The coin tossing problem

Imagine an infinite sequence of coin tosses, and suppose you win a penny every time there is a sequence of k heads in a row followed by a tail (in other words, whenever the sequence HHH...HT of k heads occurs, followed by a tail). If k is large then you will not win pennies very often, but you will certainly win some sooner or later.

How many pennies are you likely to win in the first n tosses of the coin?

Solution