NS&I or lottery with interest

barnstar2077

danlightbulb said:

@barnstar2077
£50k in savings would generate £41 per month in fixed interest at 1% per year.

A lottery ticket is £2 so that would buy you approx 20 tickets per month or 240 tickets per year. At 1 in 45 million, this makes the odds of winning the jackpot over the course of a full year to be about 1 in 188,000. However that is comparing a £1m prize on premium bonds to a c. £10 million prize on the lottery.

Instead how about looking at the euromillions which is £2.50 per ticket but includes a millionaire maker draw entry with each ticket. Forgetting the euromillions draw itself, the millionnaire maker has an odds of 1 in 1.9 million on Tuesdays, according to wikipedia. Instead of buying 20 lottery tickets, if you bought 16 euromillions tickets for Tuesdays each month, that would be 192 entries to the millionnaire maker per year. Over a year, the odds of winning would be 1 in 9900. That is significantly better than the 1 in 77k from the NS&I. However, you're sacrificing lower end prizes in exchange for a better chance of winning big.

Because there are so many lotteries and prize tiers within those lotteries, it is a complex problem to calculate all the different combinations and compare them to NS&I.

The odds are still terrible.  Meanwhile your original sum is still being eaten by inflation.  Wouldn't you be better off just investing the original sum?

The_Green_Hornet

I've done some back of the envelope calculations, as follows:

For the sake of argument lets say you put £50k in a savings account which pays the equivalent of the Premium Bond annual prize fund interest rate (which is 1.0% from December). At the end of the year you will receive £500 in interest which you then use to buy 250 tickets in the UK National Lottery Lotto draw. The odds of winning any prize in Lotto is 1 in 9.3 so if you had average luck you would win 27 prizes. Of these prizes, again with average luck, you would win 3 x £30 (Match 3 odds are 1 in 97) and 24 Lucky Dips (Match 2 odds are 1 in 10.3). So after the first draw your £500 investment in lottery tickets may return you £90. Your 24 Luck Dips would then be entered in the next draw and with average luck you would win 2 prizes, most probably Luck Dips. These 2 Lucky Dips would then be entered in the next draw where with average luck you would win absolutely nothing.

So with average luck you would turn your £500 of interest into £90. But then again you may win the jackpot. You have to be in it to win in. Fingers crossed.

coyrls

wmb194 said:

coyrls said:

danlightbulb said:

ColdIron said:

So what happened to the £2 that you paid for the ticket that lost?

That was bought from the interest you earned on the capital, not from the actual capital itself.

With premium bonds, you wouldn't have ever got the £2 in the first place, only two draw entries which you may not win on.

So they are equivalent principles.

No, your premium bond draw entries are based on your capital, not the nominal interest on the capital.  The nominal interest is used to pay the prizes.

Dan is referring to the opportunity cost i.e. you can earn interest elsewhere with your principal and you're effectively gambling that interest you've forgone. I'm surprised at how some people struggle with this. Either way, meh. There must be a lottery calculator somewhere that'll give you your odds on a few hundred pounds a year. I can guess it won't look great.

I know exactly what he is saying but the statement:

With premium bonds, you wouldn't have ever got the £2 in the first place, only two draw entries which you may not win on.

is factually wrong, the interest does not buy you draw entries, it is, as you say, the opportunity cost of being in the draw.  The number of entries you have in the draw is determined by the number of premium bonds purchased by your capital.

eskbanker

Q. How many MSE posters does it take to change a light bulb?

A. Apparently more than four pages worth....

gatters

There's an actual, more simple case similar to what the op is suggesting? I can't remember the exact figures but a few years ago Virgin offered a savings account with a poor interest rate, but with a bonus payable if Man Utd won the league. I believe at the time there were other accounts that offered much better interest rates, where you could use the difference to place a bet with a bookie and increase your expected payout if United won the league. 

eskbanker

gatters said:

There's an actual, more simple case similar to what the op is suggesting? I can't remember the exact figures but a few years ago Virgin offered a savings account with a poor interest rate, but with a bonus payable if Man Utd won the league. I believe at the time there were other accounts that offered much better interest rates, where you could use the difference to place a bet with a bookie and increase your expected payout if United won the league. 

But that's not really similar at all - your example involves canny punters identifying a way of actually improving their returns, but OP's proposition collapses as soon as it's understood that the average return on lotteries (wherever the stake money has come from) is negative, so the odds are never going to be in your favour if you aspire to improving your position by buying lottery tickets and therefore it makes no financial sense to do so.  Much like backing Man United to win the title....

gatters

I see where the op is coming from though. It just needs an account with a much higher interest rate than premium bonds, that doesn’t exist at the moment. How much higher will depend on the expected payout of the most efficient lottery available. 

danlightbulb

The_Green_Hornet said:

I've done some back of the envelope calculations, as follows:

For the sake of argument lets say you put £50k in a savings account which pays the equivalent of the Premium Bond annual prize fund interest rate (which is 1.0% from December). At the end of the year you will receive £500 in interest which you then use to buy 250 tickets in the UK National Lottery Lotto draw. The odds of winning any prize in Lotto is 1 in 9.3 so if you had average luck you would win 27 prizes. Of these prizes, again with average luck, you would win 3 x £30 (Match 3 odds are 1 in 97) and 24 Lucky Dips (Match 2 odds are 1 in 10.3). So after the first draw your £500 investment in lottery tickets may return you £90. Your 24 Luck Dips would then be entered in the next draw and with average luck you would win 2 prizes, most probably Luck Dips. These 2 Lucky Dips would then be entered in the next draw where with average luck you would win absolutely nothing.

So with average luck you would turn your £500 of interest into £90. But then again you may win the jackpot. You have to be in it to win in. Fingers crossed.

Thanks for this.

You're right (and other's saying it too of course) that on average the returns will be lower, in return for the chance of winning a bigger prize. That's the trade off.

So person A might not want any trade off at all and therefore he puts his savings in a fixed account.

Person B might want a bit of a trade off so he puts his savings in premium bonds, where there is a chance at winning a bigger prize in exchange for a lower average return.

Person C (me in this case) might want to explore even more trade off - hence seeing all the possible combinations of alternatives and their average returns and other (albeit unlikely) prize distributions. Although I know my average return will be lower than the above two options, there is a higher chance at a bigger prize.

My original post was saying, essentially, MSE have looked at case 1 and case 2 but why not case 3? 

A poster above said why not scratchcards, or why not sports betting, or online casino's or whatever other options there are. I think absolutely they are also valid options. But as with the lotteries, very difficult to work out.

The overall point I think is that without the data, the full extent of the decisions are unknown. Why do people put their savings into PB? If its to win a big prize and that's it (because savings returns are so low right now that you may as well just go for the big prizes), they might get better odds by playing one of the lotteries (to be clear - playing with the interest NOT the original capital). If its to get some lower returns whilst having some chance at a million, then PB might be the best for them. If people don't want any variance at all, then a fixed rate account offers that.

danlightbulb

Here's three hypothetical examples of what I'm trying to illustrate:

1. £50k in fixed savings @ 1%, guaranteed £500 per year, and that's it.
2. £50k in premium bonds, average return £400 per year, but you have a 1 in 77,000 chance of winning a million, over a year.
3. £50k earning interest at 1%, interest used to buy lottery tickets - average return only £90 per year but you have a 1 in 10,000 chance of winning the million, over a year.

As you can see, all you're doing as you progress through the options is trading off more of your average, likely, return for better odds of winning a big prize.

All options are positive against the original capital (you are winning 'something' even in option 3). Your capital does not go down in any of the above scenarios, it only ever goes up as long as you compound the 'winnings' back into your capital.

All of the options are negative against inflation, say at 2% per year, by varying degrees.

eskbanker

danlightbulb said:

So person A might not want any trade off at all and therefore he puts his savings in a fixed account.

Person B might want a bit of a trade off so he puts his savings in premium bonds, where there is a chance at winning a bigger prize in exchange for a lower average return.

Person C (me in this case) might want to explore even more trade off - hence seeing all the possible combinations of alternatives and their average returns and other (albeit unlikely) prize distributions. Although I know my average return will be lower than the above two options, there is a higher chance at a bigger prize.

danlightbulb said:

1. £50k in fixed savings @ 1%, guaranteed £500 per year, and that's it.
2. £50k in premium bonds, average return £400 per year, but you have a 1 in 77,000 chance of winning a million, over a year.
3. £50k earning interest at 1%, interest used to buy lottery tickets - average return only £90 per year but you have a 1 in 10,000 chance of winning the million, over a year.

You'd effectively choose to spend £410 per year in return for the chance of winning a million once every 10,000 years (by which time you'd have spent more than double that on average)? Wow.

Not that there's anything intrinsically wrong with dreamers falling for the 'it could be you' marketing by the way, but they're kidding themselves if they believe that doing so forms part of any rational plan to get the most out of their money, which is of course why MSE won't go anywhere near this idea with a bargepole....