The foolproof way to win any lottery, according to maths

How can you guarantee a huge payout from any lottery? Take a cue from combinatorics, and perhaps gather a few wealthy pals, says Jacob Aron

By Jacob Aron

3 July 2025

How can maths help you win the lottery?

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I have a completely foolproof, 100-per-cent-guaranteed method for winning any lottery you like. If you follow my very simple method, you will absolutely win the maximum jackpot possible. There is just one teeny, tiny catch – you’re going to need to already be a multimillionaire, or at least have a lot of rich friends.

Let’s take the US Powerball lottery as an example. To play, you pick five different “white” numbers from 1 to 69, and a sixth “red” number from 1 to 26 – this last number can be a repeat of one of the white ones. How many different possible lottery tickets are there? To calculate that, we need to turn to a field of mathematics called combinatorics, which, as the name suggests, is a way of calculating the number of possible combinations of objects.

Picking numbers from an unordered set, as with a lottery, is an example of an “n choose k” problem, where n is the total number of objects we can choose from (69 in the case of the white Powerball numbers) and k is the number of objects we want to pick from that set. Crucially, because you can’t repeat the white numbers, these choices are made “without replacement” – as each winning numbered ball is selected for the lottery, it doesn’t go back into the pool of available choices.

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Mathematicians have a handy formula for calculating the number of possible results of an n choose k problem: n! / !). If you’ve not encountered it before, a mathematical “!” doesn’t mean we’re very excited – it’s a symbol that stands for the factorial of a number, which is simply the number you get when you multiply a whole number, or integer, by all of those smaller than itself. For example, 3! = 3 × 2 × 1 = 6.

Plugging in 69 for n and 5 for k, we get a total of 11,238,513. That’s quite a lot of possible lottery tickets, but as we will see later on, perhaps not enough. This is where the red Powerball comes in – it essentially means you are playing two lotteries at once and must win both for the largest prize. This makes it a lot harder to win. If you just simply added a sixth white ball, you’d have a total of 119,877,472 possibilities. But because there are 26 possibilities for red balls, we multiply the combinations of the white balls by 26 to get a total of 292,201,338 – much higher.