6. What are the chances?

We’ve recently returned from a few days holidaying in deepest Pembrokeshire – a beautiful unspoilt part of west Wales with rugged coastlines and wind blown trees.

Rugged (and wind blown)

Wind blown

One of the highlights was visiting the cathedral in St Davids, which has roots that go back to the 6th century. 

St Davids cathedral

On our last evening, we tried to find a table at a small fish restaurant in the tiny coastal town of Dale. The owner explained that he had a party of eight people about to arrive but thought he could squeeze us into a corner. 

Dale in Pembrokeshire

Just as we were about to tuck in to our fresh lobster, we heard a shout from behind us, ‘I don’t believe it!’. Who should troop in but eight of our near neighbours and good friends from back home in Warwickshire.

After a fair bit of hilarity, our conversation turned to unlikely events in general and then the national lottery in particular. We were drawn into that old chestnut about what on earth we would do with those awkward Lottery millions and how much of our fortune we would want to give away. I was asked if there was a best strategy for choosing the numbers, and it caused a bit of a surprise when I said that there was! 

The UK National Lottery

But before I reveal this hot lottery tip, there are a couple of issues that need to be sorted out.

Issue 1: Is any one combination of six lottery numbers more likely to crop up than any other?

My Answer: No! Provided that the lottery numbers are chosen randomly from the lottery ball machine, all numbers (and all combinations of numbers) are equally likely to occur.

Issue 2. People say that lightning doesn’t strike in the same place twice. So I’d expect that the six numbers that came up last week are less likely to come up this week?

My Answer: This is a fallacy. As a matter of fact, lightning does sometimes strike in the same place twice, especially if that place is a tall building or tower. Indeed, several people have been hit by lightning more than once. For example, Roy (‘Human Lightning Conductor’) Sullivan who was a United States park ranger in Shenandoah National Park in Virginia was hit by lightning on seven different occasions and survived all of them. 

But anyway, even if it were true that lightning didn’t strike in the same place twice, how would this work? Are we to believe that there is some lightning god from above saying, ‘No, hang on, we hit that particular spot last year – better move this bolt’s trajectory a smidgen so that it hits the next field.  The same principle is true of the selection of lottery numbers from the lottery ball machine – last week’s numbers are as likely to appear this week as any others. Just as was true of the lightning bolt, it’s hard to believe that there’s an invisible force subtly pushing last week’s six balls towards the bottom of the machine in order to give the other 43 balls a better chance, in order to even up the outcomes. 

Now you might be thinking, ‘But surely by the Law of Averages, all the numbers should come up roughly the same number of times, so that should mean that previously favoured numbers are less favoured next time around. Well, sorry but this is not how the Law of Averages works. If you want to know why, have a look at the follow-up to this post in the Blog page of my website, MathinPictures.co.uk.

Issue 3. So if each number is equally likely to crop up, how can I have a ‘best strategy’ for choosing my numbers?

My Answer: Unless you can find a clever way of cheating the system (which would be very hard to pull off), it is true that you cannot find a way of choosing a combination of six numbers that is more likely to win than any other combination. But there is another factor here. You need to remember that if you choose the same six winning numbers as someone else, you have to share the jackpot with them. And if nine other people choose your winning numbers, your share is reduced to one tenth of the jackpot, So if you want to maximise your winnings, try to be aware of which numbers other punters are likely to choose … and avoid them! 

Here then are my hot tips for maximising your lottery winnings.

1. DON’T CHOOSE numbers between 1 and 31: people are more likely to choose numbers linked to birthday dates, so numbers in this range tend to be more widely used.

2. DO CHOOSE consecutive numbers: many people mistakenly think that a consecutive string of six numbers is less likely than any other combination and so they avoid such combinations. However, don’t choose the particular consecutive combination 1, 2, 3, 4, 5, 6 as it seems that several hundred punters regularly choose these numbers each week.

The joke

Finally, no lightbulbs this time – just this:

Teacher: What does “coincidence" mean?

Pupil: That’s funny, I was going to ask you the same thing.

Postscript
This post looked at the idea of chance in the context of the UK National Lottery… If you are interested in finding out a bit more about the mathematics of lotteries, have a look here in my website, MathinPictures.co.uk.