Monty Hall Problem

montyhall.js

/**
 * The Monty Hall Problem
 * https://en.wikipedia.org/wiki/Monty_Hall_problem
 */

// convert 0.333 to 33%
const toPercentInteger = (fraction) => {
	return Math.floor(fraction * 100);
};

// Get faction (0-1) chance of winning out of total games
const montyHallSamples = (numberOfDoors = 3, switchChoice = false, totalGames = 1) => {
	// Single game, returns true for win, false for loss
	const singleGame = () => {
		const prize = Math.floor(Math.random() * numberOfDoors);
		const choice = Math.floor(Math.random() * numberOfDoors);
		return (choice != prize) ? switchChoice : !switchChoice;
	};

	// Get total wins from total games
	const totalWins = (totalGames) => {
		let wins = 0;
		while (totalGames--) {
			if (singleGame()) wins += 1;
		}
		return wins;
	};

	return totalWins(totalGames) / totalGames;
};

// Logs info about the sample
const logSamples = (numberOfDoors = 3, totalGames = 10000000) => {
	console.log(
		`With ${numberOfDoors} doors,`,
		`switching has a ${toPercentInteger(montyHallSamples(numberOfDoors, true, totalGames))}% chance of winning,`,
		`while not switching has a ${toPercentInteger(montyHallSamples(numberOfDoors, false, totalGames))}% chance.`,
	);
};

// BEGIN SAMPLING

/**
 * Assert this, because this is actually pretty acurate with this many samples ;)
 */
console.assert(
	toPercentInteger(montyHallSamples(3, true, 10000000)) == toPercentInteger(2 / 3),
	'There should be a 2/3 chance of winning by switching!',
);
console.assert(
	toPercentInteger(montyHallSamples(3, false, 10000000)) == toPercentInteger(1 / 3),
	'There should be a 1/3 chance of winning by not switching!',
);
logSamples(3);

/**
 * Change the number of doors simulating the game where the same rules apply,
 * except the host opens all the doors except the door you chose plus one.
 * By increasing the number of doors:
 * - Chance of winning increases by switching
 * - Chance of winning decreases by not switching
 */
logSamples(4);
logSamples(6);
logSamples(50);

/**
 * Lastly, try changing the number of doors to 2.
 * The only case that switching does not matter (with more than 1 door).
 */
logSamples(2);

// The end