I'm attending a math teacher circle workshop this week. Yesterday afternoon we had a great speaker who talked about an old favorite of mine.
You and a friend play a game where each of you pick a sequence of three heads or tails. Let's say your friend chooses THH and you choose HHH. You then repeatedly flip a coin until one of the sequences shows up. So if you flipped THTHH, your friend would win. Is this a fair game?
Oh, if you have a solution feel free to write a comment, but give people a spoiler alert.