Question: suppose you are trying to predict a 4-team bracket, but you are better informed. Before the start of the tournament, each team is given a ranking (1, 2, 3, or 4) that it will keep throughout the tournament. You will use the following model to predict the results: If a team with ranking "a" is playing a team with ranking "b", the probability that the a-team will win is a/(a+b) . You always bet on whichever team has a higher chance of winning each game according to this model. There are three games in this tournament.

Compute the expected number of games you correctly predict.