I love lotteries.
Not because they are a smart way to fund schools, are a good investment or have a smart payout scheme. They are none of those things. But lotteries do make people care about probability.
And with the Powerball jackpot hitting an advertised value of $500 million for the drawing Wednesday night, people are talking about probability again. So, what are the chances at least one person wins? Let’s see what the data has to say (last year I looked at the relationship between advertised jackpot and participation).
Given the size of a jackpot, we can estimate how many tickets will be sold, based on historical data.
And given the turnout, we can estimate the probability of a winner. The chances of at least one winner Wednesday night are really good.
A $500 million advertised Powerball jackpot typically means about 191.7 million tickets will be sold, based on a polynomial regression. Given that level of turnout, we’d anticipate a 67 percent chance of at least one winner.
Keep in mind, a $500 million prize is unusually high, which means we have less data and a more uncertain forecast. I, for one, am psyched to see what the ticket-sale numbers are for this drawing, if only to get a better grasp of the characteristics of higher jackpots.
So, even if — after taxes and split jackpots — the lottery is not a great investment idea, it’s always fun to watch millions of people talk about probability on at least one day of the year, right?