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Premium Bonds Calculator query

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Comments

  • Audaxer
    Audaxer Posts: 3,547 Forumite
    Eighth Anniversary 1,000 Posts Name Dropper
    Does the chance of being equally lucky year after year diminish the odds of further winnings?


    If you have average luck with £50k in PBs you would win £450 in a year. You could win lower or higher in any one year, but I don't see the average diminishing over the year. I would think the longer you hold them you are more likely to average £450 a year.

    I've read that it is can sometimes be a bit of a problem getting your money out quickly if you need it, so I'm beginning to wonder if it is really worth for 0.9% 'interest' not guaranteed.
  • eskbanker
    eskbanker Posts: 37,525 Forumite
    Part of the Furniture 10,000 Posts Name Dropper Photogenic
    Does the chance of being equally lucky year after year diminish the odds of further winnings?

    Trying to figure this out but the answers are too variable.  Bit like flipping a coin.....
    Sometimes you can beat the average and then your luck fades away and your average plummets.
    You're mixing up two different concepts there!

    In the context of Premium Bonds, chance relates to the statistical probability of something happening in the future, whereas luck is more about a measure of actual performance versus that probability.

    The chance is static, so every bond has a 1 in 34,500 chance of winning a prize in a given month, and that's the same regardless of how many bonds you have, how long you've held them for, how many prizes you've won, etc - if a bond wins a £1m prize one month, it still has exactly the same odds as all other bonds of doing so again the next month, as they're independent events.

    However, the fact that the chances of winning are so slim means that the actual outcome is hugely variable from one month to the next, which is effectively what people mean by luck being variable.
  • EthicsGradient
    EthicsGradient Posts: 1,294 Forumite
    Sixth Anniversary 1,000 Posts Photogenic Name Dropper
    edited 18 November 2021 at 2:01AM
    The left hand side of the calculator is still broken. If you ask it ("what will I win?") for the likely win for £50k over 1 to 5 years you get:
    1 year £450
    2 years £750
    3 years £1000
    4 years £1500
    5 years £1500
    which is not just rounding errors. Or keep the time steady at 5 years, and vary the amount:
    £5000 £200
    £10000 £450
    £15000 £500
    £20000 £750
    £25000 £1000
    £30000 £1000
    £35000 £1500
    £40000 £1500
    £45000 £1500
    £50000 £1500
    Results on the right hand "how lucky am I?" question seem consistent, however.

    (well, looking at the "The full odds" 'explanation', it is in a sense a rounding problem - but the figures they round to are ridiculous. It "explains" your odds with £5000 over years of winning at least the following amounts are:
    ...
    At least £1,000
    Virtual certainty
    At least £1,500
    Virtual certainty
    At least £2,500
    30.7%
    At least £5,000
    1 in 184
    ...
    which is a pointless thing to tell you. So "what will I win?" is really answering "it is more than 50% likely I will win £1,000, £1,500, £2,500 etc." So in practice everything above £1,500 is rounded down to it, £1025-£1475 down to £1000, etc.
  • eskbanker
    eskbanker Posts: 37,525 Forumite
    Part of the Furniture 10,000 Posts Name Dropper Photogenic
    (well, looking at the "The full odds" 'explanation', it is in a sense a rounding problem - but the figures they round to are ridiculous. It "explains" your odds with £5000 over years of winning at least the following amounts are:
    ...
    At least £1,000
    Virtual certainty
    At least £1,500
    Virtual certainty
    At least £2,500
    30.7%
    At least £5,000
    1 in 184
    ...
    which is a pointless thing to tell you. So "what will I win?" is really answering "it is more than 50% likely I will win £1,000, £1,500, £2,500 etc." So in practice everything above £1,500 is rounded down to it, £1025-£1475 down to £1000, etc.
    Yes, it's not really a rounding problem as such but a careless selection of data points against which to measure, leaving huge gaps between them, thereby often missing the real median outcome by some distance, so, going back to your initial results for a £50K holding:
    1 year £450 - reasonably meaningful 54.3% chance of this 0.9% annual return.
    2 years £750 - 86% chance of at least £750 but next point chosen is £1000 (33.9% chance).  Real median presumably about £900.
    3 years £1000 - 97.7% chance of at least £1000 but next point chosen is £1500 (32.2% chance).  Real median presumably about £1350.
    4 years £1500 - 93.4% chance of at least £1500 but next point chosen is £2500 (6.87% chance).  Real median presumably about £1800.
    5 years £1500 - 'virtual certainty' of at least £1500 but next point chosen is £2500 (30.7% chance).  Real median presumably about £2250.

    As you've seen, the key is not just to look at the headline 'what will I win?' figure but to review the full odds tab too, as this tells a more meaningful story....
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