Calculate jackpot and secondary tier odds for Powerball, Mega Millions, and custom multi-ball lotteries with expected value.
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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.
\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).
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%).
The odds of winning the US Powerball jackpot are exactly 1 in 292,201,338.
The odds of winning the US Mega Millions jackpot (5 of 70 plus 1 of 25) are exactly 1 in 302,575,350.
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.
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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