Is it ever worth playing the lottery

FaceHead

I never play the lottery. I'm an economist by profession, so see it as a voluntary form of taxation. However, the most recent Euromillions looks different:

Some rough calculations on the probabilities and the number of people who won the 'match 2 numbers' prize in Friday's EuroMillions, indicates that there were about 42 million tickets sold. At £2.50 a go, that's just under £105m spent, and £115m won. Given that it was a guaranteed jackpot (i.e. no chance of the prize pot 'leaking' into a rollover) the ticket looks like a good - albeit extremely high risk where the most likely outcome is a total loss - investment. An investment where you have an overnight expected value greater than one, in my book, is an 'invest as much as you're happy losing' situation. Agree? 

Clearly the multi-rollover guaranteed jackpot situation is an unusual one, but not unheard of. In such a situation, should we all be rushing out to buy a couple of hundred quids worth of tickets - ideally as part of a mega syndicate to cut the risk?

MX5huggy

I think it would of rolled over if no one had won it? Is the £105m in sales UK only? I play it when it’s over £100m, Just not interested in £14m. 

FaceHead

MX5huggy said:

Is the £105m in sales UK only? I play it when it’s over £100m, Just not interested in £14m. 

You can see the EuroMillions: Friday 04 June 2021 Results (national-lottery.com) number of winners here: 1,836,279, of which 477,672 were UK winners. Given its a 1 in ~22.8 chance of winning this, that gives you 42m tickets across the whole draw. Sales are a bit distorted by the different currencies, so sales will actually be lower than the £105m I've suggested (making it in reality more 'worth it' than I've made out in the OP).

Agree that when it's a regular non-rollover week none of this applies.

MX5huggy said:

I think it would of rolled over if no one had won it? 

I believe I saw in the advertising that if it wasn't won, the prize would be distributed to the next category of winners - they don't just have it roll over for ever. Struggling to find evidence of that after the fact though, as it turned out not to be required. 

Alistair31

Ask some of the big winners

Malthusian

On the face of it you are right, assuming that the rules are indeed as you suggest. However, unlike with the stockmarket (another "gamble" with a positive expected return), it is effectively impossible to diversify away the risk of losing all your money, so it really is a case of not investing more than you can afford to lose.

As an economist you will be aware of the marginal utility of money and why it doesn't make sense to risk money that you can't afford to lose on a bet just because it has a positive expectation of return. If you do wager money you can't afford to lose, the bet will have a positive expected return in £ terms but a negative expected return in utility terms. 

You also have to bear in mind that the expected return becomes negative if you get hooked by the thrill of watching the draw, and think "well, I may as well enter next week, it's only a quid".

eskbanker

FaceHead said:

Some rough calculations on the probabilities and the number of people who won the 'match 2 numbers' prize in Friday's EuroMillions, indicates that there we about 42 million tickets sold. At £2.50 a go, that's just under £105m spent, and £115m won. Given that it was a guaranteed jackpot (i.e. no chance of the prize pot 'leaking' into a rollover) the ticket looks like a good - albeit extremely high risk where the most likely outcome is a total loss - investment. An investment where you have an overnight expected value greater than one, in my book, is an 'invest as much as you're happy losing' situation. Agree?

You don't have an expected value of >1 in any meaningful sense, even if total prizes exceeded ticket sales!  There were 817k UK winners (of >3m altogether) - one won £111.5m and one won £1m and the remaining 817k winners shared just over £3m, for an average return of about £4.  The vast majority obviously won nothing, so don't be swayed by the mean average (that's heavily distorted by just one massive prize) when it's the median return you need to use, which will be £0 for one ticket, although you'd expect more than zero if you bought enough tickets....

[Deleted User]

Yes, it would have been a decent bet with a positive expectation, albeit slender. If the rollover was not capped and the jackpot not won, subsequent weeks would seen financial institutions "weighing on" for an expected bumper ROI. You don't really want to see Euromillions won by Goldman Sachs or Warren Buffett.

There are other methods of slightly tipping the scales in your favour: for example numbers above 31 are less popular because people tend to include birthdays. Discernible patterns reduce returns; when Frankie Dettori went through the card at Ascot, those who had a pound at early prices landed £200,000 while those who took starting price got £25,000 and those who landed the jackpot on the tote (which is a pool on the first six races) and reinvested on the last winner got £200.

At the most prosaic level, don't buy a scratchcard from a depleted roll in a quiet sweetshop:- if the shopkeeper is also an economist, he may have calculated the optimum time for buying up the rest of the cards.

Aretnap

MX5huggy said:
Just not interested in £14m. 

If you ever win £14m by mistake do let me know - I'll be happy to take it off your hands. 

Dazed_and_C0nfused

Aretnap said:

MX5huggy said:
Just not interested in £14m. 

If you ever win £14m by mistake do let me know - I'll be happy to take it off your hands. 

I don't mind sharing 

MX5huggy

Aretnap said:

MX5huggy said:
Just not interested in £14m. 

If you ever win £14m by mistake do let me know - I'll be happy to take it off your hands. 

@Aretnap this has been causing me some anxiety so that’s a weight lifted. 

Billycock

MX5huggy said:

I think it would of rolled over if no one had won it? Is the £105m in sales UK only? I play it when it’s over £100m, Just not interested in £14m. 

Of course you aren't, 
You'd change your forum name to Lamborghinihuggy too.