One day you get a letter or email from someone you've never heard of, with no return address, saying simply that the Patriots are going to win to the Jets this weekend. You probably don't give it much thought, even after they do. The next week, you get another letter saying that this weekend the Dolphins will beat the Patriots, and again they do. This goes on week after week, with you eventually sitting up and taking notice when the predictions are correct every single week. After ten weeks of correct predictions, you get another letter which says something like this:
Hey, I hope you appreciated all the accurate predictions I've been sending you, and hopefully you put some money down on some of them and made a lot of profit. I've gotten really good at these predictions, so good that I'm barred from betting on games or going to Vegas, but I'm always right, as you saw! I wouldn't ask you to pay me for my predictions, you wouldn't trust that, so that's why I sent them to you without asking for anything. But now that I've proven myself, maybe it wouldn't be too much to ask you to give me 5% of what you've already won. Or if that's too much to ask, how about 5% of what you'll win with the next prediction I give you? That's not asking a lot, is it? Let me know and I'll send you next weekend's picks.Now, how it works. On the first week, the scammer sends out 100,000 messages, half of them predicting a Patriots win, half predicting a Jets win, and keeps track of who got which. When the Jets lose, he throws away the addresses for the 50,000 people who got the wrong prediction, and then he sends out another 50,000 messages predicting the next week's results. Again, he throws away the addresses of the half who got the wrong guess, and now he's down to 25,000. After ten weeks of this, he'll have thrown away more than 99,900 of his original addresses, but the remaining 97 people will have gotten ten accurate predictions in a row, and most of them will be convinced that the scammer is the real deal. They're unlikely to hear from any of the other 99,900 people, so they'll never guess what really happened. Many of them will indeed send money in hopes of getting a few more wins. At that point, the scammer makes off with the cash.
(The same scam works with the stock market and other "games of chance" that happen on regularly scheduled intervals, with a 50/50 chance of a prediction being right, and a chance to make money on it.)
It's delightfully clever, and at the same time, terribly instructive of the problems of anecdotal evidence and the danger of painting the target after firing the arrow. It also shows up the problem so many people have with understanding the unlikely: something that has only a one in a million chance of happening every time you get into your car will probably never happen to you or anyone you know, but at the same time, it will probably happen a dozen times today somewhere in the United States, because even the most unlikely things become inevitable when there are a lot of chances for them to happen.