simulate-monte-carlo

Remote MCP server (Cloudflare Workers) with one tool that estimates a compound event or conditional probability by actually running a Monte Carlo simulation:

• simulate_monte_carlo — declare named random variables (uniform, normal, bernoulli, binomial, poisson, exponential, discrete), an event boolean expression over those names (e.g. "a > 0.5 && b == 1"), and an optional condition expression to get a conditional probability P(event | condition) via rejection sampling. Real random sampling and real counting — not a model guess about what the probability should be.

No database, no persistent state: each call builds a fresh McpServer (see createServer() in src/index.ts) and is self-contained. The PRNG is seedable (mulberry32): pass the seed returned in a previous response to reproduce the exact same result.

Why a hand-written expression interpreter, not eval

event/condition are arbitrary caller-supplied strings. Running them through eval/Function would mean executing untrusted code inside the Worker. Instead, src/tools/monteCarlo.ts includes a small tokenizer + recursive-descent parser + AST interpreter that only understands numbers, declared variable names, arithmetic (+ - * /), comparisons (< <= > >= == !=), boolean logic (&& || !), parentheses, and a three-function whitelist (min, max, abs). There is no code execution path — the interpreter can't do anything beyond evaluate that narrow grammar.

Related MCP server: x402-api

Billing (x402)

Charges per call via x402 — real USDC payment on Base mainnet, against the Coinbase Developer Platform (CDP) facilitator. The payment travels inside the MCP JSON-RPC itself (_meta), not as an HTTP header; see src/payments.ts.

An unpaid tools/call returns isError: true with the accepts (network, amount, payTo) the client needs to pay and retry — not an unexplained exception.

Structure

src/
  index.ts            # registers the tool in the McpServer and exposes the MCP HTTP handler
  payments.ts         # x402 billing on Base mainnet via the CDP facilitator
  tools/
    monteCarlo.ts        # distributions, expression parser/interpreter, simulation loop (testable without Workers)
    monteCarlo.test.ts
scripts/
  dev-node.ts          # dev server that runs the handler in plain Node, no wrangler

Resource limits

Set from the start, not bolted on after: max 10 variables, 100–100,000 trials (default 10,000), 500-character expressions, binomial n ≤ 1,000, poisson lambda ≤ 1,000, and a discrete-outcome cap of 20. On top of the individual caps, a combined sampling-budget check (trials × sum(per-variable cost) ≤ 5,000,000) rejects combinations that would be individually within limits but jointly too expensive — e.g. 100,000 trials against a binomial(n=1000) variable.

Running it locally

⚠️ Note on wrangler dev: the real Cloudflare Workers runtime (workerd) requires macOS 13.5+. If your Mac has an older version, wrangler dev (and npm run dev) will fail. This project includes a plain-Node shim that runs the exact same fetch() handler without needing workerd.

1. Install dependencies

npm install

2. Run the unit tests

npm test

3a. If your wrangler dev works (macOS 13.5+, Linux, Windows)

npm run dev

3b. If wrangler dev fails because of the macOS version

npm run dev:node

Starts at http://localhost:8787/mcp, reading CDP credentials from ~/.mcp-tools-factory-credentials.env (shared across all tools in this factory).

4. Test with curl

# 1) initialize
curl -s -X POST http://localhost:8787/mcp \
  -H "Content-Type: application/json" \
  -H "Accept: application/json, text/event-stream" \
  -d '{"jsonrpc":"2.0","id":1,"method":"initialize","params":{"protocolVersion":"2025-06-18","capabilities":{},"clientInfo":{"name":"curl-test","version":"0.0.1"}}}'

# 2) tools/list
curl -s -X POST http://localhost:8787/mcp \
  -H "Content-Type: application/json" \
  -H "Accept: application/json, text/event-stream" \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/list","params":{}}'

# 3) tools/call — simulate_monte_carlo (two dice, P(sum > 9 | first die == 6))
curl -s -X POST http://localhost:8787/mcp \
  -H "Content-Type: application/json" \
  -H "Accept: application/json, text/event-stream" \
  -d '{"jsonrpc":"2.0","id":3,"method":"tools/call","params":{"name":"simulate_monte_carlo","arguments":{"variables":[{"name":"d1","distribution":{"type":"discrete","values":[1,2,3,4,5,6],"weights":[1,1,1,1,1,1]}},{"name":"d2","distribution":{"type":"discrete","values":[1,2,3,4,5,6],"weights":[1,1,1,1,1,1]}}],"event":"d1 + d2 > 9","condition":"d1 == 6","trials":40000,"seed":3}}}'

Responses come as Server-Sent Events (event: message + data: {...}); the data: line is the usual JSON-RPC response.

Deploy and listings

Deployed at https://simulate-monte-carlo.encodari.workers.dev/mcp (Cloudflare Workers). Published on the official MCP registry, Smithery, mcp.so, and with an open PR to awesome-mcp-servers.

What it doesn't do (yet)

• Charges on Base mainnet with real money. To switch back to testnet (Base Sepolia, eip155:84532) during development, change NETWORK in src/payments.ts.

• No database or persistent state between calls (beyond the billing config, cached in memory per isolate — see src/payments.ts).

• The 95% confidence interval uses the normal (Wald) approximation, which is imprecise near probabilities close to 0 or 1 — good enough for a quick estimate, not a substitute for exact binomial confidence intervals in high-stakes use.