How Lottery Odds Are Calculated
Jackpot odds come from simple combinatorics. A game that asks you to pick k numbers from a pool of n has C(n, k) = n! / (k! × (n − k)!) possible combinations. If there is a separate bonus ball, you multiply by the number of ways to pick it. Only one combination wins the jackpot, so a single ticket's odds are 1 in the total number of combinations.
| Game (2026 rules) | Format | Price per play | Jackpot odds |
|---|---|---|---|
| Powerball | 5 of 69 + 1 of 26 | $2 | 1 in 292,201,338 |
| Mega Millions | 5 of 70 + 1 of 24 | $5 | 1 in 290,472,336 |
| Millionaire for Life | 5 of 58 + 1 of 5 | $5 | 1 in 22,910,580 |
| EuroMillions | 5 of 50 + 2 of 12 | £2.50 in the UK (varies by country) | 1 in 139,838,160 |
| Classic 6/49 lotto | 6 of 49 | Varies | 1 in 13,983,816 |
Powerball: C(69,5) = 11,238,513 ways to pick the white balls, times 26 Powerballs = 292,201,338. Buying one ticket every second, around the clock, it would take about 9.3 years to buy every combination once.
Mega Millions: the game was overhauled in April 2025. A play now costs $5 and includes a built-in random multiplier, and the Mega Ball pool shrank from 25 to 24 numbers, improving the jackpot odds from 1 in 302,575,350 to 1 in 290,472,336.
Millionaire for Life: launched on February 22, 2026, replacing Cash4Life and Lucky for Life. Its top prize ($1 million a year for life) has much better odds than the big jackpot games — 1 in 22,910,580 — but it is still extremely unlikely.
EuroMillions: two Lucky Stars are drawn from 12, which is C(12,2) = 66 combinations (not 12 × 12), giving 2,118,760 × 66 = 139,838,160.
Lifetime Odds: Playing Every Week for Decades
Buying more tickets raises your chance, but only in a straight line, and from a tiny starting point. The exact chance of at least one jackpot from N tickets is 1 − (1 − p)N, which for small p is almost exactly N × p.
| Powerball tickets | Total cost ($2 each) | Chance of at least one jackpot |
|---|---|---|
| 1 ticket | $2 | 1 in 292,201,338 |
| 100 tickets | $200 | 1 in 2,922,014 |
| 3,120 tickets (2 a week for 30 years) | $6,240 | 1 in 93,655 |
| 4,680 tickets (1 per drawing, 3 drawings a week, 30 years) | $9,360 | 1 in 62,437 |
| 46,800 tickets (10 per drawing for 30 years) | $93,600 | 1 in 6,244 |
Even spending $93,600 over 30 years leaves you with roughly a 0.016% chance of ever hitting the jackpot.
Expected Value: Why the Average Ticket Loses Money
Under Powerball's game rules, about 50% of ticket sales go into the prize pool; the rest goes to the participating lotteries (which fund state programs), retailer commissions and operating costs. That means across all players, roughly half of every dollar spent comes back as prizes. For comparison, the house edge on an American roulette wheel is about 5.26%.
The expected value of an individual ticket does rise when a jackpot rolls over to a very large amount, but taxes, the lower lump-sum cash option and the chance of splitting the prize with other winners usually keep it below the ticket price. This calculator uses the long-run payout share (adjustable above) to estimate the average loss.
What the Same Money Could Do Instead
Two $2 tickets a week is about $17 a month. Invested every month for 30 years:
- At 7% a year: about $21,100 (from $6,240 contributed)
- At 10% a year: about $39,200
- $20 a week at 7%: about $105,700
These are projections, not guarantees: stock-market returns are volatile, and 7% is a rough long-run real-world assumption rather than a promise. The point is the direction: regular investing has a positive expected result, while lottery spending has a negative one.
If You Play, Play It as Entertainment
Spending a couple of dollars for a few days of daydreaming is a perfectly reasonable entertainment purchase. Problems start when tickets are treated as a financial plan, or when spending grows beyond what you would spend on any other hobby. If gambling stops being fun, free confidential help is available in the U.S. at 1-800-GAMBLER.
Common Lottery Myths
"I'm due for a win." Each drawing is independent. Past losses do not change future odds — this is the gambler's fallacy.
"Some numbers are luckier." Every combination has exactly the same probability. Picking 1-2-3-4-5 is as likely as any other set — though popular patterns like birthdays are more likely to be shared with other winners if they do come up.
"Someone has to win eventually." Rollovers do end eventually because so many tickets are sold, but that says nothing about your individual ticket's odds.