have been scrutinised as the lottery-style savings option means more wealthy Britons who can afford to leave larger amounts deposited stand a better chance of winning.

Provider NS&I is often contacted by frustrated customers in decades. But the reality is it’s not the length of time that is the key factor in boosting your chance of taking home a prize, but how many Bonds you hold.

Analysis from Martin Lewis’ MoneySavingExpert shows you need at least £10,000 invested to have good odds of taking home anything, with the prize fund rate currently at 4.4 percent, and likely to drop as interest rates eventually fall.

Chris Demetriou, co-founder of Archimedia Accounts, spelled out the problem. He told : “Premium Bonds are a cultural treasure for millions, but there’s no denying that pure statistical probability overwhelmingly favours those able to dump £50,000 into the draws over persons of more modest means.

“At the same time though, who among us hasn’t daydreamed about what we’d do if our own Bond number got plucked from the millions?

“Their blend of structure savings with a dash of chance has undeniably captivated the British public.

“It’s undeniable that those who can invest tens of thousands of pounds have a statistically much higher chance of winning compared to someone putting in a few hundred here and there.”

He acknowledged that the “fun and excitement” of the monthly prize draw can provide helpful motivation for people to set aside funds.

Mr Demetriou suggested some ideas for how the prize draw system could be made fairer.

He commented: “Some ideas I’ve thought could help are capping the maximum number of Bonds held to limit very high chances of winning, combining that with a tiered prize structure, and possibly rewarding longer-term investors with a small return guarantee.

“Spreading out smaller but more frequent wins across modest and significant bondholders alike also seems a sensible adjustment.

“Overall, the aim should be proportional fairness over rigid equalization. With thoughtful changes, I believe Premium Bonds could continue delighting participants both young and old for years to come while addressing criticisms in a balanced manner that respects all perspectives.

“As with many issues, the ideal solution seldom lies at the extremes, but in pragmatic compromises.”

People often choose to invest their winnings in buying more Bonds to increase their chances of winning again.

You need to invest at least £25 when buying more Bonds, with a total holding limit for each saver of £50,000.

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