Chapter 9.3, Problem 23E

Football Suppose that, when the offense calls a running play, they gain an average of 1 yard if the defense anticipates a running play, and gain an average of 3 yards if the defense anticipates a passing play. Suppose that, when the offense calls a passing play, they gain an average of 7 yards if the defense anticipates a running play, and they lose an average of 4 yards if the defense anticipates a passing play. Determine the optimal strategies for the offense and the defense, and the corresponding expected value.