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

[goodgirl]

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

Trying to convince my partner that 2 lottery tickets per week plus scratcards (arround £100 a month) is better spent on premium bonds you have the change of winning £1 million and keep your cash...not getting very far though does anyone know which has the higher probability of a win???:confused:

[JohalaReewi]

Neither really. Chances of a big win are almost zero in both cases. You would be better off paying into a cash ISA.

With the lottery, you only get one go. With premium bonds, you get entered into each draw and when you have had enough, you can get your stake back.

See martin's premium bond article

http://www.moneysavingexpert.com/savings/premium-bonds

[nilrem]

Trying to convince my partner that 2 lottery tickets per week plus scratcards (arround £100 a month)

Do you seriously spend £100 per month on the lottery?:confused:

I honestly cannot believe that people spend (waste) that much on it!

IMHO I would say that if you want to 'gamble' that much per month put it in premium bonds, you may loose interest but at least you keep your stake! :)

[davetrousers]

£100 a month £1200 a year. The guy has a problem!

[Paul_Herring]

With premium bonds, you get entered into each draw and when you have had enough, you can get your stake back.

No - you don't get your stake back. Your stake in the premium bonds is the interest you should be earning on the principle (which is what you can get back.)

Premium bonds are just like placing your money in a high interest savings account, and spending the interest received on lottery cards - your principle reduces in real terms, but you can always get the principle back.

[Aegis]

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

Trying to convince my partner that 2 lottery tickets per week plus scratcards (arround £100 a month) is better spent on premium bonds you have the change of winning £1 million and keep your cash...not getting very far though does anyone know which has the higher probability of a win???:confused:
Believe it or not, the lottery has a higher probability of winning big than Premium bonds do if you play with the interest that you'd earn on your bond value in a savings account. However, the best standard savings account has an overall higher expected "prize" than either Premium Bonds or the Lottery, so personally I'd avoid both like the plague.

I made a comparison between holding the full investment in Premium Bonds and playing the Lottery in this post: http://forums.moneysavingexpert.com/showpost.html?p=5973313&postcount=61

I state the probabilities of winning in this post, calculated using fairly basic probability theory and correct at the time of writing: http://forums.moneysavingexpert.com/showpost.html?p=5973520&postcount=62

[isofa]

This has been discussed in detail on the various PB threads, as Aegis says, as odd as it may seem, the lottery has the higher chance of winning.

However I don't play the lottery, but I have PBs, and during the last 12 months they returned a better percentage than any instant access account offered, but it's not always the way!

You do loose your stake as Paul_Herring says, the stake is the interest you'd be earning each month, so unless you are winning regularly your capital is loosing value with inflation.

[Monkey Gold]

Surely with the interest rates, being as poor as they currently are, then premuim bonds, are a better option? As depending on how much you have saved obviously, but even one win of £25, is better than 1% interest?

[barrymoney]

Surely with the interest rates, being as poor as they currently are, then premuim bonds, are a better option? As depending on how much you have saved obviously, but even one win of £25, is better than 1% interest?

This is the logic a lot of people will be following, i.e. its worth a punt and your money is safe there. But, statistically I've seen it worked out (see posts above) that you won't get a good return over time. I recently bought some bonds, but I've got more in an NS&I savings account.

If I were cynical I'd say its part of Gordon Brown's grand plan to get everyone to move their money from highstreet banks into NS&I, where he can spend it... :D

[Paul_Herring]

Surely with the interest rates, being as poor as they currently are, then premuim bonds, are a better option? As depending on how much you have saved obviously, but even one win of £25, is better than 1% interest?

Given PB's interest of (I can't be bothered looking up the rates now) roughly 1%, and of the totals subscriptions, that 1% needs to generate one £1,000,000 prize, how much of that 1% do you think is left to generate the other prizes?

If you hold a bond of £100 (as I do), how likely do you think it is that I'll get either £1 (1%) in a savings account or a £25 win (the minimum prize now)?

Or to make it slightly more relevant... How likely do you think it is that I'll get either 10p (0.10%) in a savings account or a £25 win?

That £100 is there purely on the off-chance it'll win something. It hasn't yet, I'm treating it as lost money in that it won't. And it'll depreciate over the years.

[G_M]

£100 per month?!
Either go to a casino for a night out once a month, or sign up to gamblers anon.

[Doomcow]

both are a rip off.. put it in a savings account and look towards the future.

[Energize]

With lotto hotpicks the chance of winning £130,000 is 1/317,814 and £7,000 is 1/14,126 I'd prefer those odds to premium bonds.

[leveller2911]

well someones got to win on the premiums bonds, so why NOT me?:rolleyes: :D

statistics, statistics and more blo@dy statistics.......:rotfl:

Look at Santanders ISA advertised on TV, 1.5% interest with a 2% (variable) bonus at the end of the year..................key is is the "variable" bit, just sneeked in quietly, so from that we can assume it could be 0.5%???

All savings and investments are a gamble at the moment ,I have a bond maturing tomorrow and will get some PB,s for a while, got to be worth a punt.:D

[chopperharris]

With lotto hotpicks the chance of winning £130,000 is 1/317,814 and £7,000 is 1/14,126 I'd prefer those odds to premium bonds.

You all got me thinking about the odds and returns of my pbs now.

My math skills are as rough as the proverbial badgers behind , no doubt theres a ten year old that knows better then I do....or a bent bookie.

I failed my maths o level at the first question , and that was only NAME.

So math guys please help me understand the winning odds of my 30k.

PB data - Using the new rates and max holding.

All 30,000(b) numbers are drawn against each of the single random generations of the 1,075,065(d) prizes every month , even a winning one is re-entered.

SO is it (d) divided by (b) if so it gives me an answer of 35 ... so is that giving me a one in 35 chance of a win or the answer that I am really 35x more likely for a win than any single bond.

Perhaps its really as simple as total amount of all the pbs in existence divided by prizes and that gives me the true odds , ie for anyones single bond , then its divided by my 30000 to give me the answer of my odds?

you see my problem....yes I am both those peices of wood.

[chopperharris]

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

Trying to convince my partner that 2 lottery tickets per week plus scratcards (arround £100 a month) is better spent on premium bonds you have the change of winning £1 million and keep your cash...not getting very far though does anyone know which has the higher probability of a win???:confused:

I have another way of thinking about this for you and convincing oh.

You put it into pbs , theres a chance of winning , just like the lottery..but you keep the stake thats a gimmie.

If you dont use the stake your chances are increasing , unlike the money on lottery and scratchers which were a one time deal , thats a gimmie.

Do you maybe pay credit for a holiday every year?

If you do then treat it as a "kind of gambling yet saving piggy bank" , rather than paying interest on a holiday your simply saving for it....once you get enough in well thats your hols paid for and cheaper.You can roll any winnings into it like an accumulator.

If you are spending 1200 quid a year on lotto and getting nothing back from it then this way your definately getting a return , even if its only the stake back.

Work out how much you have won over the years on lotto and any other gambling v loses....you will see even with no winnings as a return your still up.

Wife and I have 60k in pbs.We get on average at least one win between us a month best was 350 quid combined so far and thats since october....hers is from jan.

We must have spent thousands since lottery began , or on bingo (well down), fruits (well down), nags (barstart crooks).

No-one wins at gambling if they have to replace a lost stake for every chance at a win....its diminishing returns unless you double your stake each time or quit...but I suspect you die before your double down comes.

I figured out once that our return on bingo was udner 1/3rd of what we spent , and that was quite high as a return compared to others.Our return on lottery was well under 1 percent.Nearly no return on fruits and nags.

[ChuckCash]

I agree with Aegis to a large extent on this. But like a flutter so here's my reasoning:

The effective rate on premium bonds is now down from 1.8% to 1%. This means that someone with £30,000 invested would win £300 on average over a 1 year period.

There are plenty of savings accounts which still pay >2% interest, so if i put the £30,000 into a savings account i can earn £600 in interest over 1 year. I can add £300 to the principle and gamble the remaining £300 on the lottery, thus giving me guaranteed interest (1%) + possible jackpot prize.

I tend to be more unlucky than the national average, so this formula is good for those born with such an affliction ;)

[Aegis]

You all got me thinking about the odds and returns of my pbs now.

My math skills are as rough as the proverbial badgers behind , no doubt theres a ten year old that knows better then I do....or a bent bookie.

I failed my maths o level at the first question , and that was only NAME.

So math guys please help me understand the winning odds of my 30k.

PB data - Using the new rates and max holding.

All 30,000(b) numbers are drawn against each of the single random generations of the 1,075,065(d) prizes every month , even a winning one is re-entered.

SO is it (d) divided by (b) if so it gives me an answer of 35 ... so is that giving me a one in 35 chance of a win or the answer that I am really 35x more likely for a win than any single bond.

Perhaps its really as simple as total amount of all the pbs in existence divided by prizes and that gives me the true odds , ie for anyones single bond , then its divided by my 30000 to give me the answer of my odds?

you see my problem....yes I am both those peices of wood.

Combinations of probability unfortunately aren't simple to work out. In this case you were looking at holding 30000 numbers compared with 1075065 prizes. Imagine that you could hold 1075065 bond and consider if there is a possibility of getting zero return. There is a slim chance that this will be the case, likewise if you held 2000000 bonds there is an extremely small chance that none of your numbers will come up.

What you need here is a fairly complicated binomial expansion which looks at the overall probability of each prize. I believe this is the basis for Martin's Premium Bond probability calculator, which can show you what you would expect to win over the whole year.

In short, better to stick to the calculator than to try and work it out for yourself. That goes for me too!

[RichardJW1]

I have the full 30k and last year it returned +1.5%. This year after 3 months I already have +0.8%

[iltisman]

The only attraction of PBs and the lottery is a life changing win something you will never get with saving.I now only play the lottery when its a rollover.

[Paul_Herring]

£100 per month?! No, £100 total.

[rb10]

If you look at this page on the NS&I site (http://www.nsandi.com/news/pbnotice.jsp), you can see some interesting things about Premium Bonds.

The 'lower value' prizes are those which are up to £100 in value. They make up 99.8% of the number of prizes available - so are by far the most likely category for most people to get in to.

If you assume that you will only receive lower value prizes in a year (a fair assumption, given what I said above), you can expect a return of around 0.89%. This is the figure that people should be using when considering how much interest Premium Bonds give, as it reflects how much you are likely to get back at the end of the year. On the maximum of £30000, it works out at £267, about 1/4 of what you could be getting in a bank.

Ask yourself the question: can I get 0.89% or more (after tax) in a good savings account?

[Dopple]

If you want to win a smaller amount (say £100,000) then you will get better odds doing the lotteries on Bookmakers sites. For example Pick 5 numbers on the UK lottery at Paddypower, and if all 5 come up you get 110,000-1 odds.
Still a long short put much better odds then trying to get 6 out of 6 on the National Lottery.

[Energize]

If you want to win a smaller amount (say £100,000) then you will get better odds doing the lotteries on Bookmakers sites. For example Pick 5 numbers on the UK lottery at Paddypower, and if all 5 come up you get 110,000-1 odds.
Still a long short put much better odds then trying to get 6 out of 6 on the National Lottery.

Your better off with hotpicks for smaller amounts, you can win £7k on hotpicks (4 balls) with 14,000:1 odds.

[paulw19]

A combination of both perhaps? I dont see why it has to be one or the other. The odds on either are terrible. I admit to spending £20 a month on lottery which I believe is a reasonable amount, but I also spread my money around a variety of products and investments.

[McSaver]

The 49s and the Irish Lottery offer better odds than both PBs and the National Lottery

[chopperharris]

Your better off with hotpicks for smaller amounts, you can win £7k on hotpicks (4 balls) with 14,000:1 odds.

So if I purchase 14001 I can have certainty of winning 7k , is 7k a shared pot ie one prize?Then theres any other prizes to add if any.

15 permutations of 4 from 6 , if theres no shared pot then I would have those permutations too so 15 multiples of 7k?

I cant my head around that if its not a shared pot , i wonder why someone just doesnt do it every week if they had 14k.

[Aegis]

So if I purchase 14001 I can have certainty of winning 7k , is 7k a shared pot ie one prize?Then theres any other prizes to add if any.

That's not the way probability works, unfortunately.

The probability of winning with 14000 entries is the same as 1 minus the probability of NOT winning with 14000 entries, or:

P(winning) = 1 - P(not winning)
P(winning) = 1 - (13999/14000)^14000
P(winning) = 63.2%

As you continue to increase the number of entries this will asymptotically tend towards certainty until you buy literally every combination available and make a huge loss because of the purchase cost.

I hope that clarifies things a little.

[alared]

This is a no brainer,you NEVER lose your money with PB unlike the lottery where you never see your money again.

[ChuckCash]

This is a no brainer,you NEVER lose your money with PB unlike the lottery where you never see your money again.

An alternative would be to put the money in a high interest savings account instead and blow the interest on the lottery.

Can any maths geniuses out there do a comparison?

[alared]

An alternative would be to put the money in a high interest savings account instead

Please find me one of those:confused:

[ChuckCash]

Please find me one of those:confused:

Yup, high interest ain't what it used to be.

Slim pickings but i'd say 3%+ is high interest, especially relative to the effective interest rate for PBs which has dropped from 1.8% to 1%

In the context of premium bonds vs lottery, i'm scratching my head over which is best... the prize fund for PBs based on 1% interest rate or flutter on lottery based on 3%

[steve23144]

In the context of premium bonds vs lottery, i'm scratching my head over which is best... the prize fund for PBs based on 1% interest rate or flutter on lottery based on 3%
£30,000 on PB gives a chance of a jackpot win of 1 in 100,000 over one year.

Put the money in a savings account with 2% interest = £600. Spend that on lottery tickets gives odds of 600 in 14 million = 1 in 23,000, 4 times better than PB. Plus lottery jackpots are bigger on average (average size of shared jackpot = £2m). And you've still got your £30,000 sitting safely in your savings account.

Average winnings over a year it's the other way round:

PB is £300.

With the lottery I'd guess at 600 / 60 * £10 = £100, based on a roughly 1-in-60 chance of matching 3.

[exel1966]

This is a no brainer,you NEVER lose your money with PB unlike the lottery where you never see your money again.

You obviously didn't read or understand the posts above. You DO lose money with PB's. It's called inflation and todays CPI figure of 3.20% shows just how more expensive everyday items are getting and how each pound is slowly being devalued.
Your £1 put into a PB today could be worth next to nothing in a few years time.

THEY ARE A GAMBLE ! If you can afford the gamble then go for it, if not save it.

[alared]

Lets put it this way,you DON`T lose your capital unlike buying lottery tickets which you do lose every time,with a slim chance of a win.
I used to play an online lottery game every day for free and did this for a couple of years,which would have cost £730.
I can count on my hands the number of times I got three up,which made me realise the only winner of the National Lottery is the government who pocket 12.5% in the £.
PB every time,it`s a no-brainer.

[exel1966]

You will lose a portion of your capital as it's value gets erroded in time, but that's the gamble as you could also win, though as explained above the odds are slim whether it be lottery or PB's and with the BOE coming down so much, there's certainley not much incentive to save.

[alared]

Would you put a safe,secure £30k on PB --- YES

Would put £30k on the lottery ----- NO

End of story.

[withnell]

45p in each £ from the lottery goes for prizes, 1% goes for prizes on Premium bonds

=> if you have a savings account earning over 2.22% net, then you'll get a better return putting the interest from this into the lottery than you will in Premium bonds

Many people on this thread don't seem to have got the point, that it's only INTEREST being put on the lottery, not the capital - so exactly the same as premium bonds

[Aegis]

Lets put it this way,you DON`T lose your capital unlike buying lottery tickets which you do lose every time,with a slim chance of a win.
I used to play an online lottery game every day for free and did this for a couple of years,which would have cost £730.
I can count on my hands the number of times I got three up,which made me realise the only winner of the National Lottery is the government who pocket 12.5% in the £.
PB every time,it`s a no-brainer.
Sorry, you've still missed the point completely. You don't go out and put £30k on the Lottery, you put the difference between the expected winnings in Premium Bonds and the interest you get from savings into the Lottery tickets. That way your expected "winnings" (including the savings interest) are still higher than with Premium Bonds and you have about a 4 times greater chance of winning big.

This is especially true for ISA accounts or of basic/non taxpayers.

[alared]

Well I know where my money`s staying.
Every month I get a free bet with PB and I cannot lose my stake.
With the lottery,12.5% is grabbed right away by the gov.,so much is "wasted" on "good causes" and you have a very tiny chance of winning a tenner.
Don`t forget that when they realise that the 2012 olympics are going to cost a great deal more than they estimated,we know where all the "good cause" money will go.

[ChuckCash]

Well I know where my money`s staying.
Every month I get a free bet with PB and I cannot lose my stake.
With the lottery,12.5% is grabbed right away by the gov.,so much is "wasted" on "good causes" and you have a very tiny chance of winning a tenner.
Don`t forget that when they realise that the 2012 olympics are going to cost a great deal more than they estimated,we know where all the "good cause" money will go.

Well I guess you can argue that from a moral standpoint, PB beats lottery every time, what with olympics and other such "good causes" ;)

But from a purely financial standpoint, keeping the money in a high interest savings account and spending the interest, or a proportion of, on lottery would give a better return on average than PB.

[chopperharris]

£30,000 on PB gives a chance of a jackpot win of 1 in 100,000 over one year.

Put the money in a savings account with 2% interest = £600. Spend that on lottery tickets gives odds of 600 in 14 million = 1 in 23,000, 4 times better than PB. Plus lottery jackpots are bigger on average (average size of shared jackpot = £2m). And you've still got your £30,000 sitting safely in your savings account.

Average winnings over a year it's the other way round:

PB is £300.

With the lottery I'd guess at 600 / 60 * £10 = £100, based on a roughly 1-in-60 chance of matching 3.

As I see it 600 quid interest put into lottery only gives those odds if put in in one draw.The odds of 14m to 1 for the jackpot will always be 14m for every single draw due to random generation , 14m divided by 600 is 23333.3r - 1. IF you are only entering say 10 quid from the interest you will only get 1,400,000-1 odds for that jackpot.

the odds of matching 3 from 6 for a single entry is 56.7-1 , would you back horses with those odds regularly?

[alared]

http://cstadvertising.com/casestudies/nsi/

Well here`s a guy who knows how to make a bob or two and he`s dead keen on PBonds:T

[steve23144]

As I see it 600 quid interest put into lottery only gives those odds if put in in one draw.The odds of 14m to 1 for the jackpot will always be 14m for every single draw due to random generation , 14m divided by 600 is 23333.3r - 1. IF you are only entering say 10 quid from the interest you will only get 1,400,000-1 odds for that jackpot.


With 10 different tickets in a single draw, you're right - you have 1 in 1.4 million chances of the jackpot.

However, with £600 the chances are 1 in 23,000. It scarcely matters whether you spend it all in one go or spread it over the year, because you're covering such a small proportion of the possible outcomes.

[Paul_Herring]

Would you put a safe,secure £30k on PB --- YES

Would put £30k in a savings account and spend the interest on the lottery ----- NO

Why are you finding this second concept so difficult? Why do you think the two are that different when they aren't?

[alared]

:rotfl: :rotfl: Why are you finding this second concept so difficult? Why do you think the two are that different when they aren't?

Of course they are different.
My money is safe and secure in PB and I have a chance to win prizes every month.
If I put £30k in a bank account paying 3.5% (which may be hard to get just now) after tax this earns me £840 to waste on the lottery with very little chance of scooping a prize.
Meanwhile by not investing in the safest bet in town,I`m missing out on the chance of winning.
You cannot lose your capital with PB, unlike the N lottery where the chance of even winning a tenner is slim.

Your theory is just that because when it comes to the crunch of gambling £840 on the lottery most people would bottle out and probably look for a safer bet such as --------------------------- PBonds:rotfl:

[Shyofrisk]

Just joined.....consider me a voice in the wilderness. I used to win at least 100 per month on P.Bs and became accustomed to the extra income. I haven't won a bean in three months - three months! But given how little interest I am losing I am not about to cash them in just yet. Besides, there is nothing quite like the thrill of possibility every first of the month..... I have never won more than 250 in all and no bigger prize than a 100, but still I dream.

Shy

[alared]

Shy welcome to the forums.
At least you know your money`s still there with PB and not "gone down the swannie" on the lottery.

[Paul_Herring]

Of course they are different. They aren't that different - which is what I said in my last post.
My money is safe and secure in PB As it would be in a bank's savings account. and I have a chance to win prizes every month. As you do with spending the interest on the lottery.

If I put £30k in a bank account paying 3.5% (which may be hard to get just now) after tax this earns me £840 to waste on the lottery with very little chance of scooping a prize. As opposed to the '1%' from April that your Premium bonds are 'earning,' (£300) meaning that your chance of winning a prize is lower...

Meanwhile by not investing in the safest bet in town,I`m missing out on the chance of winning.
You cannot lose your capital with PB, nor will you lose your capital in the bank unlike the N lottery where the chance of even winning a tenner is slim. which also applies to premium bonds.

[chopperharris]

They aren't that different - which is what I said in my last post.
As it would be in a bank's savings account. As you do with spending the interest on the lottery.

As opposed to the '1%' from April that your Premium bonds are 'earning,' (£300) meaning that your chance of winning a prize is lower...

nor will you lose your capital in the bank which also applies to premium bonds.


They are as much different as they are alike imo , bit i still reckon pbs win , heres my thinking.

Both - 30k is secure.tick

Lottery-:Using interest only is dependant on roi and tax rate.Limited number of entries based on interest accrued , it wont ger higher than a lock in rate , but nor will it get lower.All on one draw increases the odds of a win but not by any great deal , and not in any means near that of pbs.Your wating the first 12 months for the stake money to maximimise the odds of any win.

Pb , 30000 entries each time from the beinging of the 2nd month , 11 draws first year , so thats 330000 entries .Beats the number of lottery entries from savings interest hands down.

For defining which one has better odds you have to consider the odds winning of each prize in each of the systems versus the stake.EG compare established lottery odds for one draw(the odds of winning are decreased by spreading across more draws with stake hence only one draw) and all prizes divided by 850 entries(interest gained) , versus , pb odds for all prizes divided by 30000 over 11 months.

I can see where the idea of savings interest for lotto comes from , but in no way do I reckon it approaches the staggering entries v odds ratio in its favor in this scenario....BUT as we know my maths looks up to poo.

The only way it could is if the odds ratio of a win on pbs were astronomically high , not merely in reduced payout interest , but also in proportion to the stake itself.

For anyone with considerably less than in the thousands it is most likely better to just bung a few quid on the lotto if it would take too long to amass the full and protected stake for pbs....but in reality the odds on the nags would be an even better choice for them , preferrably less than a 15-1 shot , no accumulators , with a bent irish trainer and jockey.

[Aegis]

Well I know where my money`s staying.
Every month I get a free bet with PB and I cannot lose my stake.

You can and do lose your stake. Every month you fail to win at least £60-70, you have lost your stake. Given that you have a 45% chance of winning exactly nothing in any one month, you are losing part of your stake in the majority of months.

Your stake is lost, but because you aren't given it in the first place you don't notice that you are losing so much.

With the lottery,12.5% is grabbed right away by the gov.,so much is "wasted" on "good causes" and you have a very tiny chance of winning a tenner.

I agree, I wouldn't want to play the Lottery because I think it;s a mug's game. However, I've done the calculations myself, and the expected winnings are higher if you use savings account interest (minus 1% to account for the expected winnings from Premium Bonds) to fund Lottery ticket purchases.

Premium Bonds are popular because they're a poor gamble dressed up as a decent savings product. Popular with the people who believe the hype, and popular with the government because they get to borrow money at an absolute pittance of an interest rate.

[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]

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]

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]

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.