Mega Millions Odds Calculator
Use this calculator to determine your odds of winning various Mega Millions prizes based on the number of tickets you purchase.
Understanding Mega Millions Odds
Mega Millions is one of the most popular lottery games in the United United States, known for its massive jackpots. To win the jackpot, a player must match five white balls drawn from a pool of 70 numbers (1-70) and one Mega Ball drawn from a separate pool of 25 numbers (1-25).
How the Odds Are Calculated
The odds of winning Mega Millions are determined by the principles of probability and combinations. Since the order in which the white balls are drawn does not matter, we use the combination formula:
C(n, k) = n! / (k! * (n-k)!)
- White Balls: You need to choose 5 correct numbers from 70. The number of combinations for this is C(70, 5).
- Mega Ball: You need to choose 1 correct number from 25. The number of combinations for this is C(25, 1).
To find the total number of unique combinations for the jackpot, you multiply the combinations for the white balls by the combinations for the Mega Ball. For Mega Millions, this results in:
C(70, 5) * C(25, 1) = 12,103,014 * 25 = 302,575,350
This means there are 302,575,350 possible unique combinations of numbers, and only one of them will win the jackpot. Therefore, the odds of winning the Mega Millions jackpot with a single ticket are 1 in 302,575,350.
Impact of Buying Multiple Tickets
When you purchase multiple tickets, you increase your chance of winning, but the odds per individual ticket remain the same. For example, if you buy 10 tickets, you have 10 chances out of 302,575,350 to win the jackpot. Your effective odds become 1 in (302,575,350 / 10), which is 1 in 30,257,535. While this improves your chances, the odds still remain astronomically high.
Other Prize Tiers
Mega Millions offers nine different prize tiers, ranging from matching just the Mega Ball to hitting the full jackpot. Each tier has its own set of odds, calculated based on the specific combination of white balls and Mega Balls required to win that prize. For instance, matching five white balls but not the Mega Ball has significantly better odds than the jackpot, but still represents a rare event.
Realistic Expectations
It's important to approach lottery games with realistic expectations. While the dream of winning a massive jackpot is enticing, the mathematical odds are heavily stacked against individual players. Playing for entertainment and managing your budget are key aspects of responsible lottery participation.
Mega Millions Odds Calculation
"; resultHTML += "Odds of winning the jackpot with a single ticket: 1 in " + totalPossibleCombinations.toLocaleString() + ""; if (ticketsPurchased > 1) { resultHTML += "With " + ticketsPurchased.toLocaleString() + " tickets, your odds of winning the jackpot are approximately: 1 in " + Math.round(effectiveJackpotOdds).toLocaleString() + ""; resultHTML += "This means you have " + ticketsPurchased.toLocaleString() + " chances out of " + totalPossibleCombinations.toLocaleString() + " to win the jackpot."; } // Prize Tiers and their ways to win var prizeTiers = [ { name: "Match 5 White + Mega Ball (Jackpot)", ways: combinations(chosenWhiteBalls, 5) * combinations(totalWhiteBalls – chosenWhiteBalls, 0) * combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0) }, { name: "Match 5 White only", ways: combinations(chosenWhiteBalls, 5) * combinations(totalWhiteBalls – chosenWhiteBalls, 0) * combinations(chosenMegaBalls, 0) * combinations(totalMegaBalls – chosenMegaBalls, 1) }, { name: "Match 4 White + Mega Ball", ways: combinations(chosenWhiteBalls, 4) * combinations(totalWhiteBalls – chosenWhiteBalls, 1) * combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0) }, { name: "Match 4 White only", ways: combinations(chosenWhiteBalls, 4) * combinations(totalWhiteBalls – chosenWhiteBalls, 1) * combinations(chosenMegaBalls, 0) * combinations(totalMegaBalls – chosenMegaBalls, 1) }, { name: "Match 3 White + Mega Ball", ways: combinations(chosenWhiteBalls, 3) * combinations(totalWhiteBalls – chosenWhiteBalls, 2) * combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0) }, { name: "Match 3 White only", ways: combinations(chosenWhiteBalls, 3) * combinations(totalWhiteBalls – chosenWhiteBalls, 2) * combinations(chosenMegaBalls, 0) * combinations(totalMegaBalls – chosenMegaBalls, 1) }, { name: "Match 2 White + Mega Ball", ways: combinations(chosenWhiteBalls, 2) * combinations(totalWhiteBalls – chosenWhiteBalls, 3) * combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0) }, { name: "Match 1 White + Mega Ball", ways: combinations(chosenWhiteBalls, 1) * combinations(totalWhiteBalls – chosenWhiteBalls, 4) * combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0) }, { name: "Match Mega Ball only", ways: combinations(chosenWhiteBalls, 0) * combinations(totalWhiteBalls – chosenWhiteBalls, 5) * combinations(chosenMegaBalls, 1) * combinations(totalMegaBalls – chosenMegaBalls, 0) } ]; resultHTML += "Odds for Other Prize Tiers (per single ticket):
- ";
for (var i = 0; i 0) {
var odds = totalPossibleCombinations / tier.ways;
resultHTML += "
- " + tier.name + ": 1 in " + Math.round(odds).toLocaleString() + " "; } else { resultHTML += "
- " + tier.name + ": Impossible (0 ways to win) "; } } resultHTML += "