This fall we are going through Frederick Mosteller’s 50 Challenging Problems in Probability. Our first project was last week, today we tackled problem #2. The problem goes like this:

You are challenged to win two games in a row in a series of three games against opponent A and B. B is a better player than A. You can choose to play the the three games in order ABA or BAB – which order gives you a better chance of winning two games in a row?

Here’s the problem and some initial thoughts from the boys – they found the problem to be pretty challenging:

Next we chose some specific probabilities of winning the games against player A and against player B and calculated the exact probability of winning two games in a row in each case:

Having worked through a specific calculation, next we solved the problem in general:

Finally, we went to Mathematica to run some simulations and see if our results matched with theory (and also to introduce the boys to some basic logical operations in programming):

Thanks for the post! I had fun learning from all you. I was even inspired to convert your Mathematica code to Python.