I bought £25,000 of Premium Bonds but won nothing for a year – am I just unlucky?

In November 2020 I bought £25,000 of National Savings & Investments Premium Bonds in one transaction, all with consecutive numbers. 

They became eligible to be entered into the draw in January 2021, but in 2021 I won nothing at all. However, in 2022 and 2023 I have won quite a few prizes.

I am concerned that I received no prizes at all in the whole of 2021 on such a large number of bonds. 

I appreciate that the draw is random, but my lack of success does seem statistically improbable, and I worry that, due to an IT error, my bonds were not included in the database from which prizes are selected for the whole of 2021, because they were wrongly identified as being first eligible for prizes in January 2022 instead of January 2021. Via email

Sam Barker, of This is Money, replies:   Premium Bonds are Britain’s most-loved savings product, with more than 22million people owning them.

Most £1million jackpot wins come from NS&I customers with large stakes – Britons can save up to £50,000 in Premium Bonds each.

Many savers love the excitement of a chance to win £25 upwards in each month’s Premium Bonds draw.

With a £25,000 stake, winning nothing at all for a whole year seems extremely unlikely.

So has there been some sort of mistake, or are you just an unlucky Premium Bond holder – and just how unlucky?  

NS&I denied that there had been any sort of error with your bonds, and suggested it was all just very bad luck.

You should have won a prize 12 times during 2021 with average luck, data shows. 

I spoke to an expert statistician to find out what the exact odds of our reader winning nothing at all during 2021 were.

Statistician Michael Dunne-Willows said the probability of going all year without winning anything with £25,000 in Premium Bonds is equal to 0.00000373.

That assumes that all 25,000 £1 Premium Bonds were eligible for 12 monthly prize draws in 2021.

Dunne-Willows added: ‘That’s an extremely small probability and is equivalent to odds of over 260,000 to 1. This is extremely unlikely. 

‘In fact, with holdings of 25,000 Premium Bonds, and given the above assumptions, the customer should have generally expected to win on average about 12 times a year. 

‘Most of these winnings would generally be the lowest prize value of £25 but even so, that corresponds to an expected total winning of over £300 annually.’

An NS&I spokesman said: ‘Mrs S opened a formal complaint with NS&I, which was originally responded to on July 5. Further letters were sent to Mrs S on July 15, July 29, September 26 and October 22, 2022. 

‘These letters explained that the generation of Premium Bonds numbers is completely random and that Mrs S’s Bonds were eligible for the prize draws in which they should have been.’