Supppose that Army trails by 14 points in the Army–Navyfootball game. Army’s guardian angel has assured the Army coach that his team will have the ball two more times during thegame and will score a touchdown (worth 6 points) each time it has the ball. The Army coach has also been assured that Navywill 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 determinewhether to go for 1 or 2 points after each touchdown. A 1-point conversion is always successful, and a 2-point conversion issuccessful 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 assignedto 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!
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!
Step by step
Solved in 3 steps
