What are your chances of winning the lottery?

By Matthew Allen

People often say that you’re more likely to get struck by lightning than win the lottery, but is it true? If so, it makes you wonder: what other unlikely events are more likely to happen to you than winning the lottery?

It sounds simple – pick six numbers between 1 and 59 and if you get them all correct, you win millions of pounds. It sounds like there should be a few winners every week, because only picking between numbers 1-59 doesn’t sound that difficult. However, it’s only when you do the maths that you realise how bad the odds really are of winning the lottery. If the odds of winning the lottery are indeed bad, then how do your odds of winning compare to other unlikely events, such as say, being struck by a meteorite, or marrying a millionaire?

1 in 45,057,474 (or 0.00000221%) chance

How do we calculate the odds of winning the lottery? Well, there is a bit of maths needed to work it out, but it’s not too complicated. The equation we need is:

where NPossibilities is the number of possible balls (59) and Nballs is the number of balls that are picked out each time (6).

You might be mistaken to think that I was very enthusiastic when I wrote out the equation, putting an exclamation mark(!) at the end of every value. However, this exclamation mark is something called a factorial. A factorial means you multiply the number before the exclamation mark by every positive whole number which is less than it. For example, 5! is equal to 5x4x3x2x1, which equals 120. 8! is equal to 8x7x6x5x4x3x2x1, which equals 40,320. Therefore, 59 factorial is 59x58x57…x3x2x1, which as you can imagine is a very big number!

If we use the equation above, along with our knowledge of what a factorial is, we can calculate the chances of winning the lottery…

… which equals 45,057,474. This means there are over 45 million different combinations of numbers that can come up, or put another way, if you buy a single ticket you have a 1 in 45 million chance of winning the lottery!

Are you more likely to be hit by a meteorite?

Your odds of winning the lottery are clearly pretty low, but how do they compare to some other unlikely events?

You’re better off trying to woo Richard Branson than buying a lottery ticket – By Gina Hughes, CC BY 3.0

Roll 5 dice and get all 6’s – Let’s begin with a nice easy task, rolling 5 dice and all of them being a 6. It might sound easy, but surprisingly the odds are 1 in 7,776. The odds of getting all 1’s, 2’s, 3’s, 4’s and 5’s are also the same odds!

Date a millionaire – Your odds of becoming a millionaire through winning the lottery are low, but what about by dating a millionaire? Well, if you take the number of people in the world, around 7 billion, and divide it by the number of millionaires in the world, around 13 million, you get odds of 1 in 538 of dating a millionaire. Compared to the lottery, that seems like pretty good odds!

Hit by a meteorite – Let’s go up a notch, what are your chances of being hit by a meteorite? Unsurprisingly your odds are pretty low at 1 in 20,000,000,000,000, or one in 20 thousand billion. You rarely hear of someone being hit by a meteorite, so it makes sense that the odds are that low. To put that in to perspective, that means you’re over 40,000 times more likely to win the lottery than be hit by a meteorite!

A deadly meteorite! – By No machine-readable author provided. Calips assumed (based on copyright claims). – No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY 2.5

Being hit by a meteorite is very rare, but there are some things which are even less likely to happen to you. Get two decks of playing cards and shuffle both of them for a few minutes. What do you think the odds are that you shuffled both decks of cards so that they are now both in the same order? 1 in a thousand? 1 in a million? 1 in a trillion? Not even close. The odds of shuffling two decks of cards in to the same order is 1 in 20,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, or 1 in 20 thousand billion billion billion billion billion billion billion.

In case you’re interested, that large number is only 10,000,000,000,000 times less than the total number of atoms in the entire Universe, so it’s pretty big!

In conclusion, your chances of winning the lottery are pretty low, which makes you more likely to marry a millionaire than become one by winning the lottery. However, you are much more likely to win the lottery than be hit by a meteorite, so that’s one thing to be happy about!

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