Premium Bonds: random?

When I purchased my bonds in November of last year one reason was the surprising fact that in 2003 23 1 million pound winners had only purchased their bonds a few months prior to winning and, I believe, a third had done so in the previous 14 months. In fact, it could have been 3 who had won and who had purchased just a few months previously.

However, in the past year or so the bonds have seen a ridiculously high number of purchases.

I've heard this claim many times before. I bought my first premium bonds a month or 2 ago, so currently I'm not bothered, and if it's true then I'll cash mine in every few years and buy replacements. But has there been any proper studies of this claim? It would appear to be easy to prove or disprove.

In message , John Smith writes

This is the answer I believe. Since the minimum purchase was increased to £100, and because of the extra drive by National Savings for business number of bonds bought and the average number per purchaser has increased hugely thereby by skewing the statistics towards more recent purchasers.

There was a thread about this on thisismoney.com's forum a while back. There were some people who swore that regularly changing small amounts of bonds improved their chances. However, I seem to recall one lady who had something like 500, could have have been less, and she claimed to keep on winning small amounts all the time plus the odd K prize.

I work in IT and I know that, technically, there is no such thing as a computerised random number generator. All computer systems that choose numbers are biased in some way. This can be seen in some of the computerised US state lottery draws where a certain town, even a certain store, has a ridiculously high number of winners time after time after time.

In message , John Smith writes

National Savings are at pains to point out that ERNIE is NOT a computer and it shouldn't be compared with such. The basis of this assertion is that it is not programmable, and its existence and technology pre-dates IT as we know it. AIUI it is regularly actuarially audited for 'randomness' and it doesnt use modern computer technology as you know it.

As a side issue, a truly random data population will have groupings. It was the existence of such groupings that proved that V1s weren't 'aimed' but just pointed in the general direction of London. The population believed they were aimed at targets because of this grouping, but in reality it was an example of 'random' selection.

'ERNIE' no longer exists. The Premium Bonds are now drawn by a system put in by, I believe, LogicaCMG.

"John Smith" wrote

That's strange. My win last month came in an envelope with a "letter" clearly marked as follows :-

"Dear Bondholder A prize from ERNIE! - Congratulations"

It seems that whoever sent the prize forgot to remove ERNIE's name - if he no longer exists!

LOL

From ;

"Over the years, the notoriously difficult process of generating random numbers has changed significantly, while each of the ERNIEs has got progressively smaller and faster as technology has advanced. ERNIE 1 was 24 sq ft and used gas to generate the numbers, whereas ERNIE 4 uses thermal noise generated by a chip and measuring 0.01 sq ft, requires considerably less space."

First of all, bear in mind that if you plotted the year bought (most recent first) against the number of outstanding PBs for that year, you'd see a rapidly-decaying exponential curve, as many people cash in their Bonds after a year or three.

Secondly, NS&I have doubled the minimum investment, and raised the maximum, recently, which will also have the effect of increasing the proportion of recent purchases in the mix.

Finally, there does seem to have been a bit of a Renaissance in PBs in the last couple of years, probably down to a combination of NS&I increasing the payback levels, and the top investment level meaning that maximum investors should get, on average, one or two wins every month -- at which point, you can start to think of them as an investment, rather than a gamble.

I really, truly, don't believe there's any inherent bias in ERNIE (or, rather, his most recent offspring). There's way too much auditing involved.

In any case, it's actually a good thing for existing Bond holders if there is a flood of new purchases: since Bonds don't go into the draw for a couple of months after purchase, they're helping to pay for the payouts for everyone else for a while before they become eligible.

Jon

Not strictly correct; to get technical for a second, it depends on your entropy source. If that entropy source is, for example, a radioactive decay event counter, or an electrical noise generator (you have to be very careful about the type of generator you use for that), you're going to be about as random as it's possible to get, assuming of course that you haven't introduced any flaws in how you process the entropy data.

ERNIE 4, the latest in the series, which was introduced into service this April, uses a heat-stimulated electrical entropy source.

There's a brief but interesting New Scientist article about ERNIE 4 at .

Anyone got any information?

Jon

No, but I think the most amusing entropy source I've heard of is the humble lava lamp

"Tumbleweed" wrote

LOL!

Please explain why. I can understand the second (raising the maximum) would be likely to encourage increased investment from HRTPs for whom the tax-free status boosts the gross-equivalent interest rate to be competitive with alternative investments. But the first (increasing the minimum) would not affect them, but would tend to put the others off. There must be loads of people who'd be happy to "gamble" with £50 but not with £100.

In message , Ronald Raygun writes

That is what the civil service union said when the minimum was put at £100 (fearing job cuts), but for some reason, perhaps due to the increased marketing, the amount invested jumped considerably. Perhpas its a strange snob thing, like the estate agent who *raised* the price of a house that wasnt selling to over £250k and it sold immediately.

Yes, but strangely the facts were different.

A strong encryption algorithm (good old 56-bit DES will do just fine, and there are much better ones) will also generate data which will be as random as anything one can get.

The reason against using something like that (i.e. the reason for using e.g. semiconductor thermal noise or rad decay) is that if somebody got hold of the key they would know what's coming up.

Thermal noise / decay should guarantee that the sequence cannot ever be predicted, but that's only true if the subsequent processing (A-D conversion, or whatever) has been done extremely carefully.

I've got the max PB investment and win £50 on average every month.

Exactly. For something like PBs, *any* computational number generator is simply unacceptable, since any given number can be predicted with sufficient knowledge of the preconditions, and the software/hardware developers would have the potential for holding privileged information that could compromise the generator.

To be honest, you *could*, given that all the numbers are generated in a short period of time, get away with a really secure PRNG, seeded by a true entropy generator, but I don't think the market would buy into that. Pragmatically, I think they did the right thing, going for pure entropy instead.

Um, wasn't that what I said? ;-)

Jon

There are good PRNGs, and if predicting the winning bond required knowing to the exact milisecond the time when a button is pressed, it would be hard to exploit. You would also need to be able to buy a bond with a number you specify. How do you know that the current gadgetry is not designed the draw the programmers' bonds more often? A lot of things could be hidden in the way the true random source is converted into the winning numbers.

Details, please. This is not how a weak PRNG would fail. Is it possible, that with thousands of small town, a fairly rare event happens in one of them? Od that once a particular place or store is established as "lucky", lottery player flock there, and the higher number of tickets purchased there make the probability of winning higher?