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, at every occurrence of the sequence HHH...HT of k heads 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?
