Calculate lottery odds, expected value, and prize probabilities for any lottery format. Generate random numbers and compare Powerball, Mega Millions, EuroMillions odds.
The Lottery Calculator turns lottery rules into exact odds. Whether the game is Powerball-style, a simple Pick 3, or a custom format, the page calculates combinations, jackpot probability, expected value, and prize-tier odds from the pools you enter.
You can configure the main number pool, bonus ball pool, and pick count, then generate random tickets if you want a sample entry. The comparison table helps you see how different lotteries stack up by odds, jackpot size, and ticket price.
That makes the page useful for odds checks, classroom examples, or a reality check before buying a ticket.
Lottery odds are easy to misunderstand because the headline jackpot number hides the size of the number space underneath. This calculator makes that space explicit and turns the format into combinations, probabilities, and expected value.
It is also a straightforward teaching example for combinations and expected value because the result is concrete and the odds are usually very small.
Jackpot odds = C(mainPool, mainPick) × C(bonusPool, bonusPick). C(n,k) = n! / (k!(n-k)!). Expected value = (Jackpot / Odds) − Ticket Price. 50% threshold weeks = ln(0.5) / ln(1 − 1/odds).
Result: Odds: 1 in 292,201,338. EV: −$0.97 per ticket. Need ~14.6 million years of weekly play for 50% win chance.
Powerball has C(69,5)×C(26,1) = 292,201,338 combinations. Even at $300M, each $2 ticket has an expected value of about −$0.97 (losing nearly half per ticket on average).
Lottery odds come from combinatorics — specifically the combination formula C(n,k) = n!/(k!(n-k)!). For Powerball's main draw: C(69,5) = 11,238,513 ways to choose 5 numbers from 69. Multiply by the bonus ball options C(26,1) = 26, giving 292,201,338 total combinations. Each has probability 1/292,201,338 ≈ 0.000000342%.
Expected value (EV) = Σ(prize × probability) − ticket cost. For most draws, EV is deeply negative (−40% to −50%). Even record-breaking jackpots rarely achieve positive EV because: (1) taxes take 37–50%, (2) lump sum is ~60% of advertised prize, (3) multiple winners split the pot, (4) lower-tier prizes have fixed, small payouts.
The lottery's true product isn't money — it's the dream. Behavioral economists call it "possibility weighting" — humans systematically overweight tiny probabilities, making a 0.0000003% chance feel much larger than it is.
If you enjoy playing the lottery, treat it as entertainment with hard budget limits. Never chase losses, never spend money needed for essentials, and never believe in "hot numbers" or "due numbers." Each draw is independent — the lottery has no memory. The odds are identical whether you play your birthday numbers for 30 years or use random picks for one draw.
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No. Every combination has identical probability. Quick picks and personal numbers have the same chance. However, common patterns (1-2-3-4-5) are more likely to be chosen by others, meaning more jackpot splits if you win.
It depends on the game, ticket price, taxes, and whether the payout is annuity or lump sum. In practice, the jackpot usually has to be extremely large before the expected value gets close to break-even.
Mathematically identical. 10 tickets in one draw vs 1 ticket in 10 draws both give you 10 chances. Neither strategy changes the fundamental odds.
Pool size drives it exponentially. Going from 6/49 (13.9M combos) to 5/69+1/26 (292M combos) makes the game 21× harder. Larger pools = bigger jackpots but much worse odds.
For Powerball, about 1 in 24.9 — much better than the jackpot odds. Most lower-tier prizes are $4–$7, which just covers a couple more tickets.
It uses the browser's Math.random() to pick numbers uniformly from each pool without replacement. Every valid combination is equally likely.