Roll up for the great rollover

As punters dream of a jackpot, William Hartston looks at the odds on pulling off a lottery coup

Forty million pounds eh? That must be worth a small flutter. The renewed outbreak of lottery fever this week, thanks to the double rollover and promise of the biggest jackpot ever, shows that our nation of gamblers has again fallen for the lure of a gigantic crock of gold. Now there are reports of syndicates mounting military-style operations to buy all 14 million combinations of numbers to ensure they scoop the jackpot.

It has been done in other countries. It's just a question of waiting until the prize becomes big enough, backing every possible combination, and you cannot fail to win. A reporter from the Daily Star even claimed to have had Barings Bank thinking for half an hour over his request for a pounds 14m loan to finance his sure-fire lottery coup. Yet Barings was quite right to turn him down. Considerably less than half-an-hour's thought is needed to realise that the gamble is still a bad one, even if you could find an army of friendly local newsagents with the time to process 14 million lottery tickets for you.

The problem is that you will probably have to share the top prize with other winners - more other winners than is financially comfortable. In an average week on the lottery, 65 million tickets are sold. With only 13,983,816 different ways of picking six numbers from 49, each combination will be subscribed an average of 4.6 times, which is therefore the average number of people expected to have to share the dividend. This week, however, we are told to expect sales of 115 million tickets, which works out at an average of more than eight to each possible combination. And pounds 40m shared among eight is a measly 5 million quid each.

Ah yes, but it's not only the top prize we'll win, is it? Our 14 million tickets will reap plenty of other dividends, too. All the other dividends, in fact. We'll win six prizes of five numbers plus the bonus, and thousands of the lower dividends.

But all that still does not add up to your investment. Of the pounds 115m spent on tickets, half goes into prizes. Of that half, 52 per cent is earmarked for the jackpot, which leaves a return on investment of just 24 per cent from the non-jackpot prizes. So your total return is your pounds 5m share of the top prize, plus 24 per cent of your pounds 13,983,816 investment - which adds up to less than pounds 8.4m.

That figure may be boosted a little by the guaranteed pounds 10 prizes that are independent of the number of tickets sold, but your syndicate still stands to make a considerable loss. And that's not counting the tax bill: since you have eliminated all risk from the flutter, the Inland Revenue might decide to treat your prize as investment income.

Similar coups have been successful in Australian and American state lotteries, and in Ireland - but all of these locations have considerably fewer overall ticket sales, and thus less likelihood of having to share the jackpot with too many other punters.

There is, however, one strategy that guarantees lottery success. A very clear pattern has emerged in the number of people sharing the jackpot each week. The largest numbers of winners occur when the six numbers are well spread. The weeks when nobody wins at all have been those where two or three of the winning numbers have been close together. The first ever rollover had 29 and 30, the next had 21, 22, 25, the third had 41, 42, 44 and so on. People aren't betting on birthdays, or numbers with sevens in them as was originally claimed. They are betting on superficial randomness. So all you have to do is buy your tickets only in rollover weeks, when the jackpot is sure to be more than pounds 20m, and select a batch of closely grouped numbers. Every 14 million weeks or so, you will win pounds 20m and will not have to share it with anyone.

Since you will also have picked up around pounds 3.5m in smaller prizes, it all adds up to a 68 per cent return on your investment. The only trouble is that if you buy just one ticket a week, it would take half a million years before you could expect to move into profit.

But if 100,000 of us were to get together in a syndicate and bet on all the unpopular, closely grouped combinations, we'd make a killing by the turn of the millennium. Unless, of course, somebody else had the same idea.