Ref: 98/201 21 December 1998

Southampton scientists reveal how Lottery players choose their numbers

Using techniques normally applied to the study of large numbers of atoms, a group of Southampton scientists has conducted an analysis of the numbers chosen by lottery prize winners to assess how players make their selections. While there is no scientific way of predicting the actual winning numbers in advance, their study has shown that by choosing unpopular sets of numbers, players could significantly increase their chances of not having to share the jackpot if they did win.

Dr Simon Cox and Dr Denis Nicole of the Department of Electronics and Computer Science, together with Dr Geoff Daniell of the Department of Physics and Astronomy, combined ideas from statistical physics and the power of a supercomputer to discover patterns in the way we fill in our lottery tickets.

Using a concept called entropy they have shown that players prefer certain numbers; for example, seven, the most popular number, is chosen 25 per cent more often than 46, the least popular.

Dr Cox explains: `There is no scientific way of predicting the winning numbers in advance but choosing unpopular sets of numbers increases one’s return in the long term because any winnings are shared with fewer other players. Of course the lottery organisers know how often we pick different numbers and for foreign lotteries this data is sometimes released. The popularity of the number seven, for example, is well known. In the UK, however, this information is not released, but by using entropy we have been able to show the patterns in the numbers of winners.’

He adds: `While the discoveries about the lottery have thrown up some interesting facets of human behaviour, they are not in themselves important. The major significance of the work is seen when it is applied to other important situations in patterns of illness or disease, or in investor behaviour. There the "maximum entropy" technique can help deduce information buried in data.’

The team’s analysis is published in the December issue of the *Journal of
the Royal Statistical Society*. They explain that there are 13,983,816
different possible ways to fill in a lottery ticket, and that on average each
combination of numbers is chosen by about five people, with the result that, on
average, there are five jackpot winners. Their computer calculations revealed
differences in number selections ranging from tickets with an unpopular set of
numbers, which are only bought once every couple of draws, to a popular ticket
with over 50 buyers per draw.

However, anyone using the technique in the hope of winning the jackpot would have to realize that the figures the team have produced only reflect what is expected to happen after millions of years of choosing a particular set of numbers!

A summary of the research team’s findings:

The team estimated the popularity of each of the 13,983,816 tickets and deduced from this certain patterns in the players’ choices of numbers. These showed that lottery players tend to select numbers towards the centre and top of the lottery ticket.

The remarkable draw on 14 November 1995 when there were 133 jackpot winners is a clear example of the effects the team had deduced. The winning numbers were 7, 17, 23, 32, 38, 42 and 48 which all lie in the second and third columns of the ticket and were hence picked by lots of players.

Numbers greater than 31 are chosen less often, probably because players use birthday dates for their numbers. Picking numbers on the edges and lower part of the ticket will usually increase the size of any prizes that are won. There is also evidence that players prefer not to choose consecutive numbers, for example 31 with 32, or pairs of numbers greater than 31, such as 44 with 46.

Using the information about popular and unpopular tickets has allowed the team to determine which tickets to choose to avoid sharing the higher prizes. Choosing a ticket at random produces a long term return of 45p in the pound, this being the amount returned in prizes after money for good causes, tax and profits has been deducted. For a very unpopular combination of numbers like 26, 34, 44, 46, 47, 49 the return can be raised to about 95p in the pound. Unfortunately, although it is possible to double one's long term winnings this is not enough to make a profit in the UK lottery at present.

These figures are all long term winnings and only reflect what is expected to happen after millions of years when the particular choice of numbers has won the jackpot many times. This is hardly relevant to the ordinary punter. On the other hand a syndicate or national tabloid buying around 75,000 tickets a week since the lottery started would have actually won £10.3m using the maximum entropy method compared with £6.9m buying random tickets. Unfortunately they would have had to spend £15.3m buying the tickets!

The technique of `entropy’ that the team employed is used by physicists as a way of making predictions while `keeping an open mind.’ A typical question concerns how fast the gas molecules in the atmosphere are moving; are they all moving with the same speed or is there a range of speeds? We know no reasons to pick out any particular speed so the `completely open mind’ answer would be that all speeds are equally likely. In fact there are fewer very fast or slow molecules because the total energy of all the molecules is fixed by the temperature of the gas.

By analogy, in the absence of any data at all, we would assume that lottery players are equally likely to choose any ticket. However, the large fluctuations in the numbers of lottery prize winners which we observe from draw to draw implies that some tickets have to be more popular and some less popular.

Notes for editors:

The research is published in, S.J.Cox, G.J.Daniell and D.A.Nicole, "Using Maximum Entropy to Double One's Expected Winnings in the UK National Lottery", J.R.Statist.Soc.D 47, 1998, 629-641.

The large computations required were performed on a parallel commodity cluster of Alpha based PCs running Windows NT built by the team.

For further information:

Dr Simon Cox, Department of Electronics and Computer Science, University of Southampton (01703) 593116; email sc@ecs.soton.ac.uk

Sarah Watts, Public Affairs, University of Southampton (01703) 593807