Montehall: a Monte Carlo machine for the Monty Hall problem

An over-engineered CLI app, and an experiment with TypeScript/JavaScript (ECMAScript) aimed at:

1. Creating a simulation of the famous counterintuitive Monty Hall problem
2. Solving the strategy problem with Monte Carlo methods
3. Creating a simulation of a general Montehall Problem with $n$ number of doors
4. Producing fairly readable code and Node.js solution suitable for a pretty good practice tutorial.

Inspired by Numberphile's Monty Hall problem video.

Setup

Node.js (latest v16.x, or higher) and NPM (v9.x) are required to run the app:

shell npm install npm run build

Or, using Docker and Bash (recommended)

bash docker pull node docker run --rm --volume=$(pwd):/src --workdir="/src" node npm install docker run --rm --volume=$(pwd):/src --workdir="/src" node npm run build

Running the CLI app

Running the default simulation with a player that does not switch:

shell npx montehall

or, with Docker and Bash

bash docker run --rm --volume="$(pwd):/src" --workdir="/src" node npx montehall

A player who does not switches their door pick should statistically win 1/3 of the games, given a sufficiently large number of random game attempts. However, a prudent, or "wise," player who switches pick should win 2/3 of the games, which can be simulated using the --wise option:

shell npx montehall --wise

A list of available options is accessible from the CLI:

shell npx montehall --help

Number of game simulations

The default number of simulated games is 16384. This can be changed using the --games option, or by changing the value for the games key in the config.json configuration file.

General Monte Hall problem

A standard (default) game has three doors. A general game has $n$ doors.

The CLI option --doors <number> can be used to specify the number of doors.

Examples:

shell npx montehall --doors 100 npx montehall --doors 181 --games 1000 --wise

High-quality results

A randomness source is required to simulate the games. Achieving high-quality simulation results requires a high-quality randomness source.

The default source of randomness used is a fast pseudo one: the Math.random() function.

A higher quality randomness source

For a higher quality, but slower, randomness source, use the --random advanced option, which employs a cryptographically secure pseudorandom number generator (CSPRNG.)

shell npx montehall --wise --random advanced

Using pre-generated random numbers (experimental)

A text file of numbers (random positive integers) can be loaded to run a deterministic simulation.

The file path can be passed as a CLI option:

shell npx montehall --games 100 --table-file vendor/numbers.txt

Or, alternatively, the file path can be configured in config.json.

Example:

json { "numbersFilePath": "./data/numbers.txt" }

shell npx montehall --games 100 --random table

The file must have one number per text line. Example:

text 1 1 0 1 2 1 0

See vendor/numbers.txt for a sample file.

Technical showcases

Partial list of showcases, in alphabetical order:

• Asynchronous programming
• Azure Pipelines
• Behavior-driven development (BDD)
• CodeQL
• Coding without null
• Coding without classes
• Command-line interface (CLI)
• Commander.js
• Continuous integration
• Conventional Commits
• DevSkim
• Distribution package clean of development dependencies
• ECMAScript Modules
• ESLint
• Functional programming
• GitHub Actions
• High code test coverage
• Markdown
• Markdownlint
• Node.js
• NPM
• Prettier
• SonarCloud
• Strict static rules and type safety
• Symantec versioning
• TypeScript
• Unbiased pseudo-randomness
• Unit testing with Jest (and Jasmine)

License

This software is released under an MIT-style license. Copyright © 2017-2023 Omar Boukli-Hacene.

Written for the joy of it 🐻