This is more relevant than the hatcheck problem. Two teams are scheduled to play two games against each other. For simplicity, assume each of their probabilities of winning the second game are the same as they are for the first game, irrespective of the results of the first game. One of these is true. Which one?

1. The most likely outcome will be that the two teams split, each winning one game.

2. It is always more likely that one of the teams wins both games than having a split.

3. It depends. If one team is a whole lot better then it will probably win both games. Otherwise, the most likely outcome is a split.

The algebra for this is fairly simple, but check in with your intuition before doing any algebra. What it says will likely surprise you.