Lottery Jackpot Odds: What Does “1 in 175 Million” Really Mean?

images-51So you’re determined to play the lottery tonight, despite the overwhelming odds against winning. I know, $600 million is pretty tempting. But by now you’ve heard your chances are 1 in 175 million.

Ronald Wasserstein, the Executive Director of the American Statistical Association, says it’s tough to grasp the smallness of “1 in 175 million” because we never see 175 million distinct objects. Here’s what he writes in a blog for The Huffington Post (it’s a little long, but very interesting):

Imagine 175 million freshly minted one-dollar bills are being delivered to my house near Washington, D.C. One of those dollar bills is specially marked as the “lucky dollar bill.” You get to pick a dollar bill, and if you happen to pick the lucky dollar bill, you win all the dollar bills.

A straightforward mathematical calculation using the dimensions of a dollar bill reveals it will take two semi-trailers to deliver the 175,000,000 dollar bills to my house. Once these arrive, they will have to be unloaded, of course, so you will have a fair chance to pick the lucky dollar bill. So, we will lay them out end to end. How long will that line of dollar bills go?

If we start from my house, we’ll have enough dollar bills to go all the way south to Disney World in Orlando. Then we’ll still have enough to go clear across the country to Disneyland! But, even then, we are not out of dollar bills, so we can go north and make it all the way to Portland, Oregon. Still, we have dollar bills, enough to make it all the way east to Portland, Maine. And, fortunately, we’ll have enough to make it back to my house near DC, completing the loop.

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Do we have any dollars bills left? Yes! We would still have enough dollar bills to go all the way around the loop a second time!

Now imagine that you walk, bike or drive for as long as you want around the double loop, and when you decide to stop, you stoop over and pick up one dollar bill. Your chance of selecting the lucky dollar bill is one in 175 million, the same as your chance of winning the Powerball jackpot!

I have two thoughts here:

  1. I’d put a stop to Wasserstein’s little experiment once those 175 million freshly minted one-dollar bills were delivered to my house. Forget about laying them end-to-end and trying to pick one lucky bill!
  2. Wasserstein predicted what you’re probably thinking right now. “If so-and-so can do it, why can’t I?” Or, “Someone’s going to win it, why not me?” I couldn’t wait to read his answer to that, but it’ll have to wait. “I’ll explain that in a future post,” was his response.

I think playing the lottery comes down to what I read once: “Lottery tickets are about fantasizing, not winning.”

“A Statistician’s View: What Are Your Chances of Winning the Powerball Lottery?”

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