Statistics can be used prove anything. And when you hear economists claiming that it makes logical sense to buy a ticket for tonight’s lottery draw, it’s worth looking into their claims.
Of course, no-one is claiming that you’re odds-on to take home the jackpot, which is totalling out at nearly £60 million. But for the first time ever, the potential value of a National Lottery ticket is higher than its £2 cost, as research economists at KPMG explained to the Guardian.
Considering that you only stand a 1 in 45 million chance of scooping the jackpot, this seems counter-intuitive. After all, you’re more likely to win an Oscar, become an astronaut or die after being struck by a piece of plane debris falling from the sky. (Assuming, of course, you only buy one or two tickets.)
But consider this simple illustration: you’re offered the chance to pay £5 to roll a die and guess what number will come up. If you guess correctly, you win £60. Should you play? Logically, the answer is yes. If you played over and over again then you would average out at winning the £60 jackpot 1 in every 6 games. Each £5 roll of the dice therefore has an “expected value” of £10 (£60 divided by 6), so it’s well worth your time to play.
The same maths can be applied to this evening's draw. Depending on how many people buy one, each £2 ticket will have an “expected value” of somewhere between £4.50 (if as many people buy a ticket as on any other Saturday) and £3.20 (if there’s as many gamblers as there were in Wednesday night’s draw).
Of course, expected value only makes sense over the long run. If there were lotteries like this one every day and you kept playing over and over, you could expect to average out in profit. But there aren’t, and as there has to be a winner this Saturday then tickets for next week’s lottery will drop back down to their normal use value of 95p.
An American lottery which is now totalling out at $800 million (£551 million) is expected to pass $1 billion if no-one wins it this weekend, dwarfing the British prize. With odds of 292.2 million to 1, it's an even longer shot, but that didn't stop one punter from speculating on how he'd spend his winnings if he took home the prize:
Although the British jackpot has to be won this weekend, it’s most likely that the £60m will be shared amongst a larger number of people who each pick five correct numbers and the bonus ball, rather than any one individual picking out the top numbers. And you’re still overwhelmingly likely to win nothing at all.
For the wealthier amongst you, there’s an even better way to beat the system. All you have to do is buy every possible combination of the 59 numbers on the ticket. It would only cost you £90 million (45 million combos at £2 a ticket), and you’d be guaranteed to take home £40 million in standard prizes plus the £60m jackpot. Of course, if someone else happened to guess the winning combo as well then you’d have to split the jackpot, and be left badly out of pocket.
For those of us without a spare £90 million kicking around, the only “logical” thing to do is to try and ensure that you won’t have to share your potential winnings with anyone. That means staying away from patterns on the ticket, any numbers under 31 (because people like to pick birth dates) and would-be “clever” sequences such as last week’s winning numbers.
So go out and buy your lottery ticket- it’s the logical thing to do. Well, sort of.