科学美国人60秒:Powerball Lottery Winning Made Inevitable (If Not Easy)

“There’s a story in the book, a story about people who took advantage of the law of inevitability to win the lottery.” That’s mathematician David Hand, talking about his 2014 book The Improbability Principle: Why Coincidences, Miracles and Rare Events Happen Every Day. The law of inevitability comes into play in lottery drawings—some set of numbers will be drawn, so a potential winning combination is inevitable. The key word being potential, as nobody has yet won the multi-state Powerball lottery. Which means that the jackpot for the next drawing, the night of January 13^th, is up to some $1.3 billion. You could buy a ticket and hope. Or, as you may have mused, you could buy every possible set of numbers to inevitably win.

“1992, Virginia State Lottery, the Virginia State Lottery is a 6/44 lottery, you have to choose six numbers out of 44, which means it’s a 1 in 7 million chance that a particular ticket will be the jackpot-winning ticket. Seven million. So if you bought all the tickets it would only cost you $7 million. So they waited until the rollover jackpot had built up to, hadn’t been won, so it built up over several weeks to $27 million. If you manage to spend $7 million and buy all the 7 million tickets you are guaranteed to hold the jackpot winning ticket. But there’s a lot of organization involved in this.  In fact, what happened was they put together a consortium of 2,500 people, each of whom paid $3,000 or thereabouts, so they had $7 million. And then in the few days’ window they had available they ran around buying—trying to buy all the 7 million tickets.”

Trying to buy. Because the consortium only managed to buy 5 million tickets. So winning was not inevitable, their chances were only five out of seven.   

“As it happened, however, they did have the winning ticket, so they were guaranteed winning the jackpot. The organization beforehand, the logistics of running around trying to buy these tickets, the nail-biting looking through the tickets, it’s easier just to get a job.”

So if you’re thinking of getting together a consortium for the Powerball, keep in mind that for this lottery there’s only a one in 292 million chance of winning. And tickets are two bucks a pop. So you and your buddies are going to have to come up with almost $600 million to buy every combo and take advantage of the law of inevitability. And if others pick the same winning numbers and you have to split the winnings you could basically break even or even lose money.

To put the frenzy in perspective, I like to recall the wisdom of statistician Michael Orkin, author of the book What Are the Odds? Chance in Everyday Life. Back in 2001, the Powerball jackpot had reached $295 million and the odds back then were better, only 175 million to one. Orkin told me, “if you have to drive 10 miles to buy a Powerball ticket, you’re 16 times more likely to get killed in a car crash on your way than you are to win.” So if you’re dead set on buying a lottery ticket, at least walk.

—Steve Mirsky

(The above text is a transcript of this podcast)