Premium Bond Winner ?

Boa21

3 x £25 on £100k. 1.08% rolling 12 months

arealhighlander

2 x £25 this month on a £39k holding.
On a £24k holding from July 20 till Jan 21 I won £200 overall. All £25s

onthebench

josh33 said:

I'm bad at maths so my logic is most likely flawed, but I've noticed the older bonds have less characters e.g. AB123456 whilst newer bonds are longer e.g. 123AB123456.

Simplifying an example to say there are only 99 bonds numbered 1-99, that would mean 9 bonds have one digit (1-9) and 90 bonds have 2 digits (10-99). Assuming the numbers are drawn randomly, those with 2 digits are far more likely to be drawn. Bonds 1-9 would be drawn 9/99 = 9.1% of the time whilst bonds 10-99 would be drawn 90/99 = 90.9% of the time. Now each bond 1-9 would have 9.1%/9 = 1.01% overall, whilst bonds 10-99 would have 90.9%/90 = 1.01% overall, so in the end all bonds are likely to be picked. But can there be any bias where the newer bonds 10-99 with 2 digits are more likely to win, as more of them are drawn compared to those with 1 digit?

I know this is not the case, and I know that bond numbers are not "entered" into the draw as such, but I am still curious as to exactly how the process works in order to avoid this type of anomaly.

Eg say, in the extreme case, that the first bond issued was just numbered "1". (Obviously it wasn't, but this is a thought experiment), then the next ones were 2, 3, 4, 5, 6, 7, 8, 9, 10 and so on....

Whichever number ERNIE generated as its first digit would match a bond straight away.

Now, I am not sure exactly how the bond number length has varied over the years, but it does seem that the differing lengths have to be taken into account somehow. Does ERNIE first randomly generate a string length, and then generate the string?

NS&I say that random numbers are generated of all possible bond number combinations, and then these are matched against actual bond numbers, but I am curious how exactly this is done to ensure randomness over different number lengths.

Edit: OK I see this has been addressed above. Looks like the original bonds were AANNNNNN, A is a letter and N is a digit, and newer ones are NAANNNNNN, NNAANNNNNN and NNNAANNNNNN. Presumably they will then go to NNNNAANNNNNN, and ERNIE will have to generate four digits, then two letters, then six digits, and all of the currently issued crop of NNNAANNNNNN Bonds will only be eligible if a zero is the first digit drawn?


PS Nothing for me this month - I had £25 in August, £25 in September (my first two draws with an increased holding) and then zilch ever since (although I did reduce my holding again temporarily).

FirstTimeSolo

£43k
Feb: £25
March: £25
April: 2 x £25

pbcpdeveloper

onthebench said:

 Does ERNIE first randomly generate a string length, and then generate the string?
NS&I say that random numbers are generated of all possible bond number combinations, and then these are matched against actual bond numbers, but I am curious how exactly this is done to ensure randomness over different number lengths.

Could just use a numerical range and then translate those to the alpha numerics

YellowStarling

pbcpdeveloper said:

onthebench said:

 Does ERNIE first randomly generate a string length, and then generate the string?
NS&I say that random numbers are generated of all possible bond number combinations, and then these are matched against actual bond numbers, but I am curious how exactly this is done to ensure randomness over different number lengths.

Could just use a numerical range and then translate those to the alpha numerics

I may be misunderstanding your suggestion (apologies if so) but wouldn't this mean that, for example, a numerical range beginning 1234 would translate into more than one beginning sequence?  I.e.:
AB34
1BC4
12CD
123D
etc.

Piqued my interest, so I'll dig.  NS&I site advises the latest ERNIE (ERNIE 5) uses quantum computing to generate the winning combinations:

"Using light, ERNIE 5 generates random numbers that are matched against eligible Bond numbers to determine the lucky winners. And because it’s random, every Bond number, whether it has 8, 9, 10 or 11 digits, has a separate and equal chance of winning a prize."

https://www.nsandi.com/get-to-know-us/about-premium-bonds#:~:text=The clever bit,chance of winning a prize.

EDIT TO ADD:  May have oversimplified my interpretation above, given there are more than 9 or 10 letters!

becky_rtw

There is a reconstruction ERNIE at the national museum of computing in the same location as Bletchley.
It's the original one so I suspect they use a piece of software now, but I'm sure the volunteers there can explain how the calculations work. It's in the same room as the enigma machine I think. Obviously closed at the moment!

lr1277

£25 on a 32k holding

pbcpdeveloper

YellowStarling said:

pbcpdeveloper said:

onthebench said:

 Does ERNIE first randomly generate a string length, and then generate the string?
NS&I say that random numbers are generated of all possible bond number combinations, and then these are matched against actual bond numbers, but I am curious how exactly this is done to ensure randomness over different number lengths.

Could just use a numerical range and then translate those to the alpha numerics

I may be misunderstanding your suggestion (apologies if so) but wouldn't this mean that, for example, a numerical range beginning 1234 would translate into more than one beginning sequence?  I.e.:

I meant instead of trying to generate random alpha numerics that have a fixed set of numerics but varying number of alphas, just generate a purely numerical range of numbers, and then translate the generated numbers into their alpha numeric bond number equivalents. So using hex as a simplified example a generated number of 10 would equal 'A' or 43,557 would equal 'AA25' .

YellowStarling

pbcpdeveloper said:

YellowStarling said:

pbcpdeveloper said:

onthebench said:

 Does ERNIE first randomly generate a string length, and then generate the string?
NS&I say that random numbers are generated of all possible bond number combinations, and then these are matched against actual bond numbers, but I am curious how exactly this is done to ensure randomness over different number lengths.

Could just use a numerical range and then translate those to the alpha numerics

I may be misunderstanding your suggestion (apologies if so) but wouldn't this mean that, for example, a numerical range beginning 1234 would translate into more than one beginning sequence?  I.e.:

I meant instead of trying to generate random alpha numerics that have a fixed set of numerics but varying number of alphas, just generate a purely numerical range of numbers, and then translate the generated numbers into their alpha numeric bond number equivalents. So using hex as a simplified example a generated number of 10 would equal 'A' or 43,557 would equal 'AA25' .

With you - cheers