The odds of winning Division 1 in Lotto are about eight million to one, but what if you were a mathematician and knew exactly how many combinations were needed to rig the system?

It’s been done before and suddenly, maths becomes really interesting.

It’s happened here in Australia (mathematician Stefan Mandel won 14 international lotteries by figuring out how to buy every possible number combination) and also in Ireland with mathematician Stefan Klincewicz, who’s the subject of a documentary at ANU called Beat the Lotto.

So wegot on the phone to a local mathematician quick smart.

Katharine Turner is Associate Professor at the ANU’s Mathematical Sciences Institute and she’s crunched the numbers.

“In the ‘90s, mathematically [Lotteries] created this loophole by having too few balls and that the number of combinations you needed was a lot less,” Professor Turner said.

“It cost less to buy all those combinations than you would get from the jackpot. So all [lotteries] needed to do was add a few more balls and all of a sudden that was no longer possible.”

Lotteries have also limited syndicates as a result of these two mathematicians buying every single combination.

“They just increased the number of balls,” Professor Turner said. “In 1992, it was 36 balls and you draw six of them and the probability of a ticket winning was about one in 1.9 million-ish.

“Since then, they’ve been gradually increasing the number of balls so that the probability of winning is so low that the number of tickets you would need to buy is unfeasible. Even if you could buy all the tickets, for Lotto in Australia you would need a bit over 8 million.”

I wonder what the probability is of having two scheming mathematicians who are both called Stefan.

“A few extra balls doesn’t sound that much but it grows exponentially,” Professor Turner said. “From 36 balls to 47 balls, it’s more than five times harder.

“With the Powerball, which is the one that gets even bigger, they have seven balls instead of six, which dramatically changes the odds because you need all seven to match rather than six. So that makes it much more unlikely.”

For those playing at home, the term for all of this counting, arranging, and analysing is “combinatorics”.

“It’s basically the maths of counting and if you talk to any mathematician, they’ll tell you that counting is hard,” Professor Turner said.

“Because you have to think about all different ways that things could intersect like the probability of getting three numbers versus four numbers. You have to make sure you don’t over-count the different arrangements of things. You may think that the probability is easy because as long as it’s done fairly, which it should be, everything is equally likely. But you have to count how many different ways you could draw six balls out of 36.”

Maths is starting to look very enticing.

“It’s sort of like a really fun game where the stakes are really high,” Professor Turner said.

“Occasionally I have fun thinking about the combinatorics of problems but not from the standpoint of winning the lotto. It might be more about what’s the optimal way to play a board game, which is a bit more mundane.”

Mathematicians may seem like mild-mannered academics, but just take a look at the scheming Stefans who rorted the system.

“People have a thing in mind of what a mathematician will look like or what a scientist will look like, and the truth is that they have the same span of personalities as any other profession,” Professor Turner said. “We’re just human.”

If you want to see how mathematician Stefan Mandel rigged the lotto, Beat the Lotto is free and screens on Thursday 23 July, 6.30pm at ANU Cinema, Lowitja O’Donoghue Cultural Centre.

Professor Turner will also give a pre-screen talk about the “birthday paradox” that will blow (or expand) your mind.

To register for a free ticket: maths.anu.edu.au/beat-the-lotto