I’m sure you’ve seen the photos of many of those many delighted lottery winners! Yes, they do exist.

As we all know, though, winning the Powerball requires a lot of luck. For every smiling winner there are millions of people with nothing to show for their money.

How much luck does it take to win the lottery? According to this Powerball site, the odds of picking all six two-digit numbers correctly is one chance in 146,107,962. This is bleak, but how bleak? Some state lotteries show you how to do the mathematics, but I doubt that this complicated math can counteract the heavy advertising done by the lotteries–advertising that takes advantage of widespread innumeracy. How can the small chance of winning the lottery be conveyed in a visual and understandable way?

I decided to use plain M&M’s (not peanut) and a football field for my thought experiment. I didn’t really do this demonstration, but you could. If you’d like to do it, just go out and buy 146,107,962 M&M’s. Instead of actually buying the M&M’s, I used mathematics.

I decided to allow all six lottery numbers to serve as the coordinates for ONE M&M in a big pile of M&M’s. I started by wondering whether 146,107,962 M&M’s might cover a football field (the field between the goal lines, not including the end zones). A football field, between the goal lines measure 300 ft long x 160 feet wide = 48,000 square feet. That equals 6,912,000 square inches. Based on my experiments with M&M’s at home, I found that 17 M&M’s will cover about 3 square inches. 146,107,962 M&M’s would thus completely cover three football fields, from goal line to goal line.

So . . . here’s the proposition. Assume that ONE M&M was painted silver and mixed into the M&M’s that covered 3 adjacent football fields that had been completely covered with M&M’s. Then assume that a lottery company allowed you to pay $1 to walk out into those 3 huge fields blindfolded to pick up only one M&M with a tweezer–the silver one. Would you do it, or would you rather keep your dollar? Or how about this option: would you scoop up one liter of M&M’s (enough to fill about one quart, which you could do by scooping up a bit more than a square foot) for $549?

BTW, I refered to this site to determine how many M&M’s there are in a specific volume. It turns out that one liter (which is a little more than a quart) of M&M’s is about 1098 M&M’s.

This thought experiment helped me to understand the low odds of winning the lottery, but I’m curious. Would this visual have the power to cure anyone else of the urge to spend their hard-earned money on the lottery? Could this serve as an “anti-lottery ad”?

If none of this cures you of the urge to play the lottery, consider this: coming into large sums of money will only temporarily change your happiness level.