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Lotto changes tonight - Many a mickle maks a muckle

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October 5th, 2013


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02:32 pm - Lotto changes tonight
Probably the least interesting of the world's games with which I am obsessed is the UK's own national lottery game, "Lotto". Players choose six numbers from 1 to 49 and aim to match at least three of the six winning numbers; ideally all six for a share of the jackpot, but there is a bonus prize for matching five out of the six and the bonus ball. There are some moderately large changes to Lotto, starting with this evening's draw.

What are the main changes?
  • The entry fee is increasing from £1 to £2 per play.
  • The (theoretically not quite) guaranteed prize for matching three numbers is more than doubling from £10 to £25.
  • The prizes for matching all six numbers and four of the six numbers are expected to increase, but not quite double.
  • The prizes for matching five out of the six numbers, with or without the bonus ball, are expected to fall.
  • There will be an additional raffle in each draw, which will see at least fifty tickets per draw selected to win £20,000 each. Rollover draws will have more than fifty winners.
Are your chances of winning improving?

Not so you'd notice. Technically: yes, but only very marginally, as a result of the introduction of the raffle.

Do the changes make the game more generous?

Er.... probably, a bit, but it depends what you count? The truth is disappointingly opaque and a little complicated. On the other hand, I probably wouldn't be posting if this had an easy answer. You can find the old structure in context courtesy of the Internet Archive's Wayback Machine, but here's the summary:


In general, 45% of sales revenue were intended to be returned as prizes in that draw - and the "intended" part relates to the possibility of the jackpot rolling over - but another 5% of sales revenue was returned as additional prizes in occasional Super Draws and used to juice scratchcard prize payments.

You can find the new structure here, for the Wayback Machine has not got around to archiving it yet, but here's the summary:


...and it's a looooooooooot longer.

Now a great deal of the increased length was due to being specific about the prize capping procedures, which always existed as part of the terms and conditions, but are only likely to be required once every, ooh, few centuries or so.
(Suppose the winning numbers turn out to be 1, 2, 3, 4, 5 and 6, which are no less likely to happen than any other set of six, though still pretty damn unlikely. Apparently the jackpot will need to be split tens of thousands of ways - maybe 30,000 - and the other prizes are likely to be so small as to need capping as well. The historic prize values point to a couple of draws where the 4-match prizes got pretty low; on the other hand, isn't it interesting to see how strong the 4- and 5- match prizes were in the very early draws, when the "people playing their birth dates" phenomenon was at its strongest?)
However, that's a distraction. The headline figure is that it used to be the case that 45% of sales revenue was intended to be returned as the Prize Fund for that draw and 47½% of sales revenue is now intended to be returned as the Prize Fund for that draw, just under 42½% by the lottery draw and just over 5% by the raffle. That's an increase, so more generous, right? Er...

So it's true that 47½% of sales revenue goes into the Prize Fund, but not all of the 5% of sales revenue that is earmarked for the raffle prizes has to go to raffle prizes that draw. Under normal circumstances there will be fifty £20,000 prizes, which will require £1,000,000. However, when there are rollovers, there will be more than fifty £20,000 prizes; £2 million will be required to fund the raffle prizes for a single rollover, £3 million for a double and so on up to £5 million for (the maximal) quadruple rollover. The 5% of sales revenue earmarked for the raffle prizes might fund that draw's raffle prizes exactly; if not, the excess will be saved to cover later shortfalls, or the shortfall will be covered by previous excesses. An excess of excesses might be used to top up lottery draw prizes, as has long been the tradition with Super Draws. (The lower the sales figures are, the more challenging it will be to pay out all the raffle prizes - and, worse still, the lower the sales figures are, the higher the likely of rollovers which makes the issue more challenging still.)

So it's still not possible to say the proportion of sales revenue that will be distributed in prizes on any particular draw in advance because of these uncertainties. On the other hand, this represents no change; it was not officially announced what proportion of sales revenue was returned as prize money in lottery draws, accounting for the Super Draw fund. Richard Lloyd's excellent lottery site estimated that about one sixth of the Super Draw fund was used for Super Draws and the rest went to scratchcards, which would point to the long-term average return being close to 46%. If the long-term average return under the new schedule really does trend towards 47½%, then I think it is reasonable to conclude that the new schedule is a fraction more generous. (It also provides an indication of an effective cap for the proportion of lottery draw sales going towards scratchcard prizes going forwards.)

There might have to be another Freedom of Information request to get the people who might be expected to know to check my working.

Hmm. So why have these changes been made?

It's probably fair to note that the price of a lottery ticket has always been £1 since the game's start in 1994, and £1 then is worth around £1.69 now. (70% inflation over 20 years? Strikes me as fairly low.) On the other hand, I thought £1 was a pretty aggressively high price at the time when the game started. As a point of reference, I know three sandwich shops within walking distance of work where you can still get a mighty good sandwich for £1.

I have three theories:

1) Any publicity is good publicity

This change has not attracted positive comment. Lotto sales figures have been falling for years. Making an unpopular change and then changing back within reasonably short order might be the shot in the arm to attract attention. (On the other hand, it didn't really work for Coca-Cola.) I reckon there is at least a 10% chance that the raffle element will be removed by the end of 2015. They might or might not wind the price increase back, too.

2) Profit

I suspect that the reason why these changes have not proved popular is partly the increase in price and partly because it will be awfully fiddly to check whether your ticket has won the raffle or not. (Checking against one winning number is fine, checking against fifty is... laborious. It's possible to get ticket sellers to check for you, but I think people will think it's rather lame in practice. You don't often see people getting their tickets checked - people think it just holds up the queues - and I don't think people will get into the habit.) Consequently, I think a lot of raffle prizes will end up going unclaimed, and I suspect that this may not be accidental.

Now it's not the case that Camelot get to keep these unclaimed prizes; prizes unclaimed after 180 days go to the good causes along with the statutory 28% of sales revenue. On the other hand, Camelot are only permitted, by the terms of their licence to operate the national lottery, to keep profit according to how much money is generated for good causes - the more they generate for good causes, the more profit they can keep. That said, if sales suffer as a result of the changes, it's hard to see this route for diverting more money to good causes making up the difference.

3) Perhaps they're right

There's always the outside possibility that Camelot might actually have got things right and know things that we don't...

I'd be prepared to believe that Camelot have done their research and found that players can't get excited about winning a few thousand pounds these days and that £20,000 is the lowest sum which starts to excite people. It's roughly the price of a top-end family car, or a deposit on a house. TV producers may also have some useful input into current trends in mass psychology in this regard. It's not as if there hasn't been a reasonably consistent undertone of "there are too few big winners and the big prize is too big", so this seems like an obvious response to it.

If this is the case, then going from maybe a jackpot winner or two and a handful of winners of 5+bonus per week to at least a couple of thousand winners of £20k per year might actually prove popular; the chance of you knowing someone who has had such a pleasant, but not overwhelming, win will go right up. It might be hard to get excited about winning £20,000 and sharing it as part of even a small syndicate, though.

Tonight's draw, as the first of the new format, has a guaranteed £10,000,000 jackpot and a guaranteed thousand £20,000 winners. Is it worth playing?

Depends on how many players there are.

Let the number of players be p, each paying £2 to play. Total sales revenue is 2p.

Of this 2p, 42.47% goes into the prize fund for the lottery draw, or 0.8494p, and 5.03% goes into the prize fund for the raffle, or 0.106p.

Let us assume that on average 246820 / 13983816 (source) of the tickets match exactly three numbers. Each of these wins £25 (and we're considering returns rather than net profits here). Thus the sum paid out as match 3 prizes is 25 * 246820 / 13983816 * p, or approximately 0.4413p. This leaves 0.4081p to pay the match-4 and higher prizes. Of this, 66.4% goes to the match-6 prize, thus the expected jackpot will be 0.2710p. We know the jackpot is guaranteed to be £10 million, so the sum added to the jackpot is 10,000,000-0.2710p. We also know that there are 1,000 prizes of £20,000 in the raffle.

We would expect the sum to be paid out through the lottery draw to be 0.8494p+10,000,000-0.2710p and we know that the sum paid out through the raffle will be 20,000,000 regardless of the number of players. Then the total sum paid out can be expected to be 0.8494p+30,000,000-0.271p or 30,000,000 + 0.5784p. The lottery will pay out more than its sales revenue if 30,000,000 + 0.5784p exceeds 2p, or if 30,000,000 exceeds 1.4216p. We can expect there to be more paid out in this draw as prizes than taken in ticket revenue if there are fewer than roughly 21,100,000 tickets sold.

So how many tickets will be sold?

Now that's the interesting question. Let us look at Richard K. Lloyd's sales figures page. The general trend is that Saturday draws were getting about 26 million tickets sold - slightly more during rollovers, but they don't make anything like the difference that they used to.

Reasons why sales might fall include, but are not limited to:
  • Some people have said they'll stop playing now the tickets have gone up from £1 to £2;
  • Other people have said that they'll transfer from playing Lotto to playing EuroMillions for the same reasons;
  • Other people have said that they'll cut the number of tickets they buy in half;
  • Tickets have only been on sale for this particular draw on Thursday, Friday and Saturday, rather than the whole week as usual, which I reckon may be a huge factor;
  • Multi-draw tickets have only been sold up to and including the last £1/ticket draw, so anyone wanting to put a multi-draw ticket on has had to do so in the last two days likewise.
However, there are many people who will have not registered the price change at all, many people who are so attached to their numbers that they will keep playing no matter the price and other people who don't normally play but might be attracted by all the added money this week. (The added money strikes me as being a huge factor, but there's only been one draw in the last 18 months with over 32 million tickets sold, so I don't think it's going to have as much of an effect as might appear to be the case.)

Perhaps the most telling indication is Camelot's own estimate quoted above that Wednesday draws might be expected to have 9 million Lotto entries and Saturday draws might be expected to have 16 million Lotto entries. Putting it all together, I reckon that there will be 22 million sales for tonight's draw, but am no more confident than estimating a range of 16 million to 28 million sales. Another way of looking at it is that I expect the number of drop-outs, cut-downs and (most significantly) those who intend to play but don't get around to it to exceed the number who don't normally play but choose to do so for tonight only.

So will you be playing tonight?

I haven't decided. I wouldn't go so far as to say that this Lotto draw is a good one to play, but - at the very least - it is rather less bad than usual.

Please redirect any comments here, using OpenID or (identified, ideally) anonymous posting; there are comment count unavailable comments to the post already. Thank you!

 


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