Winning the Lotto by the Melbourne Method

 

On February 15, 1992 a syndicate held the single winning ticket for the Jackpot of the Virginia Lottery, worth US $27 million. The syndicate was headed by Romanian-born Melburnian Stefan Mandel, who had previously won thirteen lottery jackpots. How incredibly lucky!

Of course, the explanation has nothing to do with luck. Rather, Mandel and his associates would simply buy tickets covering all possible combinations, thereby guaranteeing they held a winning ticket. Obviously, this strategy can only make sense if the jackpot is large, so that the combined prizes will hopefully exceed the cost of all those tickets.  However, even when the jackpot is huge the strategy is still a gamble, since there is always the chance of having to share the jackpot with winners outside the syndicate. So, what is called for is a really, really huge jackpot, with as few participants as possible. The Virginia Jackpot in 1992 was the State’s largest up to that point, making it a perfect target for Mandel.

Despite Mandel’s expertise, things almost went wrong. The Virginia lottery required the picking of 6 numbers out of 44, meaning the syndicate had to fill out and purchase a total of 7,059,052 individual tickets.  The 35 people assigned this enormous task managed to buy around five million tickets, but this still left much more of a gamble than Mandel had planned upon. On this occasion, fortune favoured the brave.

What made the Virginia lottery a logistical nightmare was the fact that each combination had to be covered with an individual entry. By contrast, many lotteries offer system tickets, covering numerous combinations with the one entry. For example, this Saturday’s Tattslotto requires you to pick six numbers out of 45, and a System 8 ticket allows you to choose eight numbers: this one ticket costs $18.30 and gives you all 28 six-number combinations from these eight numbers. Or, for those who prefer a slightly larger flutter, there is the System 20 ticket, covering 38,760 combinations and costing a mere $25,349.05.

When available, system tickets streamlined Mandel’s operation, but even then there remained some very tricky mathematics. For example, if we were to apply Mandel’s strategy to Tattslotto then we would buy System 20 tickets to cover all six-number combinations. But how many tickets would we need? No one knows!

There are 8,145,060 combinations in Tattslotto, and so the arithmetic says we need at least 211 System 20 tickets. But in fact we will need more: in trying to cover all combinations, our System 20 tickets will unavoidably overlap.

However, Mandel didn’t require the very best mathematical solution, as long as his method didn’t involve too much overlap. Indeed, he succeeded so well that many lotteries responded with rules to counter such schemes. Not that syndicates in themselves lower the profits for the lottery owners, but apparently the regular suckers – sorry, participants – were becoming annoyed.

You can also apply Mandel’s idea in trying for smaller prizes. For example, suppose you want to choose enough tickets in Tattslotto to guarantee having three of the six numbers: including the supplementary numbers, that gives you a good shot at a smaller prize. Again, the mathematics is difficult, and no one knows the minimum number of tickets required to achieve this. However, it is known how to choose 154 tickets that suffice, for a cost of about $100.

But what’s the point of such small-prize hunting? It doesn’t make much sense outlaying $90 in an attempt to win a prize of about $50; in the long run, you can still only expect to get back about 60% of what you gamble, just like everyone else. And, these 154 choices are no magic ticket to winning larger prizes. It’s all pretty silly. Nonetheless, there are hucksters – sorry, businessmen – selling such schemes, and there are suckers – sorry, participants – buying them.

And finally, what became of Mandel? His story ends sadly. The Virginian authorities, who were not at all pleased with Mandel’s coup, launched an inquiry involving all manner of American and Australian law enforcement. Although no wrongdoing could be proven (since obviously there was none), the US tax department imposed a 30% tax upon the syndicate, claiming their winnings amounted to professional income. Eventually the members of the syndicate fell out, and in 1995 our hero Mandel was declared bankrupt.

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator. 

Marty Ross is a mathematical nomad. His hobby is smashing calculators with a hammer.

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