$1.5B Powerball Frenzy: The Odds and where the money goes

*First post since my move to New York
Src: Getty Images

Src: Getty Images

At the time of writing this post, the nation is on a lottery frenzy. I see queues in many locations, people frantically trying to buy their last chance to riches, before tonight's draw (13/1). No one has picked all 6 numbers (more to it later) since the Multi State lottery association changed the odds in October'15. And the jackpot has rolled over, ever since, rising to an incredible $1.5 Billion, making it the largest ever in the United States.

I wrote a long and technical post a few years back on estimating the odds of winning a lottery. Before the draw happens tonight, thought it would be fun to revisit this again here.

Rules of winning the big prize are pretty easy. 5 white balls are picked at random from a drum that holds 69 balls (numbered from 1 to 69), and 1 red ball is picked from a second drum with 26 balls (1-26). You win when you have all 5 white numbers in any order, and the red. When you win, you can chose a lump cash sum (tax liable) or an 5% growth annuity over the next 29 years. Each ticket costs $2 and ticket sales usually stop an hour before the draw. 

Besides the jackpot, you can also win an amount ranging from $4 to $1 million, depending on number of matches you can get. And the powerball site courteously lists all the prizes and the odds of winning.

 It's pretty easy to calculate the odds. The total possible combinations of the 6 numbers are C(69,5) x C(26,1). You can use WolframAlpha to instantly get the results ~292 Million, 201 thousand. Hence, the odds of winning the jackpot for each ticket is 1 in 292 Million. And even if you win, the 35-40% tax will limit your dreams of becoming an overnight billionaire.

That was some fun with elementary math. Let's talk about where the money goes.
According to the poweball website, this multi-state lottery is a non-profit association, profits of which are used for state legislative projects. In NY for instance, 60% of proceeds go to winners, and ~30% is used to fund state education programs. This varies from state to sate.

That doesn't sound that bad right? Gamblers funding state education programs!

I wish it was that easy to conclude. My main gripe with the entire program is that even though it's voluntary, a typical lottery buyer is a low income individual/household, who is funneling a significant share of their savings into lotto. Which feels like a regressive tax and not an optimal way to reallocate wealth in a society. My feelings aside, let's see if there is a winner tonight who walks home with this huge jackpot!

 

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