You’re still not going to win the lottery. But you might have more fun not doing so

http://www.theguardian.com/commentisfree/2015/jun/17/national-lottery-balls-bigger-prizes

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You are not going to win the lottery. But winning the lottery is not the point of the lottery. As much as I love the statistics behind the lottery, it is all a distraction. And with the changes to be made in October by Camelot (who run the National Lottery), the odds of your numbers being drawn will be even more irrelevant.

Related: It could be you (but probably won't be) as Camelot revamps National Lottery

As of October the number of balls in the bucket will increase from 49 to 59. The lottery website cheerily sells it as a new feature: “more numbers to choose from”. The reality is there are now more numbers you’re not going to choose. The odds have become much worse. As a UK citizen, it’ll be more likely that Prince Charles is your dad than you choosing winning lottery numbers.

Up until now, to win the jackpot you had to match six balls out of 49, which has a probability of one in 13,983,816. A reasonably straightforward calculation. From October, matching six balls from 59 increases the odds to one in 45,057,474, an increase of 3.2 times. Sort of.

For us number nerds, the new rules are a gift because the probabilities have become more interesting. As well as increasing the number of balls, Camelot have also changed how the game works in two fundamental ways. First, while there are still the same smaller prizes for matching five, four and three balls, they have also added a new prize if you match exactly two. You win another lottery ticket. Which does not feel like a great prize. Is being allowed to try and win the same prizes again next time count as a prize in its own right?

Mathematically, it means that the probabilities are not quite as clear-cut. I calculated that the odds of matching only two numbers in a draw is one in 10.258, which means you have a 9.748% chance of playing again. This second chance comes in the form of a lucky dip ticket: six numbers picked at random.

I spoke to the press office at Camelot and confirmed that it is possible to then match two numbers on your lucky dip and win a third ticket, and so on. Technically, you could buy one ticket and keep winning free tickets for the rest of your life. But that is exceedingly unlikely, even by lottery standards.

This means the new odds of winning the jackpot of “one in 45,057,474” is actually incorrect. Because there is a 9.748% chance you’ll get a second go; a 0.9503% chance you’ll get three goes; 0.09264% four goes; 0.009031% five and so on. We can mathematically roll up all these vanishingly small probabilities and calculate the new odds of winning the jackpot on a single initial ticket purchased: one in 40,665,099. Only 2.9 times worse than before.

But the lottery is not for mathematicians. It’s not even really about maths at all. One thing has not changed: you’re not going to win the lottery. In the grand scheme of things, if you start with unbelievably terrible odds, making them three times worse is not going to have much of an impact. The lottery is not about winning the jackpot, it’s about having a tiny non-zero probability of winning the jackpot. A lottery ticket is permission to dream; to know there is a small chance all of your money and work woes could vanish in a blink of an eye.

If anything, because the jackpot will now be won less often, there will be much larger pay-outs. Seeing the occasional news story of someone winning a now truly massive amount of money will only enhance the escapism of buying a lottery ticket.

Pragmatically, far smaller amounts of money could change lives. Winning a mere million pounds would be enough for most people. Which is where the second change to the lottery comes in, and this is genius. Along side each “proper” lottery draw, there is also a lotto raffle where one ticket is pulled out at random (which is as mathematically dull as you can get). Whereas there used to be £20,000 raffle prizes, there is now one £1m winner and a further 20 winners of £20,000 .

This is why the lottery can claim you are now more likely to become a millionaire. The main draw is really a glorified raffle. But they are correct: it is more likely to win a large chunk of money. That said, the wording on the lottery website “All of this will all be made possible by the fact you’ll pick 6 numbers from 59, instead of 49.” is somewhat disingenuous. It is the structural changes to how prizes are awarded which makes it possible, despite (not because) of the increase to 59 numbers.

The National Lottery has shuffled the probabilities around so fewer people will win the jackpot, but when they do they will win more money. And they will get the media coverage. Thus bizarrely, even though the odds are now worse, the fun of playing and dreaming has increased. In some twisted way, it conceivably makes the lottery better value.