# So what are the chances of winning the lottery?

Whether you realise it or not, there are two kinds of gamble – and we don’t just mean the lucky kind and the kind that leaves you wondering what else you could have done with the money you’ve just lost. There are positive odds, and negative odds; up sides, and down sides, whichever way you look at things. Take the National Lottery, for instance.

UK National Lottery

 Number of balls matched Approximate Odds of winning 3 54 to 1 4 1,031 to 1 5 55,490 to 1 5 plus bonus ball 2,3330,635 to 1 6 13,983,816 to 1

The chances of winning a prize with just 3 numbers in the traditional basic draw? Just 54 to 1 – or, if you’d like us to put it another way – slightly under two in 100. But the chances of winning the big prize, with all six numbers coming up? That’s 1 in 13,983,816. Still, much, much better than the US Mega Millions draw, which asks for a dollar a ticket, but has odds of winning the jackpot stacked at 135 million to one.

Be in it, to win it?

On the other hand, you could say the chances of winning something  in a lottery are a lot more straightforward, you’ll either win it, or you won’t (as long as you’ve bought a ticket, that is). Mike McDermott knows that: when he played his regular ticket, it came up as five numbers plus the bonus ball, so that he beat the odds of winning at 2,330,635 to one.

But when he won a second time with exactly the same numbers, he beat odds of over 5,400,000,000,000 to one: the two draws were independent of each other, so the chances of them happening again were the same. In case you got lost in the zeros, that’s over 5 trillion to one – which is almost impossible to put into context. So let’s try some smaller odds.

• What are the chances of rolling two 6s in a row, with just one die? One in 36.
• What are the chances of having twins? In the UK, about 1 in every 65 mothers has a twin pregnancy, which means about one in 32 babies born is a twin.
• But what are the chances of having a 100th birthday, these days? Surprisingly high, as our population is ageing and living longer: about one in three people could have the 100th birthday party of a lifetime.

It’s a fact...

“The chances of anything coming from Mars are a million to one, they say...” – or so sang Jeff Wayne, in his War of the Worlds. Out of this world, a bit like the odds of winning the National Lottery. But when you think about probability simply being a case of ‘either it will or it won’t happen’, then, as you can see, the chances of having that lucky ticket may not always be as bad as they seem!