If you watch television or get mail, you have probably seen the commericals or received the letter from Publishers Clearing House. This time it’s for a contest to win $10,000 a week for life. All you have to do is return the envelope with a completely and correctly filled-out entry form. My parents and Leah’s parents sometimes returned those forms. And why not? After all, it just costs a First Class stamp.

When we received our entry in the mail, I looked through its contents. Making sure the entry is complete is not as easy as it seems. You have to make sure every sticker is put in the right place on the entry form. Those stickers seem to be distributed throughout the contents of the envelope, and I counted more than 30 separate pieces of paper in the envelope.

Hidden in the depths of those papers was one titled “Sweeepstakes Facts.” Does anyone read that? I did. It says that the estimated odds of winning the “Up to $10,000 A-Week-For-Life” is 1 in 1,700,000,000. That’s one in 1.7 billion. Back not quite two years ago I wrote a post about the Megamillions lottery and scoffed at the idea that any individual player could expect to win at the absurdly overwhelming odds of one in 259 million. And here, this contest has odds of one in 1.7 billion.

It’s very hard to get any kind of intuitive understanding of just how ridiculously bad the Publishers Clearninghouse odds are. These odds are so high that it’s pretty clear to me that Publishers Clearinghouse has absolutely no intention of ever awarding the grand prize. There is not even a guarantee that the prize will be awarded, which, if you think about it, makes perfect sense. They almost certainly don’t print and distribute 1.7 billion entry forms, so they might not even print the winning number on any form. Of course,  they do offer a $1,000,000 prize to be awarded from a random drawing of all eligible entries if (when) no one wins the grand prize. It appears that at least that prize will be awarded.

Still, should you enter the contest? As I said, all it will cost to enter, other than a few minutes of your time, is a First Class stamp worth 49 cents.

Well, let’s answer that question. In the gambling world there is a concept called expected return. It is calculated by multiplying the prize amount by the probability of winning that prize. So, if a prize is $100 and the odds of winning are one in a thousand, the expected return is $100 multipled by 0.001 (or divided by 1000). That’s 10 cents. So, if the entry costs more than 10 cents, you should expect to lose money on the entry. Sometimes the Megamillions jackpot is high enough that the expected return on a one-dollar entry approaches, or in some cases exceeds, a dollar. That might seem like a reasonable contest to enter. Most of the time the expected return is more like 10 cents.

How does the Publishers Clearinghouse prize stack up in terms of expected return? Well, someone who is 65 today will on average live about another 20 years. (What! You mean I only have 20 more years to live? Damn! I’d better get busy living!) So, at $10,000 a week, that would mean $520,000 a year, or $10,400,000 over a lifetime. Take that sum and divide by 1.7 billion and you get about 0.6 cents. That six-tenths of a penny expected return on a 49-cent entry cost — not counting the waste of extremely valuable and limited time spent filling out the form.

So, is the Publishers Clearinghouse contest worth entering? No. It’s barely worth even the time it takes to throw the entry form into the trash can.