Winning The Lottery

I thought I’d start my blogging career with a bang, a desperate push for immediate attention if you will. And what better way than by explaining how to win the freaking lottery.

Wait, don’t click away! It’s not a scam (or even a particularly practical guide to winning the lottery, but we’ll get to that). We’ve all seen the scams, either claiming you have already mysteriously won huge sums of money or asking for you to pay for their foolproof technique for picking the right numbers. I am definitely not claiming to have millions of pounds to give you and I am not asking for any payment whatsoever. Being a student I will obviously accept any donations (monetary or alcoholic), but I’m not demanding anything. I’m nice like that.

Incidentally, one of my favourite lottery ‘techniques’ is to pick your numbers based on what kind of streak they’re on, presumably because some lottery balls are better at wiggling their way out of the machine than others (although, there’s likely to be some differences in probability given the minute discrepancies in the size and weight of the balls. While I’m confident the differences in probability are negligible, the thought is worth a little digression) . Do not pick numbers based on hot streaks. Please, it makes statisticians cry.

Pictured: Mario's 'hot' balls

Of course, there are ways to maximise your potential winnings. These include  keeping your numbers secret from friends and family and avoiding popular choices of numbers. The latter requires avoiding sequences played by thousands of other people, like 1 2 3 4 5 6 (the former requires a sociopathic dislike of everyone close to you). This rules out the terrifying prospect of winning the lottery but having to split it with thousands of less deserving people. Because when it comes to winning millions, nobody likes to share.

Unfortunately, none of this actually increases your chances of winning that jackpot. There is, however, an unbelievably simple, nay foolproof, way to double your chances every time you play. All you have to do is buy another ticket. Triple your chances? Buy a third! In fact, you can increase your chances of winning by whatever factor you wish by buying more and more tickets. I think you can see where I’m going with this.

So many chances!

All you have to do to guarantee you win is buy every combination of ticket (I did warn you it wasn’t a terribly practical guide). Simple, eh? Not quite. There are nearly 14 million combinations in the UK lottery and each one is going to cost you a pound. That’s a fairly massive investment. Still, it’s still worth it, right? If the jackpot is at £15 million that’s still a £1 million profit, not a bad weeks work if you ask me.

Unless someone else also wins, then you’re in trouble. That £7.5 million return isn’t looking great compared to your original investment, and that’s if only one other person wins. It’s looking less and less worth the risk with every additional leach on your prize money. But at what point does it become worth it? What size does the jackpot have to be for it to be profitable to buy every ticket?

Let x be the jackpot. If 40% of the time no one wins, 35% of the time there’s one winner, 15% of the time there’s two winners and 10% of the time there’s three winners, then the expected value of the investment would be (0.4 *x) + (0.35*½x) + (0.15*⅓x) + (0.1*¼x) = 0.65x. This means that you would expect a profit when your investment is 65% or less of the jackpot. In the example of the UK lottery, buying every ticket would become profitable when the jackpot reached about £21.5 million (although even in this case you lose money if there’s another winner).

Ok, so the theory is pretty solid, but realistically its impossible. There’s no way anyone could raise millions and get all the tickets required to win. Unless you’re the Australian syndicate who won $27 million in the 1992 Virginia State Lottery in the USA. That’s right, these guys chucked a few quid together and literally bought as many lottery tickets as possible. Even then they only managed to buy about 70% of the combinations, resulting in what must have been the most tense lottery draw in history.

So, looking for something to do this summer? Grab some friends, find a few thousand investors and wait for a big rollover. You’ll be rolling in cash in no time.

Explore posts in the same categories: Everyday Maths

Tags: Lottery, Maths, Money

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