True randomness is not possible, because the lottery management company must know exactly how many coupons are winning, which is why the game simply cannot be completely random. It must give the impression of randomness, even though it is sort of determined from the very start.
Mohan Srivastava, who lives in Toronto and received education in statistics at the Massachusetts Institute of Technology, broke the code of a scratch lottery - and did that using pure mathematics only. In 2003 he got a number of popular scratch cards as a joke from his colleague. One of them drew his immediate attention.
It was a type of scratch ticket with a set of eight tables on the right side. The tables were identical with those used for playing tic-tac-toe, only tightly filled with numbers. On the left side of the cards, there was a square area named YOUR NUMBER, covered with a layer of latex to scrape. You won, if the numbers from the scratched field in a straight line matched any of the lines from the tables.
So, Srivasatva began to wonder about the pattern used for this lottery. He knew it could not be completely left to chance, since the organizer must keep tight control over the winnings. He assumed coupon numbers had to be generated in such a way that would create the most believable impression of randomness. Yet there had to be something that would disclose the winning card.
At work Mohan deals with quite similar mathematical puzzles: he provides detailed statistical analysis of geological research results for the presence of, e.g., noble metals. His colleagues say that he is simply smarter than most people. And indeed - after just a few hours of contemplation, the statistician managed to discover the bug in the system: the numbers shown on the right side strongly suggested, what was actually hidden under the scratchable coating. The trick turned out to be really simple.
How did he do this? First, Mohan divided all 8 tables into 72 boxes - each containing a number between 1 and 39 (numbers could repeat). Afterwards, he divided all the numbers on the basis of how many times they occurred on the scratch card. He discovered that the numbers which appear only once on the entire coupon are the key to success. And indeed, it turned out that if you find three such numbers in one row in any of the tables - such scratch card will most probably be a winner.
What might come as a surprise, Srivastava, did not used his discovery for their own benefit, but decided to notify the security department at the lottery organization. First they brushed him off, but when he provided proof they took him more than seriously. Maybe he did not win money, but certainly gained worldwide recognition. After all, he did find a crucial bug in a business worth 70 billion $ a year in the U.S. alone.