Thursday, June 24, 2010

A coin flipping game...

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.


  1. This was in the Chances Are book by the Kaplan's I think right? I'm jealous you're at the math circle. Keep blogging it so I can live vicariously through you.

  2. Knowing that this is called "Penney's game" will enable anyone who wants to to spoiler themselves :-) It's apparently discussed in Martin Gardner's "Time travel and other mathematical bewilderments" too.

  3. Thanks! I've read lots of Gardner, but not that one and did not know this was called "Penney's game." And Jason, I've read Out of the Labyrinth, but not "Chances Are."