### Friday, June 19, 2015

This week the National Lottery announced that, from October, it would be adding ten more balls. If you were thinking of getting stinking rich, it's not good news.

Currently to win the jackpot you have to correctly predict six balls from 49, at odds of 13,983,815 to one against. And 14 million is a very big number, indeed so big that most people don't quite understand how big it is. But from October you'll need to pick six balls from 59 instead, at odds of 45,057,473 to one against. And 45 million is such a big number that quite frankly you ought to give up all hope. Fortunately for Camelot most people are rubbish at maths and will carry on playing because "well, somebody's got to win". Increasingly, alas, it won't be you.

Odds since 1994Odds from OctoberComparison3 balls1 in 57 1 in 97 70% worse 4 balls1 in 1033 1 in 2180 110% worse 5 balls1 in 55492 1 in 144415 160% worse 5+bonus1 in 2330636 1 in 7509579 220% worse 6 balls1 in 13983816 1 in 45057474 220% worse

Even though the odds are lengthening the prize money at each tier will remain resolutely the same. So to try to counteract any feelings of financial inadequacy, Camelot have introduced three further tweaks.

Firstly they're removing their existing limit of four rollovers before the top prize must be won. People won't be winning the jackpot so often once the odds shoot up, so rollovers will be more likely, and prize pools will reach Euromillions proportions more quickly. Camelot's research has shown that people are more likely to enter the lottery in rollover weeks, because the mega-prize money turns their heads, so if they dangle a larger carrot then punters will buy in more often. And this greed they expect will counteract the fact that fewer people will be winning big, because it's jackpot size rather than jackpot probability that lures folk in.

Secondly they're increasing the raffle element of the lottery draw. At present every ticket gives you a chance to win one of fifty £20000 prizes drawn at random irrespective of the numbers you pick. £20000 is a nice amount to win but unlikely to be life-changing, so from October they're adding a £1m prize to the raffle too. This means in every draw somebody somewhere gets to be a millionaire, which looks great as an advertising headline, and will make someone very happy. But with about 8½m tickets being sold for every Wednesday draw and 16½m for every Saturday draw, your chances of being the raffle millionaire are slim. Plus they're simultaneously cutting the number of £20000 prizes from 50 to 20, because punters' eyes are on the big prize, not the also rans.

Thirdly, and most cunningly of all, they're introducing a prize for getting two balls right. Currently this gets you nothing, apart from an exasperating "oh, so close!", but from October it'll win you a free Lucky Dip in the following draw. Camelot are claiming this means the new lottery has a 1 in 10 chance of winning "a prize", whereas in reality they're only handing back your £2 entry money and re-investing it for you. Camelot no doubt hope that when you go back to claim your free ticket you'll buy some more, so they're not being entirely altruistic here. And they also hope you'll think of this free Lucky Dip as a second chance to win the jackpot, because that sounds like a bargain, whereas in reality double a very small chance is still a very small chance.

Let's look at the new odds again, but in a slightly different way. Suppose you enter the 59-ball lottery every Wednesday and every Saturday with a single set of numbers. How long would it take you, on average, to win each prize?

Prize (approx)Odds of winningTime to win once2 ballsfree go 1 in 10 1 month 3 balls£25 1 in 97 1 year 4 balls£100 1 in 2180 20 years 5 balls£1000 1 in 144415 1250 years 5+bonus£50000 1 in 7509579 65000 years 6 ballsJACKPOT 1 in 45057474 250000 years Raffle£20000 1 in 625000 6000 years Raffle£1000000 1 in 12500000 120000 years

For the once-per-draw punter, the new Match 2 prize should come round once a month, giving the illusion of success. But actually winning some money by matching 3 balls will now happen only about once a year, whereas in the current 49-ball lottery the average is every six months. Getting four balls correct will now be a once in every 20 years event, that's maybe four or five prizes in a lifetime, rather than once every ten years as now. And as for winning more than £100, don't get your hopes up, it's very probably never going to happen. Somebody's got to win, of course, but when it takes quarter of a million years on average to win the jackpot, don't kid yourself it'll be you.

A different way to assess the impact of Camelot's new regime is to calculate what would happen if you bought two tickets a week every week for ten years. You might even be thinking of doing this yourself, because it doesn't sound like much to invest, and you've got to be in it to win it.

Here's how much you'd expect to win in a decade, on average, under the present 49-ball system.

Playing twice a week for 10 years -49 BallsPrizeExpected winsExpected winnings3 balls£25 18 £450 4 balls£100 1 £100 5 balls£1000 0 £0 5+bonus£50000 0 £0 6 ballsJACKPOT 0 £0 Raffle£20000 0 £0 TOTAL£550

£550 in winnings might sound good, but over ten years you'd have paid out £2088 for your tickets, and that's a pitiful 26% return.

OK, now let's try the same thing under the new 59-ball system. What happens if you buy two tickets a week for ten years now?

Playing twice a week for 10 years -59 BallsPrizeExpected winsExpected winnings2 ballsfree go 100 £25 3 balls£25 11 £275 4 balls£100 0.5 £50 5 balls£1000 0 £0 5+bonus£50000 0 £0 6 ballsJACKPOT 0 £0 Raffle£2K/£1m 0 £0 TOTAL£350

In the future you get lots more wins, but most of these will be Match 2 prizes of a free Lucky Dip. On average you'll get 10 of these a year, and on average one of these will win you yet another Lucky Dip. But over 10 years all these extra Lucky Dips will likely only win you one cash prize of £25 for matching 3 balls, and nothing else. Meanwhile the number of Match 3 prizes you'll win from ordinary tickets decreases. Under the current system you can expect 18 such wins in ten years, but under the new system only 11 because the odds have lengthened. As for the chance of matching 4 balls correctly, you've now only a 50% chance of that happening in ten years, which knocks down your total winnings even further. Indeed under the lottery's new 'enhanced' arrangements you can expect to win back only £350 of your £2088 outlay, which is a return of only 17%, which is rubbish.

Again, somebody's got to win the bigger prizes, so in the official statistics the expected winnings come out somewhat higher. But twelve £25s and maybe a £100 is all you can genuinely expect for your decade of lottery play, and anything larger you might be imagining is purely an illusion. The good causes that rely on collective delusion will no doubt thank the betting public for their mathematical inadequacy. But you'd be far better off spending that £2088 on a nice holiday or two, rather than pissing it away into an unachievable pot of dreams.