During the course of a football game, coaches must make many crucial decisions, including the following:

  1. It is fourth and 4 on the other team's 30-yard line. Should we kick a field goal or go for a first down?
  2. It is fourth and 4 on our own 30-yard line. Should we go for a first down or punt?
  3. We gained 7 yards on first down from our own 30-yard line. The defense was offside. Should we accept the penalty?
  4. On first and 10 from their own 30-yard line our opponent ran up the middle for no gain. They were offside. Should the defense accept the penalty?
  5. What is the optimal run-pass mix on first down and 10?

Using the concepts of states and state values discussed in chapter 20, these decisions (and many others) are ...

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