-Suppose that two individuals play a game of tennis. The situation depicted in Figure 6.5 summarizes the probabilities that the receiver will successfully return a serve that is directed to his backhand or forehand. Suppose that both players adopt his or her optimal mixing rule. The receiver's success rate will be:
A) Around 22 percent.
B) Around 48 percent.
C) Around 53 percent.
D) Around 58 percent.
E) Around 65 percent.

Question

-Suppose that two individuals play a game of tennis. The situation depicted in Figure 6.5 summarizes the probabilities that the receiver will successfully return a serve that is directed to his backhand or forehand. Suppose that both players adopt his or her optimal mixing rule. The receiver's success rate will be:
A) Around 22 percent. 
B) Around 48 percent. 
C) Around 53 percent. 
D) Around 58 percent. 
E) Around 65 percent.

Quizplus · Accepted Answer

In games involving mixed strategies where both players are playing optimally, the outcome is typically balanced in a way that reflects the strategic mix of options available to each player. Without seeing Figure 6.5, we can infer that the optimal mix would balance the server's and receiver's strengths and weaknesses, leading to a success rate for the receiver that is significant but not overwhelmingly high. A success rate around 48 percent suggests a competitive balance where the receiver has a nearly even chance of returning serves, whether directed to their backhand or forehand, assuming both players are using their strategies optimally.

-Suppose That Two Individuals Play a Game of Tennis