Lottery Odds Calculator
Calculate jackpot and secondary tier odds for Powerball, Mega Millions, and custom multi-ball lotteries with expected value.
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What Is a Lottery Odds Calculator?
The Lottery Odds Calculator determines the exact mathematical odds of winning the grand prize jackpot and every secondary prize tier in multi-ball lottery drawings. It supports US Powerball, Mega Millions, EuroMillions, and custom ball pool formats.
How to Use This Calculator
- Select a preset (US Powerball 5/69 + 1/26, Mega Millions 5/70 + 1/25, or Classic 6/49) or enter custom ball pools.
- Enter the white ball pool size and number of white balls drawn.
- Specify bonus ball pool size if applicable.
- Examine jackpot odds, overall odds of winning any prize, and ticket expected value.
Lottery Combinations Formula
\text{Jackpot Odds} = \binom{N}{k} \times M = \frac{N!}{k!(N-k)!} \times MWhere N is the white ball pool (e.g. 69), k is white balls drawn (e.g. 5), and M is the bonus ball pool (e.g. 26).
Worked Example
Scenario: Find the exact odds of winning the Powerball jackpot by matching 5 white balls out of 69 plus 1 red Powerball out of 26.
White ball combinations: C(69, 5) = 11,238,513.
Red Powerball choices: 26.
Total unique ticket combinations: 11,238,513 × 26 = 292,201,338.
Jackpot probability: 1 in 292,201,338 (approx 0.000000342%).
Tips & Key Notes
- Buying two tickets doubles your chance from 1 in 292 million to 2 in 292 million (1 in 146 million), which remains astronomically unlikely.
- You are statistically more likely to be struck by lightning (approx 1 in 15,300 in a lifetime) or become an astronaut than win a major multi-state lottery jackpot.
Frequently Asked Questions
What are the odds of winning the Powerball jackpot?
The odds of winning the US Powerball jackpot are exactly 1 in 292,201,338.
What are the odds of winning the Mega Millions jackpot?
The odds of winning the US Mega Millions jackpot (5 of 70 plus 1 of 25) are exactly 1 in 302,575,350.
Does picking "lucky" or "unpopular" numbers increase your odds?
Every combination has the exact same probability of being drawn. However, picking unpopular numbers (such as numbers above 31, which avoid birthdays) reduces the chance of having to split the jackpot if you win.
Can a lottery ticket ever have positive expected value (+EV)?
Rarely, when jackpots climb above $1 Billion, the mathematical expected value can theoretically exceed the $2 ticket price. However, federal/state taxes (approx 37%+) and the high probability of splitting the jackpot with other winners typically keep true expected value negative.
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