I am playing in a tennis tournament, and I am up against a player I have watched but never played before. Based on what I have seen, I consider three possible models for our relative strengths:
• Model A: We are evenly matched, so that each of us is equally likely to win each game.
• Model B: I am slightly better, so that I win each game independently with probability 0.6.
• Model C: My opponent is slightly better and wins each game independently with probability 0.6.
Before we play, I consider each of these possibilities to be equally likely. In our match, we play until one player wins three games. I win the second game, but my opponent wins the ﬁrst, third and fourth games. After the match, with what probability should I believe in model C (i.e., that my opponent is slightly better than me)?