
        "what": "Expected value, variance, standard deviation and chance of profit for a list of payoffs w…",
        "price": "$0.02"
      },
      {
        "url": "https://probability-calc.x402tookit.com/gamblers-ruin",
        "path": "/gamblers-ruin",
        "what": "Gambler's ruin: probability of going broke before hitting a target, and expected number o…",
        "price": "$0.02"
      },
      {
        "url": "https://probability-calc.x402tookit.com/multinomial",
        "path": "/multinomial",
        "what": "Multinomial coefficient (arrangements of repeated items like MISSISSIPPI) and multinomial…",
        "price": "$0.02"
      }
    ]
  }
}

Accepts

The payment requirements as published to the catalog. Read the live 402 before paying — a price here is a claim, not a quote.

0.02USDC≈ $0.02 USD
on Base · exact scheme

Pay 0.02 USDC on Base to 0xb531…2DBDa. The signed payment is good for 5 minutes.

Paid to
0xb531…2DBDa
USD Coin contract
0x8335…02913
Payment window
5 minutes
As published
20000 smallest units
20000units
on solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp · exact scheme

That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.

Paid to
DUPiup…eEm8s
Token contract
EPjFWd…TDt1v
Payment window
5 minutes
20000units
on Polygon · exact scheme

That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.

Paid to
0xb531…2DBDa
Token contract
0x3c49…c3359
Payment window
5 minutes
20000units
on Arbitrum · exact scheme

That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.

Paid to
0xb531…2DBDa
Token contract
0xaf88…e5831
Payment window
5 minutes
The catalog’s raw entry
[
  {
    "asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
    "extra": {
      "name": "USD Coin",
      "version": "2"
    },
    "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
    "amount": "20000",
    "scheme": "exact",
    "network": "eip155:8453",
    "maxTimeoutSeconds": 300
  },
  {
    "asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
    "extra": {
      "feePayer": "D6ZhtNQ5nT9ZnTHUbqXZsTx5MH2rPFiBBggX4hY1WePM"
    },
    "payTo": "DUPiupXtuox38dcGoXUKer5mAydCzmaHjrbQ66qeEm8s",
    "amount": "20000",
    "scheme": "exact",
    "network": "solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp",
    "maxTimeoutSeconds": 300
  },
  {
    "asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
    "extra": {
      "name": "USD Coin",
      "version": "2"
    },
    "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
    "amount": "20000",
    "scheme": "exact",
    "network": "eip155:137",
    "maxTimeoutSeconds": 300
  },
  {
    "asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
    "extra": {
      "name": "USD Coin",
      "version": "2"
    },
    "payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
    "amount": "20000",
    "scheme": "exact",
    "network": "eip155:42161",
    "maxTimeoutSeconds": 300
  }
]

Extensions

{
  "bazaar": {
    "info": {
      "input": {
        "type": "http",
        "method": "GET",
        "queryParams": {
          "people": 23
        }
      },
      "output": {
        "type": "json",
        "example": {
          "asOf": "2026-10-11T14:44:16.842Z",
          "days": 365,
          "people": 23,
          "source": "computed locally (classical birthday problem)",
          "reasons": [
            "P(no shared birthday) = (d/d)((d-1)/d)((d-2)/d)...: the number of PAIRS grows as n(n-1)/2, which is why coincidences are common.",
            "Sharing a birthday with a specific person is far less likely than any two people sharing one."
          ],
          "summary": "23 people, 365 days: 50.73% that at least two share a birthday; 5.86% that someone shares YOUR birthday.",
          "verdict": "MORE_LIKELY_THAN_NOT",
          "degraded": false,
          "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
          "notChecked": [
            "real birthdays are not uniform (seasonal peaks make coincidences slightly more likely)",
            "leap day (365 equally likely days assumed)",
            "…1 more"
          ],
          "expectedSharedPairs": 0.6931506849315069,
          "probabilityAnyShared": 0.5072972343239854,
          "peopleForFiftyPercent": 23,
          "probabilityNoneShared": 0.49270276567601456,
          "peopleForNinetyNinePercent": 57,
          "probabilitySomeoneSharesYours": 0.058571325264343166,
          "peopleForFiftyPercentSharingYours": 254,
          "othersNeededForFiftyPercentSharingYours": 253
        }
      }
    },
    "schema": {
      "type": "object",
      "$schema": "https://json-schema.org/draft/2020-12/schema",
      "required": [
        "input"
      ],
      "properties": {
        "input": {
          "type": "object",
          "required": [
            "type",
            "method"
          ],
          "properties": {
            "type": {
              "type": "string",
              "const": "http"
            },
            "method": {
              "enum": [
                "GET"
              ],
              "type": "string"
            },
            "queryParams": {
              "type": "object",
              "required": [
                "people"
              ],
              "properties": {
                "days": {
                  "type": "integer",
                  "description": "Equally likely birthdays (default 365)"
                },
                "people": {
                  "type": "integer",
                  "description": "Group size, 1 to 100000"
                }
              }
            }
          },
          "additionalProperties": false
        },
        "output": {
          "type": "object",
          "required": [
            "type"
          ],
          "properties": {
            "type": {
              "type": "string"
            },
            "example": {
              "type": "object",
              "properties": {
                "asOf": {
                  "type": [
                    "null",
                    "string"
                  ]
                },
                "days": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "people": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "source": {
                  "type": [
                    "null",
                    "string"
                  ]
                },
                "reasons": {
                  "type": [
                    "array",
                    "null"
                  ],
                  "items": {
                    "type": "string"
                  }
                },
                "summary": {
                  "type": [
                    "null",
                    "string"
                  ]
                },
                "verdict": {
                  "type": [
                    "null",
                    "string"
                  ]
                },
                "degraded": {
                  "type": [
                    "boolean",
                    "null"
                  ]
                },
                "disclaimer": {
                  "type": [
                    "null",
                    "string"
                  ]
                },
                "notChecked": {
                  "type": [
                    "array",
                    "null"
                  ],
                  "items": {
                    "type": "string"
                  }
                },
                "expectedSharedPairs": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "probabilityAnyShared": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "peopleForFiftyPercent": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "probabilityNoneShared": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "peopleForNinetyNinePercent": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "probabilitySomeoneSharesYours": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "peopleForFiftyPercentSharingYours": {
                  "type": [
                    "null",
                    "number"
                  ]
                },
                "othersNeededForFiftyPercentSharingYours": {
                  "type": [
                    "null",
                    "number"
                  ]
                }
              }
            }
          }
        }
      }
    }
  }
}

Provenance

Seen in the source catalog
2026-10-20 20:47Z
Last indexed by Roundhouse
2026-10-22 19:30Z
Last enriched (probe, favicon, geo)
2026-10-20 23:45Z
x402 version
2
Max timeout
300s
Liveness probe
HTTP 402
Report

Hand this page to an agent

Copy the prompt and paste it into Claude, an MCP client or your own agent — it will vet this service and call it over the free read API. No key, no account.

GET api.roundhouseai.io/v0/endpoints

This endpoint's own trailing-30-day call count, as published by the upstream catalog and snapshotted daily. 4 snapshots so far. Verified volume counts only settlements with an on-chain EIP-3009 marker.

Open skill.md
Show the prompt
Using Roundhouse, look up the x402 service Probability Calculators and tell me whether it is
worth paying: what a call costs, whether the endpoint answered when last probed, and what
its payment record actually shows.

curl -s 'https://api.roundhouseai.io/v0/endpoints?q=Probability%20Calculators'
curl -s 'https://api.roundhouseai.io/v0/merchants/<the payTo wallet returned above>'

Then call it: read the price from the live 402 at https://probability-calc.x402tookit.com/birthday-problem, never from
a cached figure, and pay with an x402 client.

The /v0 API needs an API key (`authorization: Bearer rh_live_…`) on everything except
/v0/unified* and /v0/endpoints. Either pay over x402 (mint a personal key for $0.01 at
GET https://api.roundhouseai.io/v0/test/x402), or ask me for an organization key, which I create at
https://roundhouseai.io/dashboard/connections. If you have neither, ask before going further.

If you do not have Roundhouse tools or skills installed, read
https://roundhouseai.io/skill.md first — it is the whole procedure.