What are the odds that NOBODY will win the Powerball jackpot? | KALW

What are the odds that NOBODY will win the Powerball jackpot?

Jan 12, 2016

Powerball says your odds of winning are about 1 in 292.2 million. Where does that come from?

There are 69 white balls – and they don't get replaced when they are drawn – so there are 69 possible balls for the first pick, 68 for the second, 67 for the third, 66 for the fourth, and 66 for the fifth. The odds of your numbers matching the five white balls is the probability of you matching the first ball (1 in 69), multiplied by the probability of matching the second ball (1 in 68), multiplied by your the probability of matching the third ball (1 in 67), and so on.

Since order doesn't matter, your numbers can be any permutation of the balls drawn.

The five balls can be ordered any of five different ways number of ways. (That's 5 factorial, or 5*4*3*2*1.) Multiply that (5 factorial, or 5*4*3*2*1) and you've got 120. This comes from having five balls to pick for the first spot, four for the second spot, three for the third, and so on. There are 120 different potential winning tickets, so the odds of winning increase by a factor of 120.

Then there is the red Powerball, which can be a number from 1 to 26. You need this for the jackpot, so your odds decrease by a factor of 26.

Therefore, your odds of winning are about 1 in 292.2 million.

So what are the odds that NOBODY wins?

The "odds of winning" + "odds of NOT winning" have to equal 1, so your "odds of NOT winning" are 1 - "odds of winning".

Buying an additional ticket decreases your odds of NOT winning by a factor of "1 in 292.2 million". So your "odds of NOT winning with two tickets" is "odds of NOT winning" multiplied by "odds of NOT winning". For three tickets, its "odds of NOT winning" multiplied by "odds of NOT winning" multiplied by "odds of NOT winning".

Stay with me.

The odds of nobody winning can be calculated if we know how many tickets are sold. Powerball reported over $1 billion in ticket sales for this past Saturday's drawing. At $2 a ticket, we can estimate 500 million tickets were sold. The odds of nobody winning is equal to the "odds of NOT winning" multiplied by itself for every ticket sold: 500 million.

The odds that nobody was going to win Saturday's drawing were therefore about 1 in 5.

While it wasn't that improbable that nobody won this weekend, it is improbable that nobody has won after 19 drawings – and that's the reason for the giant jackpot. If you flipped a coin 19 times, the probability of getting tails each time is very low, about 1 in 500,000. But unlike flipping a coin, where getting tails is always 1 in 2, the odds of nobody winning the Powerball has changed with every drawing. Since more people buy tickets as the pot grows, the odds of nobody winning DECREASES with each drawing.

We don't know exactly how many tickets were sold at each of the drawings, which date back to early November, but when the pot isn't huge, not too many tickets are sold, and so the odds that nobody wins is pretty high. When 5 million tickets are sold, the odds of nobody winning is about 49 in 50. That's actually pretty likely.

If these odds stayed the same, it would be likely that after 19 drawings nobody would had won yet. There's about a 70% chance.

But with the growing pot, people have been buying tickets – lots of them – so these odds have changed. We can only guess here, but if 5 million tickets were sold for each of the first 10 drawings, 10 million were sold for the next 5, 100 million for the next 3, and 500 million for the 19th (Saturday's), then the jackpot only had a 5% chance of still being unclaimed today, or 1 in 20.

If 750 million tickets are sold for Wednesday's draw, there is still about a 7% chance that nobody wins, so it won't be a total shock if the prize is still unclaimed. But this also means the jackpot will have made it through 20 draws without being claimed, and this would be a feat -  beating odds of about 1 in 200! 

That's still significantly better odds than YOU winning the jackpot, which is still 1 in 292.2 million.

By the way, even if 100 million tickets were sold at each and every drawing, it wouldn't be until after the 55th drawing without a winner that the odds of NOBODY winning would become as unbelievable as YOU winning the jackpot.

Good luck!