Another way to stumble upon Euler and his weird and magical constant.

accidentalEuler.js

function estimateEulersConstant () {
	const SAMPLES = 10000000;
	let s = 0;
	
	for (let n = 0; n < SAMPLES; n++) {
		let x = 0;
		let i = 0;
		
		while (x < 1) {
			x += Math.random();
			i++;
		}
		
		s += i;
	}
	
	return s / SAMPLES;
}