Imagine two people are playing tennis. The server chooses a side to serve to (forehand or backhand) and the receiver chooses a side to expect a serve. If the server chooses forehand and the receiver expects it, the receiver wins 60% of the time, but if the receiver expects backhand, the receiver only wins 20%. If the server chooses backhand, and the receiver expects backhand, the receiver wins 30%, but if the receiver doesn't expect it, the receiver only wins 10%.
- Show the payoff matrix implied by these probabilities.
- Calculate the probability that the server should use to make the receiver have no benefit from guessing either side.
- What is the probability of the server winning with this strategy?