Recently I was discussing hitting streaks with my dad and I said "If you flip a coin a million time you're bound to get a streak of a hundred." I am not sure if this is actually true and I am having some trouble figuring it out. The more general question that I would like to be able to answer is what is the probability that you will get a streak of k heads when you flip a coin n times? I found this article "http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2005/lecture-notes/l24_spcl_topics.pdf" [Broken] It explaines how to solve this however it requires k base cases. For k=100, this method is kind of useless. Can anyone think of a good way to solve this for large k and n? PS. Using a computer is certainly okay.