Coin flip probability

coinFlipExperiment.js

// You have 1,024 coins. One of those coins is double headed,
// but the rest are fair. You pick a coin at random and flip
// it 10 times and get 10 heads. What is the probability that
// the next flip will be heads?

// Constants
var TOTAL_COINS = 1024,
	NUM_DOUBLE  = 1,
	NUM_FLIPS   = 10,
	PROB_FAIR   = .5,
	PROB_DOUBLE = 1,
	NUM_TRIALS  = 10000000;

// Functions
var flipCoin, chooseCoin, isAllHeads, runTrial, runExperiment;

// Results
var allHeadsUntilLast = 0,
	allHeads = 0,
	totalDoubleHeaded = 0;

// True is heads, false is tails
flipCoin = function (coin) {
	var prob = PROB_FAIR;

	if (coin < NUM_DOUBLE) {
		prob = PROB_DOUBLE;
	}

	return Math.random() < prob;
};

chooseCoin = function () {
	return Math.floor(Math.random() * TOTAL_COINS);
};

isAllHeads = function (results) {
	return results && !(results & (results + 1));
};

runTrial = function () {
	var coin = chooseCoin(),
		results = 1,
		i;

	// Flip n + 1 times
	for (i = 0; i <= NUM_FLIPS; i += 1) {
		results = (results << 1) + flipCoin(coin);
	}

	totalDoubleHeaded += coin < NUM_DOUBLE;
	allHeads += isAllHeads(results);
	allHeadsUntilLast += isAllHeads(results >> 1);
};

runExperiment = function () {
	var i = 0;

	for (i = 0; i < NUM_TRIALS; i += 1) {
		runTrial();
	}

	console.log("Flips per trial: " + NUM_FLIPS);
	console.log("Total trials: " + NUM_TRIALS);
	console.log("Number of trials with " + NUM_FLIPS + " heads: " + allHeadsUntilLast);
	console.log("Number of trials with " + (NUM_FLIPS + 1) + " heads: " + allHeads);
	console.log("Number of times picked double headed coin: " + totalDoubleHeaded);
	console.log("Given " + NUM_FLIPS + " heads, probability next flip is heads: " + (100 * allHeads / (allHeadsUntilLast || 1)) + "%" );
};

runExperiment();