The largest-ever jackpot drawing for the Powerball lottery will take place Saturday, with a reported $800 million advertised jackpot. That means three things: First, there’s an estimated 77 percent chance that someone wins it; second, that we’re going to learn a ton of new things about how the lottery works; and third, that the effort by the group behind the lottery — The Multi-State Lottery Association — to drive jackpots higher by adjusting the odds is already an unmitigated success.
First, the estimate. I’ve developed a model that estimates turnout for the Powerball lottery based on the advertised jackpot. Right now, by plugging $800 million into the model, we’d estimate 428 million tickets sold. Based on that data and the probability of a given ticket winning, there’s a 77 percent chance that, based on historical turnout, there’s at least one winner.
But there’s a catch! Since this is the first time we’ve had a jackpot this large,1 that estimate is based on an extrapolation of previous data. We really don’t know, however, how lotteries behave at these levels. So there’s a solid possibility that my estimate is off, which brings us to the second point.
For lotto geeks like me, this is probably the most exciting lottery drawing in recent history! We’re going to get a ton of new data — namely, how many tickets get sold when a lottery jackpot is this high — that previously we could only extrapolate. Does the growth stay exponential? Are we underestimating or overestimating turnout? This might mean I’ll have to substantially recalibrate the model based on the new data, which is really cool. It’s the lottery equivalent of the New Horizons mission to Pluto: We’re going to get new data we’d only dreamed of, and even if that means we have to re-evaluate existing theories, it’s still very exciting.
The best-case scenario for me is that no one wins. This either means the model is right and we happen to have been in the 23 percent of cases where there isn’t a winner, or the model is dead wrong! Either way, the result is we might get that billion-dollar American lottery, and it would give us even more data about how Powerball behaves at the upper bound. There’s only a small chance this happens, but I’d be lying if I said I wasn’t kind of hoping for it.
Lastly, from the point of view of state revenue, this totally justifies the October change that lowered the odds of winning from 1 in 175 million to 1 in 292 million. (You are vastly more likely to get struck by lightning twice in your lifetime.) Lotteries are more profitable for their constituent states when jackpots are high, and Powerball wanted to drive jackpots higher. Only a few months after Powerball messed with the odds, that’s what’s happened.
Anyway, if yours is one of those 428 million tickets sold, I wish you the very best of luck. I hope all of you lose.
CORRECTION (Jan. 8, 7:15 p.m.): An earlier version of this article misstated the probability that there will be a winner for the $800 million advertised jackpot. It is 77 percent, not 91 percent. Thanks to a Twitter reader named Adam B. for flagging the error.