Premuim bonds versus National lottery which has the higher probability to win??

rb10

So if you have £30,000, the options are:

1) With a savings account at 3.5% gross, you'd end up with £840 in interest at the end of the year, after tax.

2) With a savings account at 3.5% gross, then putting the £840 on the lottery. Obviously this is difficult to model statistically, but, for a good approximation, we can discount prizes where five and six numbers are matched, as the odds of these are so slim. The odds of winning £10 prizes are about 1 in 57 (according to lottery.co.uk), so you'd expect to win £148 per year. Additionally, the odds of winning a 4-match prize is 1 in 1033, and the prize is around £65, so the expected annual win here is approx £53. Hence, the total expected win on the Lottery is £201.

3) With Premium Bonds, taking the rate from April onwards, you can expect to win around £267 per year.

So overall, putting it in a savings account, and keeping it all there is way out ahead. By gambling the interest on the lottery, you'd only get about 1/4 the amount of interest, and Premium Bonds would give about 1/3 the amount that the savings account would give.

Aegis

rb10 wrote: »

So if you have £30,000, the options are:

1) With a savings account at 3.5% gross, you'd end up with £840 in interest at the end of the year, after tax.

2) With a savings account at 3.5% gross, then putting the £840 on the lottery. Obviously this is difficult to model statistically, but, for a good approximation, we can discount prizes where five and six numbers are matched, as the odds of these are so slim. The odds of winning £10 prizes are about 1 in 57 (according to lottery.co.uk), so you'd expect to win £148 per year. Additionally, the odds of winning a 4-match prize is 1 in 1033, and the prize is around £65, so the expected annual win here is approx £53. Hence, the total expected win on the Lottery is £201.

3) With Premium Bonds, taking the rate from April onwards, you can expect to win around £267 per year.

So overall, putting it in a savings account, and keeping it all there is way out ahead. By gambling the interest on the lottery, you'd only get about 1/4 the amount of interest, and Premium Bonds would give about 1/3 the amount that the savings account would give.

That's more or less it, but if you instead imagine putting half the interest into lottery tickets, you end up with £420 guaranteed and the chance of a much higher return, however slim. A much better deal than with Premium Bonds, and if memory serves you actually have a higher chance of coming away with a fortune then with Premium Bonds.

chopperharris

Surely you cant just ommit the odds of a 5-6 number win on lotto , thats masaging the figures if it affects the odds , I dont think it would anyway for base prizes in these calcs.Doing so with pbs has no similar effect on the probability.

BAck to work

Can you win part of a tenner(3 balls) , or part of 65(4 balls) though , I dont think you can.

So it would be 14 probable tenner wins and 74 percent probability of another , 840/57 works because its a multiple of the odds at 14.7. ie so its 140 quid winnings not 147.

The odds of 4 balls is 1033/840 is not enough to get any certain win at all ....but merely the slightly increased chance of expecting a win....or am I wrong here?Therefore you cannot add a part win of 53 quid to the total?

Am I right then that expected minimum return is only 140 quid for 840 stake , not 201 as stated.

By my reckoning to get a garunteed four ball you would have had to had 5 or more likely 6 years worth of 840 plays?

rb10

chopperharris wrote: »

Surely you cant just ommit the odds of a 5-6 number win on lotto , thats masaging the figures if it affects the odds , I dont think it would anyway for base prizes in these calcs.Doing so with pbs has no similar effect on the probability.

Yeah, there's a 99.x% chance you won't win those prizes, so they aren't worth bothering with. Doing so with the PB's does have a similar effect on the probability - see post 22 of this thread, where I explained that the real expected 'interest rate' is actually 0.89%.

Can you win part of a tenner(3 balls) , or part of 65(4 balls) though , I dont think you can.

So it would be 14 probable tenner wins and 74 percent probability of another , 840/57 works because its a multiple of the odds at 14.7. ie so its 140 quid winnings not 147.

This is assuming you hold them for several years, in which case your average annual win could well include 'part of a tenner'.

The odds of 4 balls is 1033/840 is not enough to get any certain win at all ....but merely the slightly increased chance of expecting a win....or am I wrong here?Therefore you cannot add a part win of 53 quid to the total?

Your fraction is upside down. But you would expect to have 840/1033 wins per year, so whilst this doesn't mean that if you just did it for one year you would be likely to win that prize, over enough years it should average out to be £53 per year from this prize.

By my reckoning to get a garunteed four ball you would have had to had 5 or more likely 6 years worth of 840 plays?

None of this is ever guaranteed!

Dopple

My thinking is probably flawed on this but I see it this way:

£30,000 into Premium Bonds.
Slim chance of winning £1M once a month.
Average return = £300 a year.

£30,000 into Savings Account paying 2.5% net.
Return = £800 a year.
Put £1 on the lottery each Wednesday and Saturday, you have a slim chance of winning £1M+ twice a fortnight. Cost = £100.
Leaving you £700 left.

Savings + Lottery wins over Premium Bonds.

HappyMJ

That's assuming the OP had £30,000. I believe the question was a bit different...

If the OP wants to spend £100 per month on "gambling" then stick it on the premium bonds. It is a lower chance of "winning" but you'll get your chance to win a million and you'll even get your money back if you want it.

Me personally I'd save it in a Regular Savings Account and watch the money grow.

ChuckCash

HappyMJ wrote: »

That's assuming the OP had £30,000. I believe the question was a bit different...

If the OP wants to spend £100 per month on "gambling" then stick it on the premium bonds. It is a lower chance of "winning" but you'll get your chance to win a million and you'll even get your money back if you want it.

Me personally I'd save it in a Regular Savings Account and watch the money grow.

The same applies, regardless of whether it's £30,000 or not - PB are statistically a worse gamble than a combination of savings + lottery.

Ok if the OP wants to spend £100 a month, put it in a savings account paying monthly interest (e.g. 2-3% APR is not unreasonable). Keep half of the monthly interest in the savings account and blow the other half on lottery, horses, greyhounds, whatever... On average this would still be better than £100 per month into PBs.

surreywill

I am quite literally astounded by the flawed logic I'm reading on this thread.
So much so, I had to actually register with this forum to reply.

(Note, this thread is quite old, so if I refer to interest rates below they may no longer be current)

I'd urge anyone who is seriously incapable of making a decision like this to consult a financial advisor who can suggest the best investments and ignore all the nonsensical assertions made by the people on this thread.

That said, I'm going to go ahead anyway and say what I believe (strongly) to be correct. Some people above (Dopple, HappyMJ) seem to be on the same page, but there's some worrying stuff coming from many others.

Firstly, inflation is completely irrelevant here. Inflation applies to all cash, regardless of where it is invested, so forget that straight away. True, some investments (e.g. P.B.) may offer returns less than inflation, but you're hardly "protected" from inflation by playing the lottery.

Secondly, with regards to P.B. vs. Lottery there is unequivocally no point of contention that P.B. offers a better *expected return* than the Lottery. i.e. if you spend £1 on P.B. you expect to be able to get more than £1 back over time. If you spend £1 on the Lottery you expect to get less than £1 back over time. Expectation is a statistical measure, and the above statement is provably true.

This statement is the *only* relevant piece of information when discussing whether P.B. offers and better investment than the lottery.
The discussion of "High Interest + Lottery" is utterly specious. All you have proved by your little 1% vs. 2.5% example is that a 2.5% savings account offers a better return than a 1% savings account. Well done!
An even better return would be to take the interest you earn from your 2.5% account and stick it all back into that same 2.5% account!

Of course, if you stick all your cash into a 2.5% savings account you lose out on that all-important chance of winning a big prize. Well that is where the whole discussion becomes a little subjective. What odds are "good enough" for a big win? From a quick back-of-the-envelope calculation, I'd say that a £1 lottery ticket does have better odds of winning the jackpot than a single £1 Premium Bond, but to be honest, both prospects are extremely long odds anyway - hardly any of us can realistically expect to win a big prize like this in our lifetimes, even with a stake approaching £30k.
Of course, sticking £30k in P.B. increases your chance of winning the jackpot (I'd say roughly to a level approaching that of a single lottery ticket), but you can expect to make some return on that £30k - whereas you cannot say the same thing about 1 or more lottery tickets.

If you simply want to expose yourself to the possibility of winning a jackpot and don't like the odds of winning P.B., then why not invest as usual and spend only £1 per week of your hard-earned interest on a single lottery ticket? That would expose you to the least expected loss whilst still giving you a chance of winning.

Once again, the jackpot discussion is totally subjective, but my suggestion of a decent strategy would be as follows:
- Stick all your money in the "high interest" account - keep the interest earned in the same account
- Spend £1 per week on a lottery ticket if you like. Roll-overs offer better expected returns.

That's not to say I'm suggesting P.B. is a bad investment. Remember it's tax free, and if you've used up all your ISA allowance and can't qualify for those higher bonus rates at the moment it's better than sticking your money under the mattress, and certainly better than "investing" it in lottery tickets.

Primrose

If you're still together in 25 years time, you will look back and think wistfully of all this money that has been poured down the drain, probably with not a penny to show for it, or a few pounds at most.

If you invested that money every month in some good quality unit trusts wrapped in an ISA, you would have a nice little nest egg waiting for your retirement. Remember the old saying, 'A fool and is money are soon parted'.

choc_mouse

I'd look at both as the chance of winning big only. I wouldn't consider it a true investment. For me PB would only be a consideration if I had a spare £30k lying around and already had too much money invested elsewhere. (In my dreams.)

Here's my calculation.

Odds of winning jackpot on lotto = 1 in 13,983,816 (fixed by 6 main balls).

Approximate number of premium bonds = 52.4m * 12 * 100%/1.5% (Oct 09 prize fund weighted over 1 year) = 41,920,000,000 (e.g. odds of winning decreases as the number of bonds increases, like a raffle). So the odds of 1 of your premium bonds winning the big prize is 1 in 42 billion.

You could factor in the number of tickets/bonds held, top X prizes, frequency of draws and time of investment, you'll probably find the odds of winning big are quite similar, as surreywill says, but the reality is the big prize everyone wants has some very very long odds.