‘Why is it,’ asks the mathematician John Allen Paulos in his book about the pitfalls of innumeracy, ‘that a lottery ticket with the numbers 2 13 17 20 29 36 is for most people far preferable to one with the numbers 1 2 3 4 5 6?’ It is not an easy question to answer. All lotteries, after all, rely on a recognition by those who participate in them that the winning numbers are chosen at random, if only so that the participants can feel that their numbers have as good a chance of coming up as any others. People need to know it is random, because random translates as ‘fair’. However, all lotteries also rely on their participants having a sense that some sequences of numbers are more likely to come up than others. Once it is seen that all sequences have precisely the same chance of coming up as 1 2 3 4 5 6, the whole business of participation starts to look a lot less attractive. So participants fall back on, and are encouraged to fall back on, a belief that random-looking sequences are more likely to be chosen at random than sequences that look familiar. This belief is a delusion, but it is a peculiarly powerful one – even a probability theorist would have to be feeling fairly tough-minded to select, as an example of six numbers chosen at random, the second of Paulos’s sequences in preference to the first.

If the question Paulos asks is puzzling, what are we to make of the fact that, according to Camelot, organisers of Britain’s National Lottery, the most popular sequence of numbers chosen by its participants (or ‘players’, as their jargon would have it) is 1 2 3 4 5 6, which appears on over ten thousand tickets every week? This is truly baffling. It does not mean that 1 2 3 4 5 6 is preferred by most people to random-looking sequences – ten thousand is still only a tiny proportion of the total tickets sold. It does mean that 1 2 3 4 5 6 is much preferred to any given random-looking sequence, including the one given by Paulos. Are we to suppose that there is a small but committed band of hyper-realists out there, resolved to respect the laws of chance at all costs? If so, they are behaving in a very irrational manner. The National Lottery, as we all know, operates on a pool system, with the jackpot shared every week among all the winning ticket-holders. When 1 2 3 4 5 6 finally does come up (as it is likely to do sometime in the next 250,000 years or so), the winners will receive, at current values, between £1000 and £4000 each. The truth is that there can be no rational explanation for this sort of behaviour. If ten thousand players each week are choosing to spend their money in this way, it is simply further evidence of the mesmeric hold the Lottery has managed to exert. People are being mesmerised by numbers.

For example, what is the difference between these two randomly generated sequences, 7 17 23 32 38 42 and 12 15 26 44 46 49? The answer, perhaps surprisingly, is £17,280,000. The first sequence represents the numbers that dropped out of Camelot’s glorified tumble-drier (remember: random is fair) on the occasion of their second ever roll-over draw, on 15 January last year. The numbers were matched by 133 winners, each of whom received around £122,000. The second sequence is the one chosen for the third roll-over on 10 June. It was matched on only one ticket, the holder of which received £17.4 million. There is no statistical explanation for this discrepancy. On an average week, the jackpot should be shared between three or four tickets (there are around 14 million possible combinations of numbers and around 50 million tickets are sold). The reason for the huge number of winners on 15 January 1995, and the reason there have been many more weeks than was first expected with no winners at all, is that most players have a very clear idea of the sort of sequence that ought to win. It ought to be neat without looking too familiar, the little marks spread ‘randomly’ across the page – a couple of lowish numbers, a couple of medium numbers, a couple of highish numbers. This belief is no different from the belief of those who seem to feel that the winning sequence should look both neat and familiar (1 2 3 4 5 6). The intention is to increase the chance of winning; the result is that the chances of winning the entire jackpot are greatly reduced. The only rational strategy to adopt when playing the Lottery is to wait for a roll-over (i.e. until the jackpot gets above £14 million), then choose a sequence that is unlikely to be chosen by anyone else (say, 32 33 35 36 37 39). However, the fact that some sequences are more likely to be chosen than others suggests that ‘choice’ is perhaps too strong a word for what most people are doing. In effect, their numbers are choosing themselves.

Then again, what is the difference between £122,000 and £17,400,000? The answer, of course, is a great deal of money, but what do these figures actually mean? When the jackpot was rolled-over for two weeks running for the first time last month, it was estimated that 90 per cent of the adult population bought tickets for the £42 million top prize. How many of us could say what difference would be made to our lives by winning £42 million rather than £24 million (the previous week’s total) or £10 million (the week before that)? As Martin Amis has pointed out in another context, though it is hard to say what difference would be made by having £40 million rather than £20 million at one’s disposal, it is easy enough to see that the difference is a cool £20 million. When the total reached £42 million, a few churchmen decided that enough was enough, and called the sum ‘obscene’. Could they say why £42 million is obscene, rather than £24 million, or £10 million, or even £122,000?

Or again, what is the difference between these two sequences: 14 24 33 38 42 47 and 14 17 22 24 42 47? The answer, in this case, is life and death. The first sequence represents the numbers played every week by Tim O’Brien and Steve Sumner until O’Brien’s death last June. The second sequence is the one that came up the night before he died. O’Brien had forgotten to renew his ticket and, believing he had deprived himself and Sumner of their share of the jackpot (a share worth around £2 million), he committed suicide the next day. The sequences, however, do not match. Indeed, it is hard to see how anyone could think that they did match. All that they have in common (apart from the four numbers that they share) is a random ‘look’. That seems to have been enough for the wretched Mr O’Brien, along with a sense of the enormity of what he had missed out on. In fact, by failing to renew his ticket, he had deprived himself and his friend of £54, the prize for matching four numbers out of six.

When this incident was first reported, it was widely believed to be just the sort of publicity that Camelot could do without. Don’t you believe it. This is the sort of story on which the success of the Lottery depends. What would you do if the numbers you played every week – ‘your numbers’ – came up and you discovered you had forgotten to renew your ticket? Camelot wants its players to feel that particular sequences are theirs (irrespective of the other people who might think them theirs as well), and that having found a sequence they are bound to play it week after week. This is the theme of much of their advertising, particularly over last summer, when we were all reminded not to get caught abroad, out of the reach of their machines, during the week that it could have been us. It is also the theme of much of the coverage the Lottery gets in the tabloids, where it receives huge amounts of free publicity, almost all of it favourable. The stories that run are the stories of the near-misses – the pensioner who mistook one of his numbers and missed out on the jackpot, the woman who passed the 7.30 p.m. deadline as her ticket was being processed, thereby depriving herself of more than £8 million. This is how the O’Brien story was covered at first, as simply the most extreme example of ‘There but for the grace of God go all of us.’ When it turned out to be a tragedy of a more mundane kind – ‘a meaningless waste of life’, in the words of the coroner – interest rapidly waned.

The most powerful weapon Camelot has at its disposal is the feeling we all have that certain numbers belong to us. Most tickets bought for the Lottery feature random-looking sequences; but most of these numbers will have a special significance for those who have chosen them. This has much less to do with choice than with compulsion. After all, if we don’t stake a claim to what belongs to us, who will? It is not necessarily an idle question. In last year’s Hollywood comedy It Could Happen to You, Nicolas Cage and wife Rosie Perez win $4 million on the New York State Lottery. He falls for a waitress, the couple divorce, she sues him for his share of the winnings, claiming that although he bought the ticket, they were her numbers, the numbers she always chose – her birthday, their wedding anniversary and so on. In court, however, it turns out that he has always mistaken the date of their anniversary, and that it was only because he went for the 18th rather than the 19th that they won at all. So she takes the stand, and with a tear in her eye, tells the jury of the night before the draw, when she dreamt that she had arrived in church a day early for her wedding, only to find her long-dead father waiting there alone, intoning words of warning. She wins the case.

This is America, and only a movie. But it touches on something that is true of all lotteries everywhere, including our own. Without superstition, without self-delusion, they are nothing. All the choices we make in relation to the Lottery – the decision to play each week, the amount we spend each week, the numbers we choose each week – are attempts to unravel fate, to find the key to a particular kind of destiny. When the BBC’s astrologer, Mystic Meg, makes her predictions on a Saturday evening, who can truthfully claim they do not feel something as she hints that your initials, or your star sign, or your town are favoured tonight? (I know I can’t.) Analyse that feeling, and you will recognise it as the impulse that drove you to buy a ticket in the first place. Then you lose, and the feeling dissipates in a cloud of disgust until it is time to make another false decision. Unless, that is, you win, in which case every feeling of destiny, every inkling you had that fate was somewhere within reach, is suddenly confirmed. Each winner has some story to tell about why it had to be them, and these are the only stories we hear, just as the only predictive dreams we hear about are the ones that come true. How else could the jury in the movie decide to whom a random sequence of numbers belonged, except by trying to decide who told the best story about them?

Whenever it is pointed out to Camelot that their operation is managing to sustain itself, is indeed thriving, on a diet of ignorance, superstition and fear, the response is always the same: their job is to raise as much money as they can for the ‘good causes’. The insinuating advertising, the mind-boggling jackpots, all the relentless yet selective publicity is said to be justified by the amount it helps to raise for these causes. But this is no justification at all. No means of raising revenue can be justified simply by pointing to the amount of money raised for some or other cause unless that cause is unequivocally good. And if the cause is unequivocally good, then any means of raising the revenue is justified. Thus if it is true that the Millennium Commission must be provided with funds at all costs, then the Lottery can hardly be the single best way of doing it; better, surely, to legalise crack cocaine, advertise its benefits, then place a prohibitive tax on its consumption. If, on the other hand, it is true that the cause embodied by the Millennium Commission is only a relative good, something more needs to be said about what that good is relative to: that is, something needs to be said about the merit of the cause relative to the method employed to raise the money to support it.

Unfortunately, in the case of a lottery like ours it is uniquely difficult to discern any relation at all between the cause in which the money is to be spent and the methods employed to raise it. Alone among government sources of income, the money raised by the Lottery is set aside to further the moral life of the nation, as it might be called, in some broad or classical sense (the sense in which artistic and athletic achievements are considered also as moral ones). However, alone among government sources of income, the money to pay for these improvements is raised by fostering ignorance, superstition and fear. This is not to say that the Lottery does not also give rise to considerable amounts of pleasure (reflecting on the prospect of instant wealth is undeniably pleasurable). But feelings of pleasure are irrelevant in this context (compare crack cocaine). The fact is that the Lottery seeks to generate the income needed to improve our lives by seeking to introduce into them false hopes and false choices. This is why those critics of the Lottery who have described it as a ‘tax on stupidity’ are both mis-stating and understating the case. To call it a tax on stupidity is to imply that the state has resolved to make money out of a necessary evil, as it makes money out of cigarettes or leaded petrol. Yet in truth, by introducing the Lottery the state is treating stupidity not as an evil but as a valuable commodity, the production of which may be encouraged in order to increase revenue, as though stupidity were a good in its own right. There is no attempt here, as there is in the case of cigarettes, to balance the amount of money raised against the merits of the behaviour which allows the money to be raised. The behaviour is being brought about with the sole aim of raising as much money as possible.

The incongruity of this situation is simply added to by Camelot’s attempts to defend itself. Most of the responsibility for the running of the National Lottery has been placed in the hands of a private company, with obligations to its shareholders – and in this, it is unique among lotteries. It is only natural that Camelot should seek to justify its activities in the language of the market – the language of choice and efficiency. But choice and efficiency have no meaning here. After all, nothing is being created by the Lottery, nor is any recognisable service being offered; wealth is simply being redistributed: extracted from some in order to be spent by others. ‘Efficient redistribution’ is a meaningless concept unless some sense can be made of the act of redistribution itself. No one would claim that there is any meaning to be found in the redistribution that takes place between the losing ticket-holders and the winners. Yet if we look to the other kind of redistribution effected by the Lottery, the only constant seems to be the money itself. At one end of the operation, the object is to find the lowest common denominator; at the other end, to find the highest. Mystic Meg and Jeremy Isaacs are the two sides of what is literally the same coin – it is up to her to help raise the money, and up to him to help spend it. And this suggests an obvious question: if it takes Mystic Meg to raise the money, why should it be Jeremy Isaacs who gets to spend it?

This is a basic moral issue. It does not mean that no other issues are raised by the Lottery, some of them moral (the relation between levels of participation and levels of poverty), some of them not (its impact on our spending habits in general). Nor does it mean that we have to be prepared to make independent moral judgments about one or other side of the coin. One does not have to agree with Richard Dawkins that Mystic Meg should be jailed for fraud to wonder whether she is really the person on whom the state should rely for the funding of the arts. One does not have to agree with Terry Dicks MP that the Royal Opera House should receive not a penny of public money to wonder whether it is right to fund its operations through the exploitation of ignorance, superstition and fear.

Moreover, it is quite possible for the same person or group of people to feel the pull of astrology and numerology while still appreciating the value of opera. Defenders of the Lottery often accuse its critics of patronising the public by assuming that the sort of people who buy lottery tickets are not the sort of people who support the causes on which the money is being spent. But though this is far from being necessarily true, nothing about the Lottery encourages us to believe that it is false either. All we have is a system, which finds money to pay for a series of good causes by deceiving the people who will be paying for them. As a result, all the patronising is being done by the organisers of the Lottery itself – the real choices about how the money is to be spent are being made in the name of an institution which has nothing to offer the public but a series of false ones.

If the Lottery is to be justified at all, these false choices must be set alongside some that are real, so that some genuine connection can be established between the funds raised and the method used to raise them. There are two ways in which this might be done. One is to allow participants a choice of projects or causes for which to buy tickets, as they once had when participating in the smaller lotteries organised by particular charities and clubs. If this means that the Lottery becomes a smaller and less efficient operation, so be it. The other means of introducing real choice is to allow participants in the Lottery (i.e. almost all of us) a direct say in how it is run. If we do not wish to see a private company profiting from the licence they have been given to exploit our weaknesses (and all the evidence suggests that we do not), then they should not profit from it. If we want Richard Branson and his non-profit making consortium, then we should have them. Efficiency is simply not an issue here. This control would have to extend to the bodies who decide how the money is to be spent. If the Government wishes to appoint the members of the Millennium Commission, then its activities should be funded out of more conventional forms of taxation, concerning which we at least had the semblance of a choice at the last election. If it is to be funded out of what is nothing but a form of deception, then we must be allowed to elect its members ourselves. And if the result is that the money is spent on re-opening hospitals that have been closed, or on buying back the sports events that have been sold to Rupert Murdoch, or on organising the kind of party that would drive Prince Charles to despair, then so be it. You cannot treat people like idiots while claiming to act in their best interests, unless complete idiots is what you take them to be. There is no justification for a national lottery like the one we have got.

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Vol. 18 No. 6 · 21 March 1996

In his antic and meticulously-observed spoof of a puritan coming up to barking point over the National Lottery, David Runciman says that the popularity of the combination 1 2 3 4 5 6 is ‘truly baffling’ (LRB, 22 February). Since the Lottery started I have bought three tickets. The first two times I went for 1 2 3 4 5 6 as I thought that this was the combination least likely to be chosen by others, and that it would maximise my expected return by minimising the chance of my having to share any winnings. I then discovered that many other people reason as I had, and that 1 2 3 4 5 6 is consequently the most popular choice. I didn’t use it for my third ticket. David Runciman makes the same point when he says that one should ‘choose a sequence that is unlikely to be chosen by anyone else’. A Brazilian friend once told me that there is a non-random South American lottery based entirely on this principle. The winning tickets each week are the ones bearing that week’s least popular choices of numbers. This introduces a subtle, entertaining and competitive element of second-guessing into the game that perhaps Camelot should bear in mind. In the meantime I have adopted a strategy that guarantees a lottery win every week: I have decided to buy some shares in Camelot’s holding companies.

Adrian Bowyer
University of Bath

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