For the last few weeks, Chris Maslanka's excellent maths puzzle column in the Guardian has been running variants on the following problem. Fred and Sam play a game in which the winner is the first to flip a head. They take it in turns, Fred starting. What's the chance that Fred wins? I have been asking this to 6th form audiences and the general response is 2/3 or 3/4, but nobody can say why. Here is the solution I have been using.