Premium Bonds - Odds of winning

masonic

MILLWALLFC wrote: »

so if you had the full holding does that mean you just times everything by 3?

e.g. your chances of winning £50 are 112.2% ?

Yes, so with a full holding, on average you can expect to win at least 1 £50 prize every month.

21castlehill

£6 holding for 35 years & 0 prizes won.
Have just put in an extra £300 just for the fun of the gamble, it's better than wasting it on the lottery.:D

darich

Milarky wrote: »

This exposes the misguided belief in Premium bonds - that the more you hold, the more your chance of winning, and the more your chance of winning big (all technically correct) ergo large holdings are a better 'bet' than small ones.

No! Have £100 and and leave it at that. The chances of winning ANY prize is small enough (24000:1 each time) but should your prize come up you then have an instant 50% profit at least. That's the £50 prize. Now look at the table posted by masonic: £100 about 1/10th as likely - (chances of 100% profit about 1:250,000 each time)... £500 about 1/6th as much again (chances of 500% profit 1:1.5million) £1000 prize about 1:4.5million... and so on.

It really isn't worth saving up your pennies (in the form of monthly deposits into Premium bonds that, by the way, can't be entered in the draw for at least a month - so that's a full month's interest straight off - about the price of a lottery ticket) to get slightly 'closer' to that highly unlikely outcome each month and to be cumulatively losing 4-5% pa in interest as you so nearly get there. People just don't see this - it appalls me. Still no one will lose their shirts because of years of lost interest (including those who win prizes repeatedly that yield maybe 2-3% per year) But it is actually irresponsible to be putting your money into an almost guaranteed to lose 'investment' (in the case of a true 'investment' all investors would win or lose at the same time that invested on the same day etc) without appreciating the 'odds' - and that they really are so small as to justify NO stake larger than the minimum permitted.

Yes, I understand the 'money under the bed' analogy that is often the real reason behind people having 'faith' in government backed premium bonds - they simply don't know where to put their money - but they are a poor 'investment' almost universally (as only a small number/percentage of premium bond holders show a 'real' return of any kind - see what I said about true 'investing' above)

What you say is true but also misleading.
You've agreed that the odds of winning are 24000:1 for any prize therefore a larger holding will reduce those odds of any prize.

It may not be the way you intended but it comes across that you're advising against larger holdings because of the reduced return.
But the reduced return is in relation to larger holdings - so a £50 win for a 30k holding is small but for a £100 holding it's significant.
Put it another way, holding 30k compared to your £100 gives someone a 30times greater chance of winning a prize (not the prize) than you. It would be, relatively speaking a smaller prize but with a larger holding it's much more likely to happen.
your argument is great when arguing against the jackpot, but for the numerous smaller prizes it's not quite as strong.

Given that the chance of any bond winning is the same then the more bonds you hold, the greater the chance of winning a prize. Everyone knows the chance of the jackpot are slim...but someone has to win every month and with more bonds, you increase your chance.

dundeedoll_2

I have had a battle with Child Tax Credits since 2004 - basically I have 2 eligible children but their computer says I have none. First I had no money at all for 9 months, then a bit and then a lump sum of £5000.00 Of course they still insist I have no children and want this money back as an overpayment repayment! I therefore put the large payment from them into Premium Bonds *(just in case I do lose my case & have to repay it) so have had £9000.00 in Bonds since October 2006. Here are my winnings for the last 6 months - not bad at all!!

July £50.00
July £50.00
June £50.00
June £100.00
May £50.00
March £50.00
March £50.00
Feb £50.00

masonic

darich wrote: »

Given that the chance of any bond winning is the same then the more bonds you hold, the greater the chance of winning a prize. Everyone knows the chance of the jackpot are slim...but someone has to win every month and with more bonds, you increase your chance.

The trouble is, the more bonds you hold and the longer you hold them, the closer your returns are wont to tend to the average payout of 3.8%. Sure, a small minority of people win big, but the vast majority lose out compared with a more savvy investment, which is likely to pay out a much higher return than that average. The best approach would be to make a small investment, win big, then quit while you're ahead.

Stompa

masonic wrote: »

The best approach would be to make a small investment, win big, then quit while you're ahead.

Sounds good, have you any tips for managing the 'win big' part of that approach? :rolleyes:

InMyDreams

masonic wrote: »

MILLWALLFC wrote: »

so if you had the full holding does that mean you just times everything by 3?

e.g. your chances of winning £50 are 112.2% ?

Yes, so with a full holding, on average you can expect to win at least 1 £50 prize every month.

Err, no. You can never have a 112.2% chance of anything. 100% is certain and it doesn't go higher than that! It's certainly *not* certain that you will win *anything*! That is different to saying that your would *expect* to win at least one £50 prize each month.

If your chances of winning *anything* with £10k are ~42.65% (adding all probabilities up) then your chance of not winning anything is ~58.35% (what's left from 100%). If you have three lots of £10k, your chance of not winning anything would be about 0.5835*0.5835*0.5835 = ~0.2 or 20% In other words, your chances of winning £50 (or more) would be about 80%. Not, 112.2%. And actually, I wouldn't even say you should expect to win at least one £50 every month. You would *expect* to win something about 4 out of every 5 months, but even that is by no means guaranteed (which a probability of 100% would imply). Having said all that, given any particular month, it would be fair to say you're more likely to win something than not.

masonic

InMyDreams wrote: »

Err, no. You can never have a 112.2% chance of anything. 100% is certain and it doesn't go higher than that! It's certainly *not* certain that you will win *anything*! That is different to saying that your would *expect* to win at least one £50 prize each month.

The figure posted is derived from a mathematical expectation, not a probability. Specifically, it is the probability of winning one £50 prize, plus (the probability of winning 2 £50 prizes) x 2, plus (the probability of winning 3 £50 prizes) x 3, plus...(the probability of winning n £50 prizes) x n, where n is the number of £50 prizes on offer.

All of the figures posted, including the ones in Martin's article are as well, since they are the sum of the probability of each bond winning a particular prize. I am using "expect" in the mathematical sense as well, not saying you will win £50 every month, which you wouldn't - on average you will win just over £50 a month in £50 prizes.

masonic

InMyDreams wrote: »

If your chances of winning *anything* with £10k are ~42.65% (adding all probabilities up) then your chance of not winning anything is ~58.35% (what's left from 100%). If you have three lots of £10k, your chance of not winning anything would be about 0.5835*0.5835*0.5835 = ~0.2 or 20% In other words, your chances of winning £50 (or more) would be about 80%. Not, 112.2%. And actually, I wouldn't even say you should expect to win at least one £50 every month. You would *expect* to win something about 4 out of every 5 months, but even that is by no means guaranteed (which a probability of 100% would imply). Having said all that, given any particular month, it would be fair to say you're more likely to win something than not.

Just to add, this would be ok, but the ~42.65% you have started with is actually the chance of winning with 1 bond (1 in 24,000 or 0.004166%) multiplied by 10000 [with some rounding errors, apparently], so you have to start with one bond, then multiply up as you have done. So, that would make the probability of not winning anything with 1 bond 99.99583% (not surprising!), and the probability of not winning anything with £30,000 = 0.9999583^30000 = 28.6%. Incidentally, that makes the real figure for the probability of winning *anything* with £10k 34.08%, not 42.65%.

Who says premium bonds aren't fun.

clear_blu

I have read with interest the comments that there are more sensible investments and that savings schemes produce more interest etc. than premium bonds. Well let me say to those 'sensible' people that I have investments that return a steady sum in excess of £7000 a year, but that does not give me half the excitement and 'FUN' that the £500 bond win did this month. Premium Bonds are for the 'FUN' people the 'FUN'.................