martintale.js

const pick = odds => {
	const total = odds.reduce((a, b) => a + b); //total cards
	const index = Math.random() * total; //card to choose

	//NOTE: NOT using Math.floor(), as 'odds' can contain fractional values

	//find the rarity slot that index falls into
	let slot;
	let running = index; //the running total, counting backwards
	for (let i = 0; i < total; i++) {
		if (running - odds[i] <= 0) {
			//found it
			slot = i;
			break;
		} else {
			//count backwards
			running -= odds[i];
		}
	}

	//"remove" the card from the odds by inflating other odds
	let newOdds = [];
	const inflation = 1 / (odds.length - 1); //1 / 3 for 4 cards

	for (let i = 0; i < odds.length; i++) {
		if (i != slot) {
			newOdds.push(odds[i] + inflation);
		} else {
			newOdds.push(odds[i]);
		}
	}

	//finally
	return [newOdds, slot];
};

//tests

//test it 'amount' times
const testBy = (base, amount) => {
	let odds = [...base];
	let slot; //the resulting rarity slot

	//run it 'amount' times
	for (let i = 0; i < amount; i++) {
		[odds, slot] = pick(odds);
	}

	//map down the inflated values
	return odds.map(o => o / amount);
}

const base = [11, 3, 7/8, 1/8]; //common, uncommon, rare, mythic

//show the resulting odds for each run of 'x' iterations
console.log(testBy(base, 10))
console.log(testBy(base, 100))
console.log(testBy(base, 1000))
console.log(testBy(base, 10000))

//show the percentage (tends towards 1)
console.log(testBy(base, 10).reduce( (a, b) => a + b ));
console.log(testBy(base, 100).reduce( (a, b) => a + b ));
console.log(testBy(base, 1000).reduce( (a, b) => a + b ));
console.log(testBy(base, 10000).reduce( (a, b) => a + b ));