Will 27 tickets guarantee a lottery win?

Chris Smith put the question to the University of Nottingham's Tony Padilla...

Tony - I know the story. You have to buy 27 tickets and if you buy 27 tickets, you will win. You won't necessarily win the jackpot, but you'll win something, maybe just the lowest prize that you can get which is if you get two numbers. What was really impressive in what they did was that they actually were able to show that if you buy 26 tickets, you're not guaranteed. Proving that 27 is enough was actually the easy part.

Chris - If I bought one hundred percent of the tickets, I have to win, don't I?

Tony - So I think there's something like, I can't remember the exact number, 45 million, 47 million combinations or something. So if you bought a ticket with every single combination in, you're obviously going to win, right? That's guaranteed.

Chris - But the jackpot isn't a hundred percent return, so therefore you still lose money?

Tony - Yes. But you can bring that number down to 27, and actually they showed it using some really funky finite geometry, some really cool maths. And they were able to show that there were 27 combinations of numbers which will always have at least two of the numbers that appear on Saturday's draw.

Chris - Are they specific? Have you got to choose a certain sequence of numbers?

Tony - There's not just one set that you have to choose. You don't have to put the same 27 as me. We just have to arrange them in a certain way. The way they actually were able to show this, they were able to package your choice of numbers into a bunch of clever diagrams. And there were five of these diagrams and actually there's six numbers on the lottery ticket. So it was always guaranteed that you couldn't have all the numbers appearing in all the different diagrams, there always had to be one diagram which had two of the numbers. And that was the key to winning. But the hard part was proving that 26 was not enough. Actually the calculation for proving that 26 was not enough in principle should have 10 to the 165 steps, which is one with 165 zeros after it, which is clearly just completely impractical. There's just not enough time in the universe for that calculation. But they used some really clever software called prologue, which was able to help them with their calculation.

Chris - And when it comes down to making a profit or not, have they done any modelling to see what would happen if you did this every week at the end of a year of playing the game? But you won't necessarily win your money back each time because it's going to cost you x amount of pounds to enter.

Tony - It costs you 54 quid to buy the 27 tickets.

Chris - It's two pounds a time. Have they modelled that? How long would you have to play the lottery so that you've got a chance you're actually going to be at least cost neutral?

Tony - That's not discussed in the paper.

Chris - That's the key question, isn't it? I mean, what's the point of doing the research?

Tony - I was telling my wife about this yesterday and she was like, "well, prove it then." I was like, "what do you mean prove it? They proved it! We're going to lose. We might win, but we'll ultimately lose because it's going to cost us 54 pounds. We're very unlikely to win more than 54 pounds.