University at Buffalo Statistician Weighs in on Powerball Chances


Expert Pitch

Jeffrey Miecznikowski, associate professor of biostatistics at the University at Buffalo:

“The odds do get better when you buy more tickets, but it is such a small increase that it is really inconsequential relative to the unbelievably small odds of winning. Buying 10 tickets isn’t going to noticeably increase your chances. Your chances are so close to zero that it is such a small increase that it doesn’t really matter. Technically, you are increasing your chances as you buy more tickets, assuming you are getting different numbers, but we are talking about chances that have so many zeros after the decimal point so what you are increasing it by is so inconsequential.”

“Essentially, it is impossible to win. But someone will say, well, Joe Smith of Florida won it, so it wasn’t impossible. There is a principle of rare events called the improbability principle, which means that in the infinite number of events that happen in the world every day, something rare happens a lot. Unbelievably rare things happen every single day. With that in mind, winning this Powerball is essentially impossible, yet someone will win it because they have sold hundreds of millions of lotto tickets and that is enough that someone will win something unbelievably rare. Impossible things happen all the time. I’m confident someone is going to win and in fact, I’m surprised no one has won yet because of the amount of tickets sold so far.”

“Odds of winning a Powerball, buying one ticket, equivalent to flipping a coin 28 times and getting heads every single time. The odds are roughly the same. It doesn’t sound so bad. I can do 28 coin tosses in 5 minutes. But you would be at it for an eternity.”

“Another example, if all of the teams were equally likely to make the Super Bowl, and you get one team out of AFC and one team out of the NFC, you would have to make 7 Super Bowls in a row. That would be the equivalent of winning Powerball. Very roughly, it would be actually winning 6 Super Bowls in a row. That would be slightly rarer than winning Powerball. Caveat is everyone is equally likely to win.”

“One that might really be interesting because it is something everyone does, the NCAA basketball tournament, there your odds of picking every single game is unbelievably rare, your 32 billion times more likely to win Powerball than to pick a perfect bracket. Again, assuming each team equally likely to win every day. It would be a coin flip for every game. “

His advice:

“The machines that pull these things out are air filled drums and the balls are floating around. That is as close to random as we’ve got. But the balls are white with black ink, which adds weight to the ball, which would make it less likely to get sucked out of the top. With that in mind, maybe taking all the numbers that don’t have as much black paint on them, like the 1 or 11 or 111, those might be lighter and might float to the top.”

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