As everyone in America seems to know, the Powerball jackpot has reached new heights, with an estimated annuity prize of $1.5 billion for the drawing on Wednesday, January 13, 2016. A monster jackpot is exactly what Powerball hoped for when it changed its game structure last fall.
Prior to October 2015, Powerball participants selected five unique numbers between 1 and 59, and a separate number -- the Powerball -- between 1 and 35. As I explained in an earlier article, this led to over 175,000,000 possible six-number combinations. The new Powerball playing structure involves picking five unique numbers between 1 and 69, while choosing for the Powerball a number between 1 and 26. The arithmetic of that change is that there are now 292,201,338 possible combinations, resulting in a 1/292,201,338 chance of winning. There are 67 percent more possible combinations, making the Powerball that much less likely to win. That reduced likelihood was calculated to create the current situation -- many consecutive drawings with no winner, leading eventually to a ticket-buying frenzy and an enormous jackpot.
Stories about the massive jackpot include new ways of imagining how small your chances of winning the lottery really are. For example, in this article, we are told that our chances of winning the Powerball jackpot are less than, for example, the chances of dating a supermodel or being elected president of the United States.
Those kinds of illustrations are not particularly helpful, for three reasons:
- The chances are not the same for everyone. No way does every human being have the same chance (1 in 80,000, says someone) of dating a supermodel. As regards election to the presidency, it is hard to argue at this point in history that women have the same probability as men of being elected president, and, sorry, not everyone born in the US has the same chance (or any chance) of being elected president.
- Calculations such as these depend on assumptions that are rarely explicitly stated or understood.
- Most importantly, they don't make a great visual picture.
However, Good Morning America provided a nice visual picture of your chances of winning the jackpot. Stand in the middle of a football field, and toss a dime on the field in any direction. Lead a contestant blindfolded onto the field to take one chance at reaching down and picking up the dime. The contestant's chances, GMA said, were better than the chances of winning the lottery.
Here's one way of looking at this visual that gives us a clear probability to compute. Suppose you covered a football field with dimes by laying them side by side in row after row until you covered the nearly 48,000 square feet of playing surface on the field. Taking the dimensions of a dime and doing the arithmetic, you would need about 16.7 million dimes to accomplish this. One of these dimes is the "Powerball Winning Ticket dime," and if you pick it, you win the Jackpot. Your chance of picking up the winning dime in one try is still 17.5 times better than winning the Powerball jackpot.
Students at James Baldwin School in New York City provided me with the idea for this next illustration. Suppose you had a stack of pennies as high as the tip of the spire on the Empire State Building. You need to choose the "lucky" penny from that 1454 foot high stack of pennies in order to win. If you were to buy 1000 Powerball tickets for Wednesday night's drawing, you would have the same chance of winning the jackpot as you would selecting the lucky penny from the stack. Said another way, 292,201,338 pennies would form 1000 stacks of pennies as high as the tip of the Empire State Building.
It is therefore no surprise that winning tickets happen less frequently. The vast number of people playing guarantee that a winning ticket will eventually occur, but, my friend, it won't be your ticket.