Birthday Problem

{
  "asOf": "2026-10-11T14:44:16.842Z",
  "days": 365,
  "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.",
  "expectedSharedPairs": 0.6931506849315069,
  "notChecked": [
    "real birthdays are not uniform (seasonal peaks make coincidences slightly more likely)",
    "leap day (365 equally likely days assumed)",
    "…1 more"
  ],
  "othersNeededForFiftyPercentSharingYours": 253,
  "people": 23,
  "peopleForFiftyPercent": 23,
  "peopleForFiftyPercentSharingYours": 254,
  "peopleForNinetyNinePercent": 57,
  "probabilityAnyShared": 0.5072972343239854,
  "probabilityNoneShared": 0.49270276567601456,
  "probabilitySomeoneSharesYours": 0.058571325264343166,
  "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."
  ],
  "source": "computed locally (classical birthday problem)",
  "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"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://probability-calc.x402tookit.com/birthday-problem?people=23'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://probability-calc.x402tookit.com/birthday-problem?people=23' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fprobability-calc.x402tookit.com%2Fbirthday-problem
const res = await pay("https://probability-calc.x402tookit.com/birthday-problem?people=23");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://probability-calc.x402tookit.com/birthday-problem?people=23")
    print(res.status_code, res.text)