Question 15.45

13. In American football, if a team tries for a 2-point conversion, then the ball is placed on the 2-yard line and the team has one play to try to get into the end zone. The quarterback can decide to run the ball or pass it. Similarly, the other team can commit itself to defend more heavily against a run or a pass. This can be modeled as a zero-sum matrix game, in which the payoffs are the probabilities of getting in the end zone and earning the 2 points. Find the value of the game.

image
Defense
Run Pass
Offense Run 0.4 0.65
Pass 0.75 0.3

13.

The value of the game is 0.525.