Premium Bonds Calculator query

Audaxer

I was looking at the Premium Bonds Calculator on the MSE site, and I see that for the £50k holding, your likely winnings with average luck, over a year is £450 (0.9%). However when I input £50k over 3 years, it shows likely winnings of only £1,000, and over 5 years likely winnings of only £1,500. I would have thought over 5 years your likely winnings would be £2,250 (0.9% per year). Can anyone explain why your likely winning percentage would reduce each year?

Saga

More people buying bonds?

El_Torro

Saga said:

More people buying bonds?

That just means that there'll be more prizes, the likelihood of one bond winning a prize won't reduce just because more people have bought bonds. The number of big prizes is fixed, though for the small prizes it's dependent on how many bonds there are in existence.


Based on the little I know of Premium Bonds it seems like there's a mistake in the Premium Bonds Calculator. I'll be watching this thread to see if there is a rational explanation for this.

Aegis

Audaxer said:

I was looking at the Premium Bonds Calculator on the MSE site, and I see that for the £50k holding, your likely winnings with average luck, over a year is £450 (0.9%). However when I input £50k over 3 years, it shows likely winnings of only £1,000, and over 5 years likely winnings of only £1,500. I would have thought over 5 years your likely winnings would be £2,250 (0.9% per year). Can anyone explain why your likely winning percentage would reduce each year?

Likely it's rounding.  If you look at the expanded table below, the figures for returns are included as £1,000, £1,500 and £2,500, so the calculations will presumably only output those values.

Aceace

Audaxer said:

I was looking at the Premium Bonds Calculator on the MSE site, and I see that for the £50k holding, your likely winnings with average luck, over a year is £450 (0.9%). However when I input £50k over 3 years, it shows likely winnings of only £1,000, and over 5 years likely winnings of only £1,500. I would have thought over 5 years your likely winnings would be £2,250 (0.9% per year). Can anyone explain why your likely winning percentage would reduce each year?

You're right, the average winnings over 5 years will be £2,250. Unfortunately, they only work out the probability of at least winning some set figures. The answer it gives is the highest value in that set of figures with a probability of at least 50%. In this case the probability of winning at least 1,500 is "virtual certainty". The probability of winning at least £2,500 (the next bracket that they measure) is 30.7%. Since the first figure below 50% is £2,500 they report the next lowest bracket,  I.e. £1,500. It's pants and confusing in my opinion.

Audaxer

Aceace said:

Audaxer said:

I was looking at the Premium Bonds Calculator on the MSE site, and I see that for the £50k holding, your likely winnings with average luck, over a year is £450 (0.9%). However when I input £50k over 3 years, it shows likely winnings of only £1,000, and over 5 years likely winnings of only £1,500. I would have thought over 5 years your likely winnings would be £2,250 (0.9% per year). Can anyone explain why your likely winning percentage would reduce each year?

You're right, the average winnings over 5 years will be £2,250. Unfortunately, they only work out the probability of at least winning some set figures. The answer it gives is the highest value in that set of figures with a probability of at least 50%. In this case the probability of winning at least 1,500 is "virtual certainty". The probability of winning at least £2,500 (the next bracket that they measure) is 30.7%. Since the first figure below 50% is £2,500 they report the next lowest bracket,  I.e. £1,500. It's pants and confusing in my opinion.

Yes that does seem very confusing - not a very good calculator. I think holding £50k for a period of 5 years is more likely to give you an average of £450 a year, than your chances of winning exactly £450 if held for just one year. I assume you might only win £350 in the first year, but could win £550 in year 2.

jamei305

I noticed an error yesterday. If you tell it you won nothing in a year on £50k, it says "You have average luck! Only 100% of people who have put £50,000 in premium bonds over 1 year win more than £0, meaning you're about spot on."

Audaxer

jamei305 said:

I noticed an error yesterday. If you tell it you won nothing in a year on £50k, it says "You have average luck! Only 100% of people who have put £50,000 in premium bonds over 1 year win more than £0, meaning you're about spot on."

Yes, the wording doesn't make sense on that side of the calculator either, especially in that example.

OldScientist

FWIW, according to my version of the calculator, for 50k held for 5 years the probabilities (in %) of obtaining less than the given amount are approximately

Prob Amount
  1     1700
10     1950
50     2325 (i.e. median)
90     2900
99     3825

The mean winnings are 2512 (slightly higher than the 2500 expected).

Still quite a range of outcomes even with that number (note that the median 'interest rate', 0.93% approaches the mean rate, 1%, the longer the bonds are held)

Note: These results are from my Monte Carlo version of the code rather than deterministic results hence my use of the word 'approximately' (to give an idea of the precision, a second run with the same parameters gave the same results throughout except the mean was 2504 and the 99% prob was 3800 instead)

forgotmyname

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.

I treat it as a lottery where you can get your stake back.  Im the unlucky one that never wins...
Mum wins a lot and another family member has won but just not me, what does that do to your
calculators?

Apodemus

forgotmyname said:

Does the chance of being equally lucky year after year diminish the odds of further winnings?

We are all equally lucky all the time, it's simply that humans are good at seeing patterns where none exist. Past events don't affect future odds.