const NUMBER_OF_PERSONAL_ENTRIES = 8;

const prizeDistribution = [
    { award: "grand prize", quantity: 1, amount: "$5,000" },
    { award: "second place prize", quantity: 1, amount: "$3,000" },
    { award: "third place prize", quantity: 1, amount: "$1,500" },
    { award: "fourth place prize", quantity: 7, amount: "$500 Lowe's gift card" },
    { award: "fifth place prize", quantity: 6, amount: "$250 Lowe's gift card" },
    { award: "sixth place prize", quantity: 13, amount: "WD-40 Branded Yeti® Rambler® One Gallon Jug" }
];

console.log(`Number of prizes: ${prizes.reduce((acc, curr) => acc + curr.quantity, 0)}`); // Log the total number of prizes

function binomialCoefficient(n, k) {
    if (k > n) return 0;
    if (k === 0 || k === n) return 1;

    let coefficient = 1;
    for (let i = 1; i <= k; i++) {
        coefficient *= (n - (k - i));
        coefficient /= i;
    }
    return coefficient;
}

// Function to calculate the probability of winning exactly k prizes
function probabilityOfWinningKPrizes(totalEntries, yourEntries, totalPrizes, k) {
    if (k > yourEntries || k > totalPrizes) return 0;

    let otherEntries = totalEntries - yourEntries;
    let waysForYouToWinKPrizes = binomialCoefficient(yourEntries, k);
    let waysForOthersToWinRemainingPrizes = binomialCoefficient(otherEntries, totalPrizes - k);
    let totalWaysToAwardPrizes = binomialCoefficient(totalEntries, totalPrizes);

    let probability = (waysForYouToWinKPrizes * waysForOthersToWinRemainingPrizes) / totalWaysToAwardPrizes;
    return probability;
}

// Function to convert probability to human-readable odds
function probabilityToOdds(probability) {
    if (probability === 0) return "0 (impossible)";
    let odds = 1 / probability;
    return `1 in ${Math.round(odds).toLocaleString()}`;
}

// Function to calculate detailed probabilities for each prize category
function calculateDetailedProbabilities(totalEntries, yourEntries, prizeDistribution) {
    let detailedProbabilities = {};

    prizeDistribution.forEach(prize => {
        let probabilities = [];
        let humanReadableOdds = [];
        let totalProbability = 0;
        for (let k = 0; k <= prize.quantity; k++) {
            let probability = probabilityOfWinningKPrizes(totalEntries, yourEntries, prize.quantity, k);
            probabilities.push(probability);
            totalProbability += probability;
            humanReadableOdds.push(probabilityToOdds(probability));
        }
        console.log(`Total probability for ${prize.award} should be close to 1: ${totalProbability}`);
        detailedProbabilities[prize.award] = {
            probabilities,
            humanReadableOdds
        };
    });

    return detailedProbabilities;
}

// Function to calculate the cumulative probability of winning at least one prize
function calculateCumulativeProbability(totalEntries, yourEntries, prizeDistribution) {
    let probabilityOfNotWinningAnything = 1;

    prizeDistribution.forEach(prize => {
        let probabilityOfNotWinningThisPrize = probabilityOfWinningKPrizes(totalEntries, yourEntries, prize.quantity, 0);
        probabilityOfNotWinningAnything *= probabilityOfNotWinningThisPrize;
    });

    return 1 - probabilityOfNotWinningAnything;
}

// Function to calculate combined probabilities for winning across all prize categories
function calculateCombinedProbabilities(totalEntries, yourEntries, totalPrizes) {
    let combinedProbabilities = [];
    let combinedHumanReadableOdds = [];
    let totalProbability = 0;

    for (let k = 0; k <= totalPrizes; k++) {
        let probability = probabilityOfWinningKPrizes(totalEntries, yourEntries, totalPrizes, k);
        combinedProbabilities.push(probability);
        totalProbability += probability;
        combinedHumanReadableOdds.push(probabilityToOdds(probability));
    }

    console.log(`Total combined probability for all prizes should be close to 1: ${totalProbability}`);
    return { combinedProbabilities, combinedHumanReadableOdds };
}

// Example usage
const totalEntries = 76;
const yourEntries = 8; // Change this value to test different numbers of your entries
const prizeDistribution = [
    { award: 'First place', quantity: 1 },
    { award: 'Second place', quantity: 1 },
    { award: 'Third place', quantity: 1 },
    { award: 'Fourth place', quantity: 7 },
    { award: 'Fifth place', quantity: 6 },
    { award: 'Sixth place', quantity: 13 }
];
const totalPrizes = prizeDistribution.reduce((acc, prize) => acc + prize.quantity, 0);
const totalEntriesIncludingYours = totalEntries + yourEntries;

let detailedProbabilities = calculateDetailedProbabilities(totalEntriesIncludingYours, yourEntries, prizeDistribution);

// Display detailed probabilities with human-readable odds
Object.keys(detailedProbabilities).forEach(prize => {
    let prizeInfo = detailedProbabilities[prize];
    console.log(`Your probabilities of winning 0 to ${prizeDistribution.find(p => p.award === prize).quantity} ${prize} prizes are:`, prizeInfo.probabilities);
    prizeInfo.humanReadableOdds.forEach((odds, index) => {
        console.log(`The odds of winning exactly ${index} ${prize} prizes are: ${odds}`);
    });
});

// Calculate cumulative probability of winning at least one prize
let cumulativeProbability = calculateCumulativeProbability(totalEntriesIncludingYours, yourEntries, prizeDistribution);
console.log("Your cumulative probability of winning at least one prize is:", cumulativeProbability);

// Calculate combined probabilities for all prizes
let combinedResults = calculateCombinedProbabilities(totalEntriesIncludingYours, yourEntries, totalPrizes);

// Display combined probabilities with human-readable odds
console.log(`Your probabilities of winning 0 to ${totalPrizes} prizes across all categories are:`, combinedResults.combinedProbabilities);
combinedResults.combinedHumanReadableOdds.forEach((odds, index) => {
    console.log(`The odds of winning exactly ${index} prizes across all categories are: ${odds}`);
});

Total probability for First place should be close to 1: 1
Total probability for Second place should be close to 1: 1
Total probability for Third place should be close to 1: 1
Total probability for Fourth place should be close to 1: 1
Total probability for Fifth place should be close to 1: 1
Total probability for Sixth place should be close to 1: 1
Your probabilities of winning 0 to 1 First place prizes are: [ 0.9047619047619048, 0.09523809523809523 ]
The odds of winning exactly 0 First place prizes are: 1 in 1
The odds of winning exactly 1 First place prizes are: 1 in 11
Your probabilities of winning 0 to 1 Second place prizes are: [ 0.9047619047619048, 0.09523809523809523 ]
The odds of winning exactly 0 Second place prizes are: 1 in 1
The odds of winning exactly 1 Second place prizes are: 1 in 11
Your probabilities of winning 0 to 1 Third place prizes are: [ 0.9047619047619048, 0.09523809523809523 ]
The odds of winning exactly 0 Third place prizes are: 1 in 1
The odds of winning exactly 1 Third place prizes are: 1 in 11