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February 7th, 2004


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10:26 pm - Wotta Lotta Notta Lotta Lotto
Remarkably little fanfare about the National Lottery's new Euro Millions game, whose tickets went on sale today and whose first draw takes place on Friday. As the name suggests, the main gimmick is that the game is played across Europe: to begin with, only the UK, Spain and France are taking part, but more nations are expected to join in later.

The intention is to produce a game which will catch the public's attention like the Powerball and Mega Millions have done in the US; extremely large jackpots are to be created by requiring people to hit both separately-drawn halves of the jackpot combination. However, whereas Powerball is a 5-from-53 plus 1-from-42 game (giving a 1-in-120,556,770 chance of the jackpot and a 1-in-36.06 chance of any return) and Mega Millions is a 5-from-52 plus 1-from-another-52 game (giving a 1-in-135,145,920 chance of the jackpot and a 1-in-43-ish chance of any return), EuroMillions is a 5-from-50 plus 2-from-9 game. (One ball better!) This works out at a 1-in-76,275,360 chance of the pot of jack; minimum requirement to get any sort of return is three balls split over the two draws (3+0, 2+1 and 1+2 all win) giving an overall chance of winning of about 1 in 24.

This is pretty complicated as lotteries go. Accordingly, it gives you twelve ways to win, compared to the multi-state US lotteries' nine; all twelve pay out prizes pari-mutuel, all twelve have different odds against and different estimated prizes. The official numbers - and, indeed, the official Game Procedures - aren't on the National Lottery site yet, which I think is A Bit Naughty, but this unofficial page has all the figures. Remind me to rant about that site and its maintainer at some point; for now, I will restrict myself to commenting that he gets "x to 1" and "1 in x" confused. He also has obi-wan errors for the figures compared to the official draw even if you do take his figures as "1 in" rather than "to 1", but I'm happy to accept that this is just because Camelot always round to make the odds look more favourable whereas this site need not do so.

It's also worth pointing out at this point how the money division actually works. This game pays out 50% of sales in prizes; in the UK, 28% goes to good causes, 12% to the government, 5% to the retailer and 5% as operating costs. (The operator, Camelot, claims that the 40% of government and good-cause funding is "a higher proportion of lottery revenue back to society than any other lottery in the world", which seems a bold claim, but potentially a credible one. Certainly the proportion of 5% of sales spent on administration seems quite low compared to, say, Mega Millions' 10%. (I have no other figures from around the world, but would be interested to see some - eg Garret, Thomas A. (2001) "An International Comparison and Analysis of lotteries and the Distribution of lottery Expenditures" in International Review of Applied Economics, 15, pp. 213-227.) 50% of sales as prizes is reasonably standard.

However, the interesting part is the way the 50% of prize money is distributed. In the Powerball, that 50% is split 29% jackpot, 21% non-jackpot. In the UK National Lottery, the 50% prize money is split roughly 17% jackpot, 33% non-jackpot (a simplification; a fixed £10 prize is paid for the 3-matches, taking about 19% of the 50%, with the remaining 31% being split strictly 52-48 jackpot-not). A well-placed phone call suggests that the EuroMillions game will split its 50% prize money in the ratio of 10% jackpot, 40% not-jackpot. That's really a remarkably weedy jackpot proportion and beefy non-jackpot proportion. (Incidentally, the existence of potential SuperDraws where prize money is shifted from some draws to others artificially rather than through rollover means muddies the waters, but I have ignored them.)

There's politics at work here. In fact, it's only the jackpot game which is international; the non-jackpot games are run on a national level. So, xenophobic tabloid reader, only 10% of your stake is at risk of going into the pockets of Johnny Foreigner; 40% will be returned as lesser prizes to Brits, 40% to Great British Society and 10% to retailers and administration. This will, as a downside, mean that payouts for the lower prizes may vary very widely from country to country, though the jackpot prize is truly international.

One complication is that the French and Spanish lotteries are played in € throughout, whereas the UK remains firmly attached to the pound sterling. This leads to the entertaining consequence whereby the Euro price of the lottery is fixed (at €2) but the sterling price may vary as the pound strengthens and weakens against the euro. Currently, €2 costs £1.39, but the initial Euro Millions lottery price has been set at £1.50 per play. This price can vary, though, with four weeks notice; I would expect a reduction from £1.50 to £1.40 fairly soon. You cannot play this game for more than four weeks in advance as a consequence; no subscription feature as available for at least the main draw.

As the non-jackpot prizes are divided on a national level, the fact that UK players are paying more for their tickets than European ones has the consequence that the non-jackpot prizes in the UK are likely to be (£1.50/€2) times as high as European ones - about 7% bigger, at the moment. Someone somewhere will have a fit that 15p per UK ticket is going into the jackpot as opposed to 20c (about 13.9p) per Euro ticket, but, hey, deal with it. In compensation, to the best of my knowledge, the UK prizes are all going to be free of income tax and all paid as a single lump sum, rather than any of your annuity nonsense.

The interesting question is whether the draw will take off or not. UK main draw lottery sales figures have been dropping by about 5% per year as a result of the proliferation of lottery games. Typical sales figures peaked at just under 70,000,000 per draw in late 1996; the introduction of the second weekly draw on Wednesdays saw the Saturday draw figures erode to under 60,000,000 tickets per week a year later and the comparative figure is now well under 40,000,000 tickets per week. (Wednesday draw figures started at about 28,000,000 per Wednesday and have fallen to under 21,000,000 per Wednesday.)

This is generally thought to have been due to the introduction of other draws and games, which haven't been terribly popular, either. The first such game to be introduced was the fixed-odds Thunderball draw, which started at over 5,000,000 entries per Saturday but soon settled down at about 4,500,000 entries per Saturday, not fluctuating much, and the introduction of Wednesday Thunderball did little to change it. (Caveat: Thunderball sales figures have no longer been published since Saturday 12th July onwards.)

The next game to be introduced was Lottery Extra, later Lotto Extra, played for a jackpot only where multiple rollovers to large jackpots are the normal. Sales patterns for this have always been extremely streaky, with little peaks as each Extra jackpot grows, but Saturday figures of over a million sales were commonplace throughout 2001 when the correspondig figure today is about 650,000. (Interestingly, the Wednesday figures are reasonably close to the Saturday ones for Lotto Extra, suggesting that a very large proportion of people playing Extra are those who habitually play every single game that the National Lottery offers.)

There are a few other dots on the horizon too. Scratchcard figures have fallen; the fixed-odds Daily Play has about 12,000 cash winners and about 20,000 free-ticket winners daily, suggesting about 250,000 tickets sold per day. HotPicks is a fixed-odds numbers betting game derived from the main Lottery draws which attracts 2-3 million tickets per Saturday and 1-2 million tickets per Wednesday. Easy Play, the football scores game, saw its takeup fall from a million tickets per week in its first two months to about 300,000 per week in months seven and eight, and this was quietly dropped after 39 weeks. Even the annual Big Draw, later renamed Christmas Millionaire Maker, started by selling 16,000,000 £5 tickets per year for its 1999-2000 debut but has sunk to about 5,000,000 per annual drawing ever since.

So that's the sort of background we're aiming at. I reckon there is a hardcore audience of between 250,000 and 500,000 tickets per week from people who will play every single National Lottery game. However, given the extra cost of the ticket and the fact that further lottery games still are to be introduced in the near future, turning that hardcore into - say - a million UK tickets per week a year down the line will be a tough sell. The fact that the main Lottery, Lottery Extra and Thunderball draws have a high-profile show on the BBC weekly and the Euro Millions draw has five minutes on Sky on a Friday night can't help, either.

The other consequence of this lottery being small is that it may frequently fail to find a single UK ticket who hits the 1-in-3.6-million 5+0 prize (estimated at about £70,000), let alone the 1-in-5.4-million 5+1 prize (estimated at about £320,000), leaving the 1-in-76,000,000 jackpot very well alone. Of course this will just mean that the smaller non-jackpot prizes are disproportionately larger than planned, but having larger "smaller prizes" isn't particularly exciting; winning £20 instead of £14 isn't going to change your life. If this is a high-profile failure - and I'm really counting on the game to be more popular in Europhile, lotteryphile France and Spain than it will be here - then there is perhaps a 30% chance that UK sales figures will drop to under 400,000 tickets per week in a year's time, which is the sort of level which would cast doubt on the continued viability of UK participation.

However, there will be a big jackpot to shoot at, and it's this jackpot which the game is pinning its hopes upon. We are told that it will start with four £10,000,000 Super Draws; even guessing very optimistically at 2, 4, 6 and 8 million UK tickets respectively, and plucking wild figures out of 5, 6, 7 and 8 million tickets for each of France and Spain, there's perhaps a 85% chance of the first jackpot rolling over, a 80% chance of the second, a 75% chance of the third and a 70% chance of the fourth. If I understand correctly, a £40,000,000 jackpot will certainly be enough to catch people's attention. (Perhaps I misunderstand "four £10,000,000 SuperDraws" - perhaps the first four jackpots will each be seeded with £10,000,000? That would make more sense in the slightly longer term.)

Nevertheless, I still think that a realistic estimate of early-2004 sales figures and an optimistic estimate of late-2004 sales figures is likely to be about one million per week in the UK and seven million per week across Europe, which will be about enough for the jackpot to grow by about a million pounds per week until it gets hit. Perhaps the National Lottery's estimate that a typical jackpot will be about £14,000,000 isn't so unreasonable, just that this jackpot will only be paid out about four or five times per year.

That said, I suspect that the prospect for the game in the longer term is, in contrast, reasonably bright. Unless the European Lottery is trumped by a Global Lottery - which seems unlikely, not least while Powerball and Mega Millions rage against each other in the US - it's probably a matter of time before most of the EU nations are part of it. I can see this being a particular success in the newer EU members, where a €2 entry fee is probably quite high-end and exciting compared to their domestic games. This is only likely to lead to higher figures Europe-wide and a lottery game which grows, rather than shrinks, over time. I would have thought that by 2010, the game might attract 3,000,000 UK tickets per week and 20,000,000 to 30,000,000 tickets Europe-wide, which will give a jackpot every couple of weeks and a £50,000,000 hasn't-been-hit-for-two-months jackpot once every year or two.

Will I play the game? Hmm. All the National Lottery games offer 50% stake return (well, 45% + Superdraws) as prizes and 40% stake return to society, so there's just a small utility gap to find in terms of additional prizes, SuperDraws, rollovers and the like. Pretty much like the rest of the world, I'm likely to play the first game for novelty purposes and then thereafter only when the jackpot gets spectacularly high. Obvious question: define "spectacularly high".

Let me (inaccurately, but not unreasonably so) assume I get 0.5 tickets of utility from the prize distribution of spending 1 ticket stake, plus 0.35 tickets of utility from the 0.4 tickets which is given to good causes and the government. I thus need the sum rolled over to offer 0.15 tickets of utility. As there is a 1-in-76-million chance of me hitting the jackpot, and an expectation based on my projected ticket figures that the average number of jackpot winners per jackpot won will be no greater than 1.2, I need the rollover to be at least 76,000,000*1.2*0.15 tickets - about 14 million tickets, or about 21 million pounds. Thus it becomes good value for me to play when the jackpot reaches about £23,000,000 or so. (The figures change slightly when the ticket price changes.) As sums go, that is fairly inarguably reasonably spectacularly high.

In conclusion, I hold out hope for a good pan-European lottery, but fear that this may not be it. :-) One cheerful sign is that the Spanish portion is handled by Loterias y Apuestas del Estado who run the €2,500,000,000 Spanish El Gordo each year. As discussed, the success of that game is mostly due to historical and cultural anomaly, but we need Euro Millions to work as a step in the right direction if we're ever going to get the €10,000,000,000 Euro Gordo!
Current Mood: hungryhungry
Current Music: earworm: old "National Lottery Live" draw show theme tune

(1 comment | Leave a comment)

Comments:


From:daweaver
Date:February 8th, 2004 10:57 am (UTC)

Dis utility business

(Link)
I seem to recall distracting myself from Finals revision in summer 95 by working out what it would take for me to buy a) one ticket, and b) multiple tickets.

[digs through old diaries]

Ah yes. One ticket required a jackpot fund of £11.6 million, with an additional ticket for each £13 million in the fund. Effectively, one ticket per rollover.

I've not updated the calculation since, as I've boycotted the game since 1996 following The Lottery Corp's decision to site the Millennium Experience in London, and not near Birmingham. However, showing my working now:

I'm taking 0.35 tickets of entertainment from the potential prizes short of the jackpot, plus 0.2 tickets of goodness from the donation to Gordon and The Lottery Corp. So I need the jackpot to offer a further 0.45 tickets of utility. For the sake of my sanity, there is a 1-in-14-million chance of hitting the jackpot, and an expectation that the average number of jackpot winners per jackpot won will be 2. So the jackpot needs to be at least 14,000,000*2*.45 = £12.6 million to play once. These days, that requires a double rollover.

To buy a second main draw ticket, I'm deriving slightly less entertainment from the minor prizes, and slightly less goodness from charity donations, so assume the jackpot must cater for half the value of the ticket. The required addition to the jackpot needs to be 14M*2*.5 = 14 million.

There is one complicating factor: the almost unlimited Lottery Extra draw. When does it become viable to buy one of these, given that I must buy a main draw ticket? Well, there are no smaller prizes, so no small prize utility, but I do get the full jackpot utility from the main draw ticket. We can consider three outline cases:

Wed draw, jackpot £3m, contributes about .11 of a ticket, leaving 1.16 tickets from Extra.
Sat draw, jackpot £6m, contributes about .22 of a ticket, leaving 1.05.
Rollover, jackpot £10m, contributes about .36 of a ticket, leaving 0.91.

It's still one in 14 million to win the pot, I reckon it'll be split 1.25 ways, so the required jackpots are:

We: 14M*1.25*1.16 = 20.3 million
Sa: 14M*1.25*1.05 = 18.375 million
Ro: 14M*1.25*.91 = 15.925 million

A double rollover will (I reckon) tend toward an £18m jackpot, leaving at least 0.18 utility tickets lying around, so given a double rollover, consider buying an Extra at

R2: 14M*1.25*1.09 = 19.075 million.

We can, perhaps, deduct a million from these figures when Gopherman is presenting the draw show, and add a similar amount when it's Eamonn Howheonair.

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