And creates the first legit, private lottery company. The winning numbers, to be published each week, are just as random and unpredictable (if not more) than winning numbers from state lotteries. It can be designed so that the expected gains for participants are far more favorable and more closely aligned with what casinos offer: in short, the odds of winning and multiplying your (say) $20 bet by (say) 10 or 100, can easily be made much higher than in traditional lotteries. It even beats the stock market, if you look at the return over the last 15 years. So how is this possible, when large-scale lotteries are illegal everywhere and punished by many years of prison and gigantic fines?

The explanation is very simple. It also shows why math wizards are great candidates to run such a business. While the winning numbers generated look extremely random, just as random as traditional lottery winning numbers, they are actually produced by extremely rudimentary, short mathematical formulas. Think of the decimals of number Pi: they could be used as winning lottery numbers since they appear incredibly random, yet they can be computed very efficiently. Billions of them have been produced so far, so you could run a lottery for millions of years, just based on Pi’s decimals. Nobody ever managed to prove that Pi’s decimals are random, and it is possibly the biggest mathematical challenge of all times. We even offered a $500,000 award to solve an equally difficult question regarding another famous mathematical number.

So in reality, this lottery business is a disguised math competition, asking you a (say) $20 administrative fee to participate. A math wizard is far more likely to win than other people. You would have to change the word lottery to (say) lotteri in your business name, to avoid litigation, just like some banks called themselves banc rather than bank. Still, you are better off calling it a lotteri rather than a competition, to attract a large number of participants. And disclose the fact that numbers are indeed easily predictable, despite illusion of the contrary. It actually makes this lotteri trustworthy, as the generating formula for the winning numbers (typically a mathematical recurrence relationship) can be shared with authorities — more on this complex issue below, especially on how to do it right. Even better, while state lotteries are a tax on innumeracy, this lotteri promotes mathematical education and interest, especially if run on a large scale, as people know that a trivial mathematical algorithm generates the winning numbers. You disclose the formula and change it every year, to further boost credibility.