3 Supppose that Army trails by 14 points in the Army–Navy football game. Army’s guardian angel has assured the Army coach that his team will have the ball two more times during the game and will score a touchdown (worth 6 points) each time it has the ball. The Army coach has also been assured that Navy will not score any more points. Suppose a win is assigned a value of 1, a tie is .3, and a loss is 0. Army’s problem is to determine whether to go for 1 or 2 points after each touchdown. A 1-point conversion is always successful, and a 2-point conversion is successful only 40% of the time. The Army coach wants to maximize the expected reward earned from the outcome of the game.

Use dynamic programming to determine an optimal strategy. Then prove the following result: No matter what value is assigned to a tie, it is never optimal to use the following strategy: Go for a 1-point conversion after the first touchdown and go for a 2-

point conversion after the second touchdown. Note that this (suboptimal) strategy is the one most coaches follow!