Probabilities and games. Two simple games used to illustrate certain features of calculating probabilities are as follows: You and a friend take turns flipping a fair coin. The first person to flip heads wins. If you go first, what are your chances of winning? You and a friend take turns rolling a fair die with 6 sides. The first person to roll a 6 wins. If you go first, what are your chances of winning. These end up being very similar problems, and can be generalized. For convenience, I’ll talk about the rolling a die version. To start we’ll walk through a couple winning scenarios to look for a pattern.