Something very unfortunate has happened: several things I have recently written that could have been blog entries are instead answers on math.SE! In the interest of exposition beyond the Q&A format I am going to “rescue” one of these answers. It is an answer to the following question, which I would like you to test your intuition about:

Flip coins. What is the probability that, at some point, you flipped at least consecutive tails?

Jot down a quick estimate; see if you can get within a factor of or so of the actual answer, which is below the fold.