Premium Bond Query??

It depends how big your batches are. If you invest thousands at a time then that series of numbers are more likely to have multiple wins than, say, a series of numbers from the reinvestment of a £25 win.

At one stage I invested £20,000 in one go. Unsurprisingly that series of numbers produces a large proportion of my wins, and in consequence features most commonly where I win more than one prize a month.

I think I've only ever once won two prizes from within a £25 series - I don't mean two prizes in one month, that's two prizes in the whole time I held the £25 bond.

lowbrim wrote: »

Yes, but even with a £20k batch on the assumption every premium bond has equal chance of winning I would have thought that the chances of 2 numbers coming up in that 20,000 in one month

If the rate is 1% then you'd expect that £20k to generate on average a prize of £200 each year. As most prizes are £25 then you'd expect to win on average 8 out of 12 months from that series. That doesn't sound very high odds, in fact quite the opposite.

lowbrim wrote: »

Can anyone explain to me why when I win more than one premium bond prize in a month that invariably (around 30% of the time) the winning premium bonds are out of the same batch. I would have thought that if each bond had equal chance of winning that the chances of getting two bond winning in the same month out of the same batch would be almost impossible but it happens on very regular basis. Am I missing something ??

Maybe you're an agent for MI5

They used to pay spies in premium bond "wins" - no tax, no awkward questions..trebles all round :beer:

lowbrim wrote: »

Yes, but even with a £20k batch on the assumption every premium bond has equal chance of winning I would have thought that the chances of 2 numbers coming up in that 20,000 in one month against the billions issued would have very high odds and this happens on a regular basis. Or is it not true that each number is entered individually?. The only explanation I can come up with is that the draw is in a number of stages and in the last stage batches that have got through the initial stages are them drawn individually. Is there a statistician in the forum who can explain how it is done and if it is done the way I suspect is the claim that every bond has equal chance of winning still strictly true?

The details of how the draws are conducted are available online. But in broad terms, a long list of random numbers is generated. The first number on the list is checked to see if it corresponds to an eligible bond number. If it does, that bond is the first winner. If the number isn't an eligible bond the process moves on to the next random number in the list. That process repeats until there are no more prizes to be allocated.

It follows that the draw process has no idea of the ownership of a particular bond number, and is therefore 'blind' to whether a particular number is part of a batch of any particular size. In theory it is possible that two consecutive numbers will be drawn at some point within a monthly draw. But those consecutive numbers could belong to two different holdings, or to just one - it is random.

A way of visualising your question is to imagine each 'batch' of numbers you hold to be a paper target sized in proportion to the value of each batch. My £20k would be quite a big target, each of the £25 ones would be much smaller - about 1/800th the size. So if the £20k target was a piece of A4 paper, each £25 one would be approximately 9mm by 9mm. If you placed all of my 'targets' at the far end of a rifle range and fired a loosely fixed machine gun in the general direction of the targets you would probably find the following:
a) a lot of the bullets would be nowhere near my targets.
b) the 'A4' target is the one most likely to have a bullet hole in it.
c) most of the 9x9mm targets will be untouched.
d) if two bullets have hit a single target it is most likely to be the 'A4' one.
e) it is possible that a single 9x9mm target will have been hit by two bullets, but only if both bullets followed almost precisely the same path.

As the machine gun was not fixed firmly, and would move ever so slightly between shots due to recoil, the chances of two bullets following almost precisely the same path is very very remote.

They obviously don't use a machine gun to pick premium bond prizes (but it might make the draw more fun ) but it hopefully illustrates that even a random process can have results which, on first sight, look like they are 'fixed' or planned.

The bullets aren't magically drawn to the big target, it is just more likely (all else being equal) that the bigger target gets hit once, and if it is hit once that it gets hit for a second time.

Another way of looking at it is to model the probability of two prize-winning numbers being drawn from different batches - as pointed out further up, it obviously depends on batch sizes but this puts me in mind of the birthday problem, where in a random group of 23 people, it is statistically more likely than not that at least two will share a birthday (and if the group is 70 people it's 99.9% likely that two will share a birthday), despite this seeming counter-intuitive at first glance.