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By Root 629 0

case a New Jersey woman won her state lottery twice in four months in 1985–6. It was widely reported that the chances of this happening was 1 in 17 trillion. However, though 1 in 17 trillion was the correct chance of buying a single lottery ticket in both lotteries and scooping the jackpot on both occasions, this did not mean that the chances of someone, somewhere winning two lotteries was just as unlikely. In fact, it is pretty likely. Stephen Samuels and George McCabe of Purdue University calculated that over a seven-year period the odds of a lottery double-win in the United States are better than evens. Even over a four-month period, the odds of a double winner somewhere in the country are better than 1 in 30. Persi Diaconis and Frederick Mosteller call this the law of very large numbers: ‘With a large enough sample, any outrageous thing is apt to happen.’

Mathematically speaking, lotteries are by far the worst type of legal bet. Even the most miserly slot machine has a payback percentage of about 85 percent. By comparison, the UK National Lottery has a payback percentage of approximately 50 percent. Lotteries offer no risk to the organizers since the prize money is just the takings redistributed. Or, in the case of the National Lottery, half of the takings, redistributed.

In rare instances, however, lotteries can be the best bet around. This is the case when, due to ‘rollover’ jackpots, the prize money has grown to become larger than the cost of buying every possible combination of numbers. In these instances, since you are covering all outcomes, you can be assured of having the winning combination. The risk here is only that there might be other people who also have the winning combination – in which case you will have to share the first prize with them. The buy-every-combination approach, however, relies on an ability to do just that – which is a significant theoretical and logistical challenge.

The UK lottery is a 6/49 lottery, which means that for each ticket the punter must select 6 numbers out of 49. There are about 14 million possible combinations. How do you list these combinations in such a way that each combination is listed exactly once, avoiding duplications? In the early 1960s, Stefan Mandel, a Romanian economist, asked himself the same question about the smaller Romanian lottery. The answer is not straightforward. Mandel cracked it, however, after spending several years on the problem and won the Romanian lottery in 1964. (In fact, in this case he did not buy every combination, since that would have cost him too much money. He used a supplementary method called ‘condensing’ that guarantees that at least 5 of the 6 numbers are correct. Usually getting 5 numbers means winning second prize, but he was lucky and won first prize first time.) The algorithm that Mandel had written out to decide which combinations to buy covered 8000 foolscap sheets. Shortly afterwards, he emigrated to Israel and then to Australia.

While in Melbourne, Mandel founded an international betting syndicate, raising enough money from its members to ensure that, if he wanted to buy every single combination in a lottery, then he could. He surveyed the world’s lotteries for rollover jackpots that were more than three times the cost of every combination. In 1992 he identified the Virginia state lottery – a lottery with seven million combinations, each costing $1 a ticket – whose jackpot had reached almost $28 million. Mandel got to work. He printed out coupons in Australia, filled them in by computer so that they covered the seven million combinations, and then flew the coupons to the UShad w won the first prize and 135,000 secondary prizes too.

The Virginia lottery was Mandel’s largest jackpot, bringing his tally since leaving Romania to 13 lottery wins. The US Internal Revenue Service, the FBI and the CIA all looked into the syndicate’s Virginia lottery win, but could prove no wrongdoing. There is nothing illegal about buying up every combination, even though it sounds like a scam. Mandel has now retired from betting on lotteries