Use this calculator to determine your chances of winning various Mega Millions prizes based on the number of tickets you play. Understand the probabilities for matching white balls and the Mega Ball.
Your Odds of Winning:
Understanding Mega Millions Odds
Mega Millions is a popular multi-state lottery game in the United States. To play, you select five numbers from 1 to 70 (white balls) and one Mega Ball number from 1 to 25. The goal is to match the numbers drawn to win prizes, with the jackpot going to those who match all five white balls and the Mega Ball.
How the Odds are Calculated
The odds of winning Mega Millions are determined by the number of possible combinations of numbers. The calculator uses combinatorics (the mathematical study of combinations) to figure out how many ways there are to pick the winning numbers for each prize tier.
White Balls: There are 70 white balls, and you need to choose 5. The number of ways to do this is calculated using the combination formula C(n, k) = n! / (k! * (n-k)!), where n is the total number of items, and k is the number you choose. For white balls, this is C(70, 5).
Mega Ball: There are 25 Mega Balls, and you need to choose 1. This is C(25, 1).
Total Combinations: The total number of unique Mega Millions tickets possible is the product of the white ball combinations and the Mega Ball combinations: C(70, 5) * C(25, 1). This results in over 302 million possible combinations for a single ticket.
Prize Tiers and Their Odds
The calculator provides odds for all nine prize tiers, from the jackpot down to matching just the Mega Ball. Each tier has a specific number of ways to win, which is then divided by the total possible combinations to determine the probability. When you play multiple tickets, your chances increase proportionally, as the calculator demonstrates.
Example Scenario:
Let's say you play 1 ticket:
Your odds of winning the Jackpot (5 White Balls + Mega Ball) are 1 in 302,575,350.
Your odds of winning any prize are approximately 1 in 24.
If you play 10 tickets:
Your odds of winning the Jackpot become 10 in 302,575,350, which simplifies to 1 in 30,257,535.
Your odds of winning any prize improve to approximately 1 in 2.4.
While playing more tickets increases your chances, the odds of winning the jackpot remain astronomically high, even with many tickets.
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function factorial(n) {
if (n < 0) return 0;
if (n === 0 || n === 1) return 1;
var res = 1;
for (var i = 2; i <= n; i++) {
res *= i;
}
return res;
}
function combinations(n, k) {
if (k n) {
return 0;
}
if (k === 0 || k === n) {
return 1;
}
if (k > n / 2) {
k = n – k;
}
var res = 1;
for (var i = 1; i <= k; i++) {
res = res * (n – i + 1) / i;
}
return res;
}
function formatOdds(odds) {
if (odds <= 1) {
return "Guaranteed (or better than 1 in 1)";
}
return "1 in " + Math.round(odds).toLocaleString();
}
function calculateMegaMillions() {
var numTicketsPlayedInput = document.getElementById("numTicketsPlayed").value;
var numTicketsPlayed = parseFloat(numTicketsPlayedInput);
if (isNaN(numTicketsPlayed) || numTicketsPlayed < 1) {
alert("Please enter a valid number of tickets (1 or more).");
document.getElementById("numTicketsPlayed").value = 1;
numTicketsPlayed = 1;
}
// Mega Millions Rules
var totalWhiteBalls = 70;
var chosenWhiteBalls = 5;
var totalMegaBalls = 25;
var chosenMegaBalls = 1;
// Total possible combinations for a single ticket
var totalCombinationsWhite = combinations(totalWhiteBalls, chosenWhiteBalls); // C(70, 5)
var totalCombinationsMega = combinations(totalMegaBalls, chosenMegaBalls); // C(25, 1)
var totalPossibleCombinations = totalCombinationsWhite * totalCombinationsMega; // 302,575,350
// Calculate ways to win for each prize tier (for one ticket)
var waysToWin = {};
// 5 White Balls + Mega Ball (Jackpot)
waysToWin['jackpot'] = combinations(chosenWhiteBalls, 5) * combinations(totalWhiteBalls – chosenWhiteBalls, 0) *
combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0); // 1 * 1 * 1 * 1 = 1
// 5 White Balls only
waysToWin['5White'] = combinations(chosenWhiteBalls, 5) * combinations(totalWhiteBalls – chosenWhiteBalls, 0) *
combinations(chosenMegaBalls, 0) * combinations(totalMegaBalls – chosenMegaBalls, 1); // 1 * 1 * 1 * 24 = 24
// 4 White Balls + Mega Ball
waysToWin['4WhiteMega'] = combinations(chosenWhiteBalls, 4) * combinations(totalWhiteBalls – chosenWhiteBalls, 1) *
combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0); // 5 * 65 * 1 * 1 = 325
// 4 White Balls only
waysToWin['4White'] = combinations(chosenWhiteBalls, 4) * combinations(totalWhiteBalls – chosenWhiteBalls, 1) *
combinations(chosenMegaBalls, 0) * combinations(totalMegaBalls – chosenMegaBalls, 1); // 5 * 65 * 1 * 24 = 7,800
// 3 White Balls + Mega Ball
waysToWin['3WhiteMega'] = combinations(chosenWhiteBalls, 3) * combinations(totalWhiteBalls – chosenWhiteBalls, 2) *
combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0); // 10 * 2080 * 1 * 1 = 20,800
// 3 White Balls only
waysToWin['3White'] = combinations(chosenWhiteBalls, 3) * combinations(totalWhiteBalls – chosenWhiteBalls, 2) *
combinations(chosenMegaBalls, 0) * combinations(totalMegaBalls – chosenMegaBalls, 1); // 10 * 2080 * 1 * 24 = 499,200
// 2 White Balls + Mega Ball
waysToWin['2WhiteMega'] = combinations(chosenWhiteBalls, 2) * combinations(totalWhiteBalls – chosenWhiteBalls, 3) *
combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0); // 10 * 40920 * 1 * 1 = 409,200
// 1 White Ball + Mega Ball
waysToWin['1WhiteMega'] = combinations(chosenWhiteBalls, 1) * combinations(totalWhiteBalls – chosenWhiteBalls, 4) *
combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0); // 5 * 67900 * 1 * 1 = 339,500
// 0 White Balls + Mega Ball
waysToWin['0WhiteMega'] = combinations(chosenWhiteBalls, 0) * combinations(totalWhiteBalls – chosenWhiteBalls, 5) *
combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0); // 1 * 7927536 * 1 * 1 = 7,927,536
// Sum of all ways to win any prize
var totalWaysToWinAnyPrize = 0;
for (var key in waysToWin) {
if (waysToWin.hasOwnProperty(key)) {
totalWaysToWinAnyPrize += waysToWin[key];
}
}
// Display results
document.getElementById("resultJackpot").innerHTML = "Jackpot (5 White + Mega Ball): " + formatOdds(totalPossibleCombinations / (waysToWin['jackpot'] * numTicketsPlayed));
document.getElementById("result5White").innerHTML = "Match 5 White Balls: " + formatOdds(totalPossibleCombinations / (waysToWin['5White'] * numTicketsPlayed));
document.getElementById("result4WhiteMega").innerHTML = "Match 4 White + Mega Ball: " + formatOdds(totalPossibleCombinations / (waysToWin['4WhiteMega'] * numTicketsPlayed));
document.getElementById("result4White").innerHTML = "Match 4 White Balls: " + formatOdds(totalPossibleCombinations / (waysToWin['4White'] * numTicketsPlayed));
document.getElementById("result3WhiteMega").innerHTML = "Match 3 White + Mega Ball: " + formatOdds(totalPossibleCombinations / (waysToWin['3WhiteMega'] * numTicketsPlayed));
document.getElementById("result3White").innerHTML = "Match 3 White Balls: " + formatOdds(totalPossibleCombinations / (waysToWin['3White'] * numTicketsPlayed));
document.getElementById("result2WhiteMega").innerHTML = "Match 2 White + Mega Ball: " + formatOdds(totalPossibleCombinations / (waysToWin['2WhiteMega'] * numTicketsPlayed));
document.getElementById("result1WhiteMega").innerHTML = "Match 1 White + Mega Ball: " + formatOdds(totalPossibleCombinations / (waysToWin['1WhiteMega'] * numTicketsPlayed));
document.getElementById("result0WhiteMega").innerHTML = "Match Mega Ball only: " + formatOdds(totalPossibleCombinations / (waysToWin['0WhiteMega'] * numTicketsPlayed));
document.getElementById("resultAnyPrize").innerHTML = "Overall Odds of Winning Any Prize: " + formatOdds(totalPossibleCombinations / (totalWaysToWinAnyPrize * numTicketsPlayed));
}
// Calculate on page load with default value
window.onload = calculateMegaMillions;