How lottery odds are calculated
Every jackpot figure on this site is worked out from the number matrix rather than copied from anywhere. Here is the arithmetic, so you can check it.
The basic case
UK Lotto draws 6 numbers from 59. The number of different lines you could write down is the number of ways to choose 6 things from 59 without caring about order — written C(59, 6) and equal to 45,057,474.
Exactly one of those lines is the winning one, so a single entry has a 1 in 45,057,474 chance of matching it. That is the whole calculation.
Where the bonus ball does and does not come in
This is the part almost everyone gets wrong, and it goes wrong in both directions.
UK Lotto's bonus ball is drawn from the same machine, out of the balls left after the main numbers. It decides a lower prize tier, not the jackpot. It therefore does not enter the jackpot calculation at all — those balls are already counted in C(59, 6). A site that multiplies by the bonus is quoting a number far too long.
EuroMillions's Lucky Stars are different. They come from a separate wheel of 12 numbers, and you need both of them for the jackpot. So the odds are C(50, 5) multiplied by C(12, 2) — which is 1 in 139,838,160. A site that leaves the stars out is quoting a number far too short.
The rule underneath both: multiply only by extras drawn from their own pool that are required for the jackpot. Anything drawn from the main machine is already counted, and anything not required for the top prize is irrelevant to the top prize.
Two games that catch people out
SuperEnalotto. Its Jolly comes from the main 1–90 pool and its SuperStar from a separate wheel, but neither is required for the jackpot. So the figure is plain C(90, 6) — the longest odds of any game we cover. Sources that fold either extra in are wrong.
La Primitiva and Bonoloto. Identical 6-from-49 matrices, and different jackpot odds. Primitiva's top category needs the reintegro from its own 0–9 wheel, so its figure is ten times Bonoloto's. Same numbers on the balls, different prize structure.
Every game we cover
| Game | Matrix | Jackpot odds |
|---|---|---|
| US Powerball | 5/69 + 1/26 | 1 in 292,201,338 |
| Mega Millions | 5/70 + 1/24 | 1 in 290,472,336 |
| EuroMillions | 5/50 + 2/12 | 1 in 139,838,160 |
| La Primitiva | 6/49 + 1/10 | 1 in 139,838,160 |
| Lotto Max | 7/52 | 1 in 133,784,560 |
| Mega-Sena | 6/60 | 1 in 50,063,860 |
| UK Lotto | 6/59 | 1 in 45,057,474 |
| El Gordo | 5/54 + 1/10 | 1 in 31,625,100 |
| Set For Life | 5/47 + 1/10 | 1 in 15,339,390 |
| Lotto 6/49 | 6/49 | 1 in 13,983,816 |
| Bonoloto | 6/49 | 1 in 13,983,816 |
| Loto 7 | 7/37 | 1 in 10,295,472 |
| Irish Lotto | 6/45 | 1 in 8,145,060 |
| Thunderball | 5/39 + 1/14 | 1 in 8,060,598 |
| Loto 6 | 6/43 | 1 in 6,096,454 |
What the odds do not depend on
How long the jackpot has rolled. How many people are playing. Which numbers came up last week. Whether you pick your own numbers or take a random line. None of it moves the figure, because the figure is a property of the matrix and nothing else.
A rollover changes what you would win. It does not change the chance of winning it, and a bigger jackpot usually means more entries, so it slightly increases the chance of sharing.
How we keep these right
Every figure in our registry is checked against the combinatorics automatically, on every change, and the build fails if one disagrees. Nobody can type a jackpot figure into this site by hand — including us.