Lottery Odds Explained: Exact Jackpot Odds for 20 Games
Every lottery jackpot comes down to one question: how many different lines could be drawn? If a game has 13,983,816 possible lines and you hold one of them, your chance of matching all the numbers is 1 in 13,983,816. This guide shows how that number is calculated, lists the exact figures for 20 games, and explains which choices change your odds and which do not.
The jackpot odds for 20 games
The table below uses each game's basic number selection, as described in the operator's official rules. Each game name links to its source. The figures are calculated exactly, not estimated, and are sorted from the easiest jackpot to the hardest.
| Game | Basic selection | Chance one line matches every number |
|---|---|---|
| Loto 6 Japan | Pick 6 from 1-43 | 1 in 6,096,454 |
| Thunderball UK | Pick 5 from 1-39 + 1 bonus from 1–14 | 1 in 8,060,598 |
| Saturday Lotto Australia | Pick 6 from 1-45 | 1 in 8,145,060 |
| Loto 7 Japan | Pick 7 from 1-37 | 1 in 10,295,472 |
| Lotto 6/49 Canada | Pick 6 from 1-49 | 1 in 13,983,816 |
| Set For Life UK | Pick 5 from 1-47 + 1 bonus from 1–10 | 1 in 15,339,390 |
| French Loto France | Pick 5 from 1-49 + 1 bonus from 1–10 | 1 in 19,068,840 |
| EuroDreams Europe | Pick 6 from 1-40 + 1 bonus from 1–5 | 1 in 19,191,900 |
| SA PowerBall South Africa | Pick 5 from 1-50 + 1 bonus from 1–20 | 1 in 42,375,200 |
| UK Lotto UK | Pick 6 from 1-59 | 1 in 45,057,474 |
| Mega-Sena Brazil | Pick 6 from 1-60 | 1 in 50,063,860 |
| Oz Lotto Australia | Pick 7 from 1-47 | 1 in 62,891,499 |
| Lotto Max Canada | Pick 7 from 1-52 | 1 in 133,784,560 |
| AU Powerball Australia | Pick 7 from 1-35 + 1 bonus from 1–20 | 1 in 134,490,400 |
| EuroMillions Europe | Pick 5 from 1-50 + 2 bonus from 1–12 | 1 in 139,838,160 |
| Eurojackpot Europe | Pick 5 from 1-50 + 2 bonus from 1–12 | 1 in 139,838,160 |
| La Primitiva Spain | Pick 6 from 1-49 + 1 bonus from 0–9 | 1 in 139,838,160 |
| Mega Millions USA | Pick 5 from 1-70 + 1 bonus from 1–24 | 1 in 290,472,336 |
| Powerball USA | Pick 5 from 1-69 + 1 bonus from 1–26 | 1 in 292,201,338 |
| SuperEnalotto Italy | Pick 6 from 1-90 | 1 in 622,614,630 |
Optional add-ons, multipliers and drawn supplementary balls are not included. They change secondary prizes, not the chance that one line matches every main number and every bonus number.
How the odds are calculated
Lottery numbers are drawn without replacement, and the order does not matter. So the number of possible lines is a combination: the number of ways to choose k numbers from n, written C(n, k).
C(n, k) = n × (n − 1) × … × (n − k + 1) ÷ (k × (k − 1) × … × 1)
Worked example: Lotto 6/49
Lotto 6/49 asks for six numbers from 1 to 49.
- Multiply six descending numbers starting at 49: 49 × 48 × 47 × 46 × 45 × 44 = 10,068,347,520.
- Divide by 6 × 5 × 4 × 3 × 2 × 1 = 720, because the same six numbers in any order count as one line.
- The result is 13,983,816 possible lines.
One line wins the jackpot, so the odds are 1 in 13,983,816.
Worked example: Powerball
Powerball has two separate drums: five white balls from 1 to 69 and one Powerball from 1 to 26. The two choices are independent, so you multiply them.
- Main numbers: C(69, 5) = 11,238,513.
- Powerball: 26 possibilities.
- Total: 11,238,513 × 26 = 292,201,338.
A bonus drawn from its own pool multiplies the number of possible lines by the size of that pool. That is why a second drum makes the jackpot so much harder to win. EuroMillions multiplies C(50, 5) = 2,118,760 by C(12, 2) = 66 Lucky Star pairs, giving 139,838,160.
A note on La Primitiva
La Primitiva's top category requires six numbers from 1 to 49 and the reintegro, a single digit from 0 to 9 that the operator assigns to your ticket. Six numbers alone have odds of 1 in 13,983,816; the special category with the reintegro is ten times harder, at 1 in 139,838,160. The table shows the special category because it matches every number the generator simulates.
What changes your odds, and what does not
More lines: yes, but only in proportion
Each additional, different line adds one more winning possibility. Ten different Lotto 6/49 lines give a 10 in 13,983,816 chance, roughly 1 in 1.4 million. Doubling your spending doubles your chance; it does not change the order of magnitude. Buying the same line twice doubles the payout if it wins, not the chance of winning.
Quick pick or chosen numbers: no difference
A fair draw gives every line the same probability. A line generated at random, a line of birthdays, and 1-2-3-4-5-6 are all exactly as likely as each other. No pattern, frequency chart, or "hot number" list changes this, because each draw is independent of the previous one. A number that has not appeared for months is not "due."
Sharing the jackpot: here, your choice matters
Odds are the same for every line, but prize amounts can differ in games where winners of a prize tier share a fixed pool. If many people play the same numbers and those numbers come up, the prize is divided among more winners.
Many players choose dates, which limits them to 1–31. In Powerball, only 169,911 of the 11,238,513 possible main-number combinations use numbers from 1 to 31 alone, about 1.5%. A line spread across the whole range is no more likely to win, but it is less likely to resemble lines chosen by other players. Generating numbers at random is a simple way to avoid accidental patterns.
Generate a line for any of these games
The lottery number generator includes all 20 formats above, with presets for Powerball, Mega Millions, EuroMillions, and Eurojackpot. Each line is drawn with your browser's cryptographic random generator, without duplicate main numbers. To draw numbers for a custom raffle or game, use the random number generator and turn off duplicates.
A generated line is a suggestion, not a ticket. Randomify is not connected to any lottery operator, and generating numbers at random cannot improve your chance of winning.
Frequently asked questions
Which lottery has the best jackpot odds? Of the 20 games listed, Japan's Loto 6 has the best single-line odds at 1 in 6,096,454, followed by UK Thunderball at 1 in 8,060,598. Better odds usually come with smaller jackpots.
Which has the worst? SuperEnalotto, with six numbers from 1 to 90: 1 in 622,614,630.
Are odds the same as the probability of winning anything? No. Most games pay smaller prizes for partial matches, so the chance of winning some prize is much higher than the jackpot odds. Each operator publishes its odds for every prize tier.
Can a random number generator predict lottery numbers? No. A properly run draw is unpredictable, and past results do not influence future ones. Any service that claims to predict draws is making a promise that probability does not support.
Play for entertainment and only with money you can afford to lose. If gambling is no longer fun, contact a local support service for help.