In a departure from our usual subject matter on Sofabet, I recently found myself discussing the wisdom of holding Premium Bonds: do they, the National Lottery or Euromillions give the best chance of a life-changing big win? I couldn’t find a recent calculation online so attempted to crunch the numbers for myself, and am posting the calculations here in case others also find them interesting.
My conclusion surprised me. By my reckoning, it’s not even close – it’s the Euromillions, specifically on a Tuesday.
Before getting into the figures, it’s fair to note that Premium Bonds seem to be a very different beast from lotteries. Not for nothing are the latter known as a “tax on stupidity” – no more than half of ticket sale revenue comes back as prizes, and as it’s a random draw there’s no way to tilt the odds in your favour. To put those odds in context, if you buy a ticket from a shop seven miles away, you’re more likely to be killed driving home than to win the jackpot.
Premium Bonds feel like a much more respectable investment, because you can always sell them for what you paid for them. But they, too, involve a financial sacrifice, because your expected winnings are less than the interest you could get in a savings account. So if you’re willing to sacrifice some cash for the chance of a life-changing win – and let’s arbitrarily define “life-changing” as a million plus – it’s meaningful to consider them together.
Let’s start with Premium Bonds. The annual prize fund is currently equivalent to 1.3% interest on the total amount held in bonds. Let’s say, just for the sake of this calculation, that you hold the maximum allowance of £30,000. On average, over a year you’d therefore expect to win 1.3% of that in prizes, or £390.
(Of course, in reality, you’d almost certainly get less than £390, because that figure is skewed by the existence of the big prizes – a few will get a lot more, the vast majority will get a bit less. But it’s in the ballpark, so let’s stick with it for the sake of simplicity).
The best interest rate you could get in a bank is about 3%, meaning your £30,000 would earn £900 at the end of the year. Assume you’re a basic rate taxpayer, and you have to pay £180 of that in tax, reducing your interest to £720. So, effectively, keeping your £30,000 in Premium Bonds instead of the bank is costing you (£720 minus £390 =) £330 a year.
What do you get for your sacrifice of £330 a year? Your 30,000 bonds entered into 12 monthly draws, in which each bond has a 1 in 45,527,700,191 chance of winning a million. That equates to around a 1 in 126,466 chance of winning a million in the course of year.
What if you sold your Premium Bonds, put the money in a savings account, and instead said that you were willing to lose £330 a year on the National Lottery?
With the Lotto, 45% of ticket sales goes into the prize fund – you expect to lose 55% of your stake. So, for an expected loss of £330 a year, you would be looking at buying (330 x 100/55 =) £600 of tickets.
(In reality if you spent £600 on Lotto tickets you’d almost certainly lose more than £330, because – as with Premium Bonds – this “expected loss” figure is skewed by the existence of big prizes: most will lose more, a few will win big. But, again, it’s a ballpark figure so let’s stick with it for the sake of simplicity and consistency).
In October, the price of a Lottery ticket goes up to £2, so £600 would buy you 300 tickets over the course of the year. Each of those tickets has a 1 in 13,983,815 chance of winning the jackpot. That comes to a chance of winning a jackpot, from your willingness to lose £330, of about 1 in 46,546.
To summarise so far: I reckon that, given current interest rates, pound-for-pound you’re nearly three times as likely to win a million by playing the Lotto as you are by buying Premium Bonds – even accounting for the fact that you can always sell your Premium Bonds, whereas a losing Lotto ticket is gone forever. That surprised me.
What about the Euromillions? Here, 50% of ticket sales go into the prize fund, meaning you’d spend £660 a year for an expected loss of £330. At £2 a pop that’s 330 tickets, each of which have a 1 in 116,531,800 chance of winning the big prize. And that equates to a chance of winning a jackpot, for the expected sacrifice of £330 a year, of about 1 in 353,126.
This doesn’t look good. It’s worse odds than the Premium Bonds, and much worse than the Lotto.
However, we also have to factor in the “Millionaire’s Raffle” element of Euromillions, through which one ticket bought in the UK is guaranteed to win a million in each draw. The chance of winning this obviously depends on how many people in the UK buy tickets, which according to the Euromillions website is about 3,500,000 on Tuesdays and 9,200,000 on Fridays.
Once you factor this in, I reckon that if you bought all your 330 tickets on the Friday draws, you’d have about a 1 in 25,839 chance of winning at least a million, either from the Millionaire’s Raffle or the main jackpot. If you buy them all for the Tuesday draws, however, those odds improve to 1 in 10,296.
The conclusion, then? If you’re the kind of person who’s willing to write off some cash in return for gaining the remote possibility of a really big win, then by my calculations you’d be giving yourself a better chance if you sell your Premium Bonds, put the money in the bank and spend some of the interest on the Tuesday Euromillions instead. I make it about twelve times as likely to win you a million.
If you spot a flaw in these calculations, please do correct me in the comments below.