Yatzy probability counter

yatzy.js

function factorial(k) {
    return (k === 0) ? 1 : k * factorial(k - 1);
}

function binomial(n, k) {
    return factorial(n) / factorial(k) / factorial(n - k);
}

// Probability of k sixes from n dice
function prob(n, k) {
    return Math.pow(1 / 6, k) * Math.pow(5 / 6, n - k) * binomial(n, k);
}

// Probability of getting Yatzy with n dice and t turns
function probSixesYatzy(n, t) {
    if (n === 0) {
        return 1;
    }

    if (t === 0) {
        return 0;
    }

    let sum = 0;

    // If last turn, no need to look at any other case than getting all the remaining sixes
    for (let k = (t === 1 ? n : 0); k <= n; k++) {
        sum += prob(n, k) * probSixesYatzy(n - k, t - 1);
    }

    return sum;
}

const [nbrDice, nbrTurns] = process.argv.slice(2).map(x => parseInt(x));

const p = probSixesYatzy(nbrDice, nbrTurns);
console.log(`Sum: ${p} (${p * 100} %)`);