Dice Odds

{
  "asOf": "2026-10-11T14:44:17.363Z",
  "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.",
  "distribution": [
    {
      "cumulativeAtMost": 0.00463,
      "probability": 0.00463,
      "sum": 3,
      "ways": 1
    },
    {
      "cumulativeAtMost": 0.018519,
      "probability": 0.013889,
      "sum": 4,
      "ways": 3
    }
  ],
  "maxSum": 18,
  "mean": 10.5,
  "minSum": 3,
  "mostLikelyProbability": 0.125,
  "mostLikelySum": 10,
  "notChecked": [
    "loaded or unfair dice",
    "exploding dice, rerolls and other house rules",
    "…1 more"
  ],
  "pool": "3d6",
  "reasons": [
    "Exact: every outcome of fair, independent dice is counted (convolution, or full enumeration when dropping dice)."
  ],
  "source": "computed locally (exact enumeration and convolution)",
  "standardDeviation": 2.95804,
  "summary": "3d6: mean 10.5, sd 2.95804, range 3-18, most likely 10 (12.50%). Sum 10: exactly 12.50%, at least 62.50%, at most 50.00%.",
  "target": {
    "atLeast": 0.625,
    "atMost": 0.5,
    "exactly": 0.125,
    "oneInNExactly": 8,
    "sum": 10
  },
  "totalOutcomes": 216,
  "variance": 8.75,
  "verdict": "COMPUTED"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://probability-calc.x402tookit.com/dice-odds?dice=3&faces=6&target=10'

# 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/dice-odds?dice=3&faces=6&target=10' \
  | 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%2Fdice-odds
const res = await pay("https://probability-calc.x402tookit.com/dice-odds?dice=3&faces=6&target=10");
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/dice-odds?dice=3&faces=6&target=10")
    print(res.status_code, res.text)