Fun with probabilities

Here's a real life application of probability theory. It is similar to the sports betting company business model:

You get an mailing list (email, it is cheaper), and you pick a big football game. You send half the list an advisory that one of the teams will win, and you send the other half an advisory that the other will win, along with the opportunity to subscribe to your newsletter for a low, low price.

To the half of the people that got the correct prediction, you send another letter, picking another big game, and sending half the prediction that one team will win, half the prediction that the other team will win.

People who get two correct predictions in two weeks will be amazed and will be more likely to subscribe to your newsletter.

But you can split that group in half, and send out a third prediction, then split the people who got three weeks in a row right and send out a fourth letter, and so on. You might recycle some of the losers, too, so that some people see that your accuracy is 5 out of 6 weeks and so on.

Imagine getting a letter where the predictions were right five weeks in a row! What is the probability of that? This newsletter must be really good!

Or the newsletter writer knows some probability...