The math behind this week’s upcoming $1.4 billion Powerball drawing boggles the mind, but at least a few minds were boggled beyond the bounds of arithmetic.
One photo posted to Facebook and Instagram claimed falsely that if the Powerball pot – which was $1.3 billion at the time – were divvied up among the United States’ 300 million residents, each one would get $4.33 million. “Poverty Solved!!” the blackboard graphic read.
https://www.instagram.com/p/BAZxZbwmxLi/?taken-by=livesosa
The photo earned more than 580,000 Facebook likes and more than a million shares. Only problem is, the math is wrong. The payoff per person would actually be $4.33, or a little more than my winnings in Saturday’s $900 million Powerball drawing.
Although the posting that stirred up all the fuss was attributed to a band named Livesosa, all signs point to its origin with an Instagram user known as Esteyban. That user removed the original post and put up a somewhat apologetic graphic instead.
“Trying to solve poverty … while getting killed on social media,” Esteyban wrote. “At least my $4.33 is a start. … With everybody’s 2 cents I can buy a $5 pizza special and give it out.”
Although Powerball won’t solve poverty, it does have appeal for math geeks and lottery junkies. Millions of tickets are being sold in 44 states (including Washington) as well as the District of Columbia, Puerto Rico and the U.S. Virgin islands.
The estimated $1.4 billion for Wednesday’s payout is likely to rise even further over the next couple of days. Potentially big payouts translate into big sales. That’s why the folks behind Powerball made it harder to win the jackpot last October, while making it a bit easier to win the smaller prizes.
Before October, players faced 1-in-175 million odds of taking the big prize. After the rules were tweaked, those odds slimmed to one out of 292 million. Statisticians say that’s analogous to flipping a coin 28 times and getting heads every time.
Here’s the math behind the odds: When five balls are drawn out of a pile of 69, and an additional Powerball is taken from a pile of 26, there are 292,201,338 possible combinations. (The factors behind that are basically 69 x 68 x 67 x 66 x 65, then divided by 120 or 5! for the five balls, then multiplied by 26 for the Powerball pick.)
If you purchase two different $2 picks, you better your odds only slightly. To be absolutely sure of winning the jackpot, you’d have to cover all 292 million combinations. Buying that many tickets by Wednesday night would require a huge, highly organized syndicate.
Let’s suppose you’re able to do it: On the plus side, you’d win bunches of smaller prizes as well as the jackpot. On the minus side, paying the tax significantly diminishes your winnings, and taking the prize as a lump sum to pay off all your minions would reduce the pot even more. There’s also a chance you’d have to share the jackpot with other potential winners, which would deal the death blow to your dreams of clearing a profit.
Will there be a jackpot winner on Wednesday? The chances of that, at least, are favorable. But then, they were also favorable for Saturday’s jackpot-less drawing.
CNN reports that 440 million tickets were sold for Saturday. But wait, you say: If there are only 292 million combinations, how could everybody miss? Here’s how: Many of those combinations were duplicates.
Once again, statistics can shed light. Based on sales of 440 million tickets, the probability that at least one ticket will hit a 1-out-of-292 million pick is roughly 77 percent. That means there was about a 1-in-4 chance that Saturday’s jackpot drawing would have come up empty. That’s pretty much like flipping two coins and having both of them come up tails.
That probability assumes that the players’ number selections are truly random. Chances are that there was even more duplication of picks, due to the fact that many people choose numbers from a smaller pool of birthdates and other “lucky numbers.”
Now, if Wednesday’s drawing strikes out as well, that would be like flipping four or five tails in a row. Then we’ll really have something to talk about.
This report has been updated to account for the “birthday bias” in number selection.
