Every lottery ticket comes with a number like “1 in 292,201,338”. It isn't an estimate or a marketing figure: it is an exact count of the possible tickets. Once you know how that count works, you can work out the odds of any lottery yourself, understand why smaller prizes are so much easier to win, and spot the beliefs that don't hold up. This guide uses real games and calculations you can check.
Counting combinations: the 6 out of 49 example
Take a classic 6/49 lottery, like Canada's Lotto 6/49: you choose 6 numbers from 1 to 49, and 6 are drawn. How many different tickets exist?
The first number can be any of 49, the second any of the 48 left, and so on: 49 × 48 × 47 × 46 × 45 × 44. But the order doesn't matter, since 3, 17, 22 is the same ticket as 22, 3, 17. So you divide by the number of ways to order 6 numbers, 6 × 5 × 4 × 3 × 2 × 1 = 720. The result is 13,983,816 combinations. Only one of them is the winning one, so the jackpot odds are 1 in 13,983,816 per line.
Games with two drums
Many big lotteries add a second, separate drum. You multiply the two counts.
- Powerball: 5 white balls from 69 give 11,238,513 combinations. Multiply by 26 possible Powerballs: 292,201,338.
- Mega Millions: 5 from 70 give 12,103,014 combinations, times 24 Mega Balls: 290,472,336.
- EuroMillions: 5 from 50 give 2,118,760 combinations, times 66 pairs of Lucky Stars from 12: 139,838,160.
That second drum is why these jackpots are so rare, and also why they grow so big. Here are the odds per line for some well-known games, computed from their current rules, as shown on our generator pages.
| Game | Jackpot | Any prize |
|---|---|---|
| Powerball | 1 in 292,201,338 | 1 in 24.87 |
| Mega Millions | 1 in 290,472,336 | 1 in 23.07 |
| EuroMillions | 1 in 139,838,160 | 1 in 12.97 |
| Lotto 6/49 | 1 in 13,983,816 | 1 in 6.62 |
Why smaller prizes are much easier
To match exactly 3 numbers out of 6 in a 6/49 game, three of your numbers must be among the 6 drawn, and your other three among the 43 that weren't. Count the ways for each part and multiply: 20 × 12,341 = 246,820 tickets. Divide by 13,983,816 and you get about 1 in 57.
| Numbers matched (6/49) | Winning tickets | Odds |
|---|---|---|
| 6 | 1 | 1 in 13,983,816 |
| 5 | 258 | 1 in 54,201 |
| 4 | 13,545 | 1 in 1,032 |
| 3 | 246,820 | 1 in 57 |
| 2 | 1,851,150 | 1 in 7.6 |
Each number you give up makes a win far more likely: going from 6 matches to 5 multiplies the chances by 258, from 4 to 3 by about 18. That is why “any prize” odds look friendly: almost all of those wins are the smallest tiers, which often pay back little more than the ticket.
What 1 in 292 million really means
Big numbers are hard to picture, so turn them into time. Powerball is drawn three times a week. If you played one line in every draw, you would wait on average about 1.9 million years for a jackpot. Buying 10 lines per draw makes you exactly 10 times more likely to win, which is still 1 in about 29 million. To have an even chance in a single draw, you would need to buy half of all combinations, 146,100,669 different lines.
None of this means nobody wins. Millions of people play, so someone eventually matches. It just means that for any one ticket, the jackpot is extremely unlikely.
Lottery myths the math doesn't support
- “This number is due.” Balls have no memory. In Powerball, each white number has the same 5 in 69 chance (about 7.2%) of being drawn in every draw, whatever happened before.
- “Hot numbers keep coming.” Over a few hundred draws, some numbers come up more often by pure chance. It says nothing about the next draw.
- “1, 2, 3, 4, 5, 6 can never win.” It has exactly the same odds as any other line. It just looks less random to us.
- “Quick picks win less often.” A random line and a line you chose yourself have the same odds. The draw doesn't know how a ticket was made.
One belief does have a basis. When a jackpot is shared between winners, popular choices like birthdays (numbers up to 31) or neat patterns are played by many people, so a win could be split more ways. Random numbers don't win more often, but they may be shared less. Our lottery number generator picks lines with a cryptographic random generator, for fun.
Play for fun, with a budget
Lotteries pay out only part of what they take in, so over time players as a whole lose money. Treat a ticket like the price of a little daydream, set an amount you're happy to spend, and never chase losses. If playing stops being fun, talk to someone you trust or to a problem gambling helpline in your country.
Updated November 4, 2026