Calculate lottery odds, expected value, and prize probabilities for any lottery format. Generate random numbers and compare Powerball, Mega Millions, EuroMillions odds.
What are your real chances of winning the lottery? The Lottery Calculator reveals the exact mathematical truth behind every lottery format — from Powerball's 1-in-292-million jackpot odds to local Pick 3 games with 1-in-1,000 chances. No wishful thinking, just combinatorics.
Configure any lottery format by setting the main number pool, bonus ball pool, and how many numbers you pick. The calculator instantly computes the total combinations, jackpot probability, expected value per ticket, and a full prize tier breakdown. Then generate random number tickets with a single click.
Expected value analysis shows whether a particular jackpot size makes a ticket "worth" buying mathematically (spoiler: it almost never does). The comparison table lets you weigh different lotteries by odds, jackpot size, and ticket price. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case. Use the example pattern when troubleshooting unexpected results.
Lotteries are a $100+ billion industry built on probability illiteracy. This calculator strips away the marketing and shows you the raw math. Understanding that 1-in-292-million means playing weekly for 5.6 million years on average helps calibrate expectations.
It's also an excellent teaching tool for combinatorics, expected value, and probability — concepts directly applicable to finance, insurance, and risk management.
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.
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.
For Powerball, the jackpot would need to exceed ~$584M with no other winners for positive EV. But taxes, annuity vs lump sum, and jackpot splitting mean true positive EV essentially never occurs.
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.