Premium Bond Winner ?

cricidmuslibale

eskbanker said:

cricidmuslibale said:

The more money that is invested in Premium Bonds in total, the less likely it is that with investing the full £50,000 you will necessarily receive an average of 2 prizes per month before 24th Nov, 1.5 prizes per month now, over say a span of just a few months.

Each month's prize fund is adjusted to remain at a set percentage of the issued bonds (preserving the 1 in 34,500 chance of winning), so increases in the total number of issued bonds makes no difference to an individual's chances of winning (other than insignificantly infinitesimal fractions associated with very minor changes to the exact mix of prizes)!  Obviously that prize fund percentage has just changed but that's a different issue....

I agree that the total number of issued bonds makes no difference to an individual's chances of winnings and I know the following will probably never happen but let's say Premium Bonds were to become so unattractive for whatever reason(s) that most of the money invested in them was removed / only a few active bond numbers remained. Then, anyone with the few remaining bond numbers would be very likely indeed to win the no. of prizes they were most likely to win each month i.e. the average no. of prizes expected per month depending on the then odds of winning any prize and the total no. of bond numbers that individual held. With many Premium Bond numbers in total circulation as is the case at the moment, it is considerably more likely that over a short span of say a few months, even someone with the max £50,000 presently permitted may get very unlucky and win far fewer than the current average return of just under 1.5 prizes per month derived from the prize-winning odds at the moment of 34500 to 1. (Or, of course they may get very lucky and win far more!)

pbcpdeveloper

I built up my holding of bonds on a monthly basis so I have quite a few blocks of more or less the same size, I also keep track of how many times each block has won. Over time they all picked up wins apart from one particular block which never won. It looked a little odd, as the bonds purchased all around it picked up multiple wins, even a block 4 times smaller than it had multiple wins. Although it is down to chance, after 5 years, it looked so odd i emailed NS&I about it thinking there was possibly an admin error or something. 

I know a little about how the draw works, they always over draw the number of required bonds to allow for bonds that are no longer active, i.e. they draw a load of bonds, run through them, check if each bond is stil active, if its been sold, its discarded, if they get to the end of the batch and haven't got enough winners they darw another load of bonds until they have their quota, anything left over also gets discarded.

So instead of just asking 'are my bonds ok?', I asked if this particular block of bonds had ever had a bond drawn and then been discarded. To their credit they got back to me and confirmed there had been two bonds drawn from that block and both were discarded as they already had their quota.

So at least I knew the block was active. Of course, on the very next draw, it picked up a win.  I don't want to start any conspiracy theories or anything but I was a little suspicious of that.  It has now won twice and continues to underperform the other blocks so,  maybe it is just an unlucky block ?  

cricidmuslibale

pbcpdeveloper, thank you very much for a very interesting and informative post! I've now learnt several new things about Premium Bonds from reading it.

eskbanker

cricidmuslibale said:

I agree that the total number of issued bonds makes no difference to an individual's chances of winnings and I know the following will probably never happen but let's say Premium Bonds were to become so unattractive for whatever reason(s) that most of the money invested in them was removed / only a few active bond numbers remained. Then, anyone with the few remaining bond numbers would be very likely indeed to win the no. of prizes they were most likely to win each month i.e. the average no. of prizes expected per month depending on the then odds of winning any prize and the total no. of bond numbers that individual held.

I'm still not sure you've fully understood how the prize fund flexes but if your crazily hypothetical scenario ever arose and literally only a few active bonds were left then there wouldn't be a prize draw, as the whole scheme would long since have passed viability!

cricidmuslibale said:
With many Premium Bond numbers in total circulation as is the case at the moment, it is considerably more likely that over a short span of say a few months, even someone with the max £50,000 presently permitted may get very unlucky and win far fewer than the current average return of just under 1.5 prizes per month derived from the prize-winning odds at the moment of 34500 to 1. (Or, of course they may get very lucky and win far more!)

If the frame of reference for your argument is to make an artificial comparison with an absurdly unrealistic scenario in which the whole 1 in 34,500 principle was null and void then that's a complete waste of time.  Meanwhile, back in the real world, there were circa 99 billion bonds in this month's draw, and (unless the prize rate or fund structure were changed) the odds of winning would be the same if that dropped to 10 billion or leapt to 200 billion....

Stubod

At end of the year and we have "won" the headline rate of 1.4% on max holdings....

El_Torro

This year I have held a constant amount in Premium Bonds, so calculating my return is easy. I've managed to make a 0.9375% return. So pretty poor overall. Hopefully next year won't be any worse, even with the reduction in prizes.

redpete

concorde1966 said:

I have £20,630 invested now. 2 blocks worth £6,000 each, another block worth £4000 and I now have 121 blocks in total which are nearly all  £25’s. From now on though all my purchases will be £25’s and see what happens. I have won £150 in the last four draws which I don’t think is too bad.
I think of the draw as a dart board so the more I have scattered around the more chance the dart will land on one of mine....lol.

Each bond you buy is the equivalent of buying a new piece of the dartboard that didn't exist before, where on the board this new piece goes doesn't matter because each bit has the same chance of having a dart landing on it.

pbcpdeveloper

Using the dartboard analogy, if the dartboard represented all available bonds for the draw then for a single draw you would expect the darts to be scattered evenly around the darboard ? 

If your bonds numbers were also scattered evenly around the dartboard, it would 'appear' that there are lots of gaps between your bond numbers so it looks like there is a only small chance that a dart will land exactly on one of your numbers.  But if your bonds were in one solid slice / section of the board then there 'appears' to be a higher chance that at least one dart will land on your block?

redpete

pbcpdeveloper said:

Using the dartboard analogy, if the dartboard represented all available bonds for the draw then for a single draw you would expect the darts to be scattered evenly around the darboard ? 

If your bonds numbers were also scattered evenly around the dartboard, it would 'appear' that there are lots of gaps between your bond numbers so it looks like there is a only small chance that a dart will land exactly on one of your numbers.  But if your bonds were in one solid slice / section of the board then there 'appears' to be a higher chance that at least one dart will land on your block?

It might appear so but it wouldn't be true.

eskbanker

pbcpdeveloper said:

Using the dartboard analogy, if the dartboard represented all available bonds for the draw then for a single draw you would expect the darts to be scattered evenly around the darboard ?

No, you'd expect the darts to be scattered randomly around the dartboard, a very different concept!  Hence the well-known statistic about it being more likely than not that two people in a room of 23 will share a birthday....

pbcpdeveloper said:

If your bonds numbers were also scattered evenly around the dartboard, it would 'appear' that there are lots of gaps between your bond numbers so it looks like there is a only small chance that a dart will land exactly on one of your numbers.  But if your bonds were in one solid slice / section of the board then there 'appears' to be a higher chance that at least one dart will land on your block?

As above, that's not true, but perhaps worth noting that a maximum holding is effectively equivalent only to a one hundred thousandth of a standard dartboard segment anyway!