NS&I or lottery with interest

danlightbulb

Hi all.

This is an idea/suggestion that I emailed in to MSE a couple of months ago. Unfortunately they first got the wrong end of the stick then when I tried to re-explain I never got a reply.

The NS&I premium bonds gives you an entry into the draw for a range of prizes instead of paying a fixed interest rate. This is common knowledge obviously and MSE has produced a probability calculator that shows you the odds of winning the various prize tiers as well as whether you would expect to beat a savings account over a defined period of time.

However if one is willing to sacrifice fixed interest for a chance at prizes, there is an alternative option, or in fact several.

You could put your capital into a fixed interest account and then use the interest earned, on a monthly basis, to buy lottery tickets.

This is fundamentally the same approach as having your money in premium bonds.

The key however, is whether you expect to be better off, on average. This depends on the mix of prizes and their odds, over a period of time, between the NS&I and the various choices of lottery out there.

At the moment, anyone in NS&I could be leaving some value on the table because it could be the case that one of the various lotteries available could offer better value than premium bonds on average. This is particularly relevant now because of them dropping their prize rate, which may make alternative lotteries better value.

The problem is its very difficult to calculate.

I suggested to MSE that they commission a tool, building on their existing premium bonds calculator, to compare the value of NS&I against some of the common lotteries available. Unfortunately MSE got the wrong end of the stick and thought I was suggesting using the capital to buy lottery tickets, which clearly is just gambling and absolutely not what I was suggesting. It is the interest from the capital that is used to buy them in the exact same way that premium bonds implicitly works.

So I thought I would see if anyone else has considered this and if so, how the complex set of probabilities are calculated with a view to building my own spreadsheet calculator.

colsten

Interest becomes part of your capital as soon as you have earned it. Your idea is only good for gamblers.

eskbanker

Surely all lotteries inherently pay out less in prizes than they take in in ticket sales, so therefore on average a gambler will lose and it would always make more financial sense to keep the interest earned from the capital rather than buying lottery tickets with it.

Obviously there is always the prospect of winning less than the average on premium bonds, and losing capital value to inflation (as would also happen if withdrawing the interest from savings) but, even allowing for that, the overall expectation from buying PBs is a positive return overall, whereas spending interest on lottery tickets is a negative one on average, so it's a no-brainer not to buy lottery tickets for anything other than the thrill of potentially getting that big win.

El_Torro

Interesting idea, and one many people have considered, I'm sure.

I don't really see it working in the current climate. Premium Bonds are dropping to 1% but how much better than this can you get in an instant access account? 1.2%? So you're only gaining 0.2% or so with which to buy your lottery tickets. I'm not sure it's worth the hassle. Also remember that most lotteries have a huge jackpot with relatively few smaller prizes. I suspect the rate of return is a lot worse than Premium Bonds, especially when you ignore the miniscule possibility of winning the jackpot.

You can improve your return in savings by for example putting £1000 in a Virgin Money Current Account and getting a whopping 2.02% interest rate with which to buy your lottery tickets. I still think though that the difference between the rate of return on Premium Bonds and the rate of return on interest accounts is too low. This hasn't always been the case, but I think it is now.

Having said all that I think your idea is worth investigating to see if it returns a better return than Premium Bonds. I'm not going to do the calculation though. It doesn't look like MSE are going to do it either.

danlightbulb

colsten said:

Interest becomes part of your capital as soon as you have earned it. Your idea is only good for gamblers.

You have also misunderstood the proposal. Premium bonds 'interest' is used to buy draw entries and prizes are added back to your capital, which are then used to buy more draw entries next month. I am not proposing anything different, just using a 'different' lottery rather than the NS&I in house one.

@eskbanker I understand what you're saying about negative expected value. However this is why a calculator is needed - because how do you know whether earning 1% in a fixed account, and buying lottery tickets with that 1%, would be better or worse than earning no interest in a premium bonds account but getting the draw entries in lieu? The lottery itself is negative expected value I agree, but you're not playing it with the capital you're playing it with the interest, which itself is positive (say +1%). So it has to be the case that playing the lottery with the interest is also positive (compared to earning no interest at all), the question is is it more or less positive compared to the NS&I in house lottery. That's what needs to be calculated.

The reason people use premium bonds is that it gives a good chance of earning small prizes similar to the average interest rate but also gives a chance of 'winning' bigger prizes. An alternative lottery would work exactly the same way. The key comes down to the odds and the prize distribution - which lottery is the most efficient, the NS&I one, or an alternative?

danlightbulb

El_Torro said:

Interesting idea, and one many people have considered, I'm sure.

I don't really see it working in the current climate. Premium Bonds are dropping to 1% but how much better than this can you get in an instant access account? 1.2%? So you're only gaining 0.2% or so with which to buy your lottery tickets. I'm not sure it's worth the hassle. Also remember that most lotteries have a huge jackpot with relatively few smaller prizes. I suspect the rate of return is a lot worse than Premium Bonds, especially when you ignore the miniscule possibility of winning the jackpot.

You can improve your return in savings by for example putting £1000 in a Virgin Money Current Account and getting a whopping 2.02% interest rate with which to buy your lottery tickets. I still think though that the difference between the rate of return on Premium Bonds and the rate of return on interest accounts is too low. This hasn't always been the case, but I think it is now.

Having said all that I think your idea is worth investigating to see if it returns a better return than Premium Bonds. I'm not going to do the calculation though. It doesn't look like MSE are going to do it either.

Thanks.

It is a complex mathematical problem but one I think is worth considering.

Yes it is more work to manage the process each month, compared to leaving money sitting in NS&I or a savings account, but its no different than all the work people put in to the current account shuffle or stoozing back in the day.

The MSE NS&I calculator says that for a £50,000 savings, the average earnings over the course of a year would be £500. However there is also a 1 in 77k chance of winning a million.

If you instead earned 1% interest that would be £41 per month. What would be the expected return and odds distribution if you used that £41 to buy 20 lottery tickets per month?

We can agree it would be less than the 1% interest rate because the lottery itself is negative expected value, but 'maybe' the odds of winning more than a million would be better than 1 in 77k? We don't know without calculating it.

There is a personal decision to make currently with normal savings vs NS&I, where you're sacrificing a guaranteed rate for participating in a prize pool. The lottery approach might give more variance but that might be something people are willing to do in the current climate where fixed returns are so low anyway.  

eskbanker

danlightbulb said:

@eskbanker I understand what you're saying about negative expected value. However this is why a calculator is needed - because how do you know whether earning 1% in a fixed account, and buying lottery tickets with that 1%, would be better or worse than earning no interest in a premium bonds account but getting the draw entries in lieu? The lottery itself is negative expected value I agree, but you're not playing it with the capital you're playing it with the interest, which itself is positive (say +1%). So it has to be the case that playing the lottery with the interest is also positive (compared to earning no interest at all), the question is is it more or less positive compared to the NS&I in house lottery. That's what needs to be calculated.

But the point is that it doesn't need to be calculated!  The fact that lotteries have a negative expected return means that they can be discounted entirely, leaving a straight comparison between savings interest and PB expected winnings, which is the way MSE shows it.

danlightbulb

It really is a question of variance vs chance of hitting it big.

Fixed savings at 1% - no variance, no chance of hitting it big, no chance of zero returns.
NS&I - some variance, more chance of hitting it big, some chance of zero returns.
Another lottery - high variance, more chance of hitting it big, more chance of zero returns.

But to understand this trade off, we would need to know the full odds of each approach. It's a perfectly legitimate question to ask.

msallen

@danlightbulb I think it is you that has misunderstood eskbanker's point.
The "NS&I in-house lottery" (using you description) returns 100% of the money that is staked in prizes.
All other lotteries return less than 100% of the money that is staked in prizes (many around the 50% mark).
Therefore no complex calculation is required. For the return from your method (on average) to be better than PBs, the interest rate on the non-PB savings would have to more than make up for the difference between 100% payout and the particular lottery's payout rate. So if your lottery returns 50% of the monies raised in prizes and the PB prize fund equates to 1% (after December) then you would need to find an account paying over 2% to do better than PBs

danlightbulb

eskbanker said:

danlightbulb said:

@eskbanker I understand what you're saying about negative expected value. However this is why a calculator is needed - because how do you know whether earning 1% in a fixed account, and buying lottery tickets with that 1%, would be better or worse than earning no interest in a premium bonds account but getting the draw entries in lieu? The lottery itself is negative expected value I agree, but you're not playing it with the capital you're playing it with the interest, which itself is positive (say +1%). So it has to be the case that playing the lottery with the interest is also positive (compared to earning no interest at all), the question is is it more or less positive compared to the NS&I in house lottery. That's what needs to be calculated.

But the point is that it doesn't need to be calculated!  The fact that lotteries have a negative expected return means that they can be discounted entirely, leaving a straight comparison between savings interest and PB expected winnings, which is the way MSE shows it.

Some people might be willing to trade off fixed returns for a bigger chance of hitting it big but at the cost of more variance. In a very low returns environment, this becomes more viable.

But it needs to be calculated to understand the impact on average returns and the odds of hitting the bigger prizes compared to NS&I.

barnstar2077

danlightbulb said:

El_Torro said:

Interesting idea, and one many people have considered, I'm sure.

I don't really see it working in the current climate. Premium Bonds are dropping to 1% but how much better than this can you get in an instant access account? 1.2%? So you're only gaining 0.2% or so with which to buy your lottery tickets. I'm not sure it's worth the hassle. Also remember that most lotteries have a huge jackpot with relatively few smaller prizes. I suspect the rate of return is a lot worse than Premium Bonds, especially when you ignore the miniscule possibility of winning the jackpot.

You can improve your return in savings by for example putting £1000 in a Virgin Money Current Account and getting a whopping 2.02% interest rate with which to buy your lottery tickets. I still think though that the difference between the rate of return on Premium Bonds and the rate of return on interest accounts is too low. This hasn't always been the case, but I think it is now.

Having said all that I think your idea is worth investigating to see if it returns a better return than Premium Bonds. I'm not going to do the calculation though. It doesn't look like MSE are going to do it either.

Thanks.

It is a complex mathematical problem but one I think is worth considering.

Yes it is more work to manage the process each month, compared to leaving money sitting in NS&I or a savings account, but its no different than all the work people put in to the current account shuffle or stoozing back in the day.

The MSE NS&I calculator says that for a £50,000 savings, the average earnings over the course of a year would be £500. However there is also a 1 in 77k chance of winning a million.

If you instead earned 1% interest that would be £41 per month. What would be the expected return and odds distribution if you used that £41 to buy 20 lottery tickets per month?

We can agree it would be less than the 1% interest rate because the lottery itself is negative expected value, but 'maybe' the odds of winning more than a million would be better than 1 in 77k? We don't know without calculating it.

There is a personal decision to make currently with normal savings vs NS&I, where you're sacrificing a guaranteed rate for participating in a prize pool. The lottery approach might give more variance but that might be something people are willing to do in the current climate where fixed returns are so low anyway.  

If the odds of winning a million were better than 1 in 77k wouldn't someone with a million pounds be practically guaranteed to double their money every draw?