Writing and studying for an exam is a game played between Professor and student.  In this game the Professor has to pick which questions to ask and the student has to pick which topics to study.  The game has the flavor of rock-scissors-paper in that the Professor would like to be unpredictable.  That way the students will have to devote studying time to all topics rather than focus on just one that they know the Professor will ask about.

But the Professor might not want the students to spend too much time memorizing concepts from the book.  Instead he may want them to spend their time thinking about how to apply those concepts to new problems.  How can the Professor be unpredictable and still deter the students from trying to memorize the book?  The solution is to use an open book exam.  This way the Professor is committing not to ask rote questions which would turn the exam into nothing more than a contest to see which students are the fastest to search through the book and find the topic.

With an open-book exam, the students can predict that the Professor will not ask such questions and they will not bother studying for them.  They bring their books to the exam and never have to open them.  And they still cannot predict which questions (apart from the mundane ones) the Professor will ask.

Keep in mind that this means students should dislike open-book exams.  Many students don’t understand this and are always asking for open-book.

Also, the worst possible format is the common practice of allowing students to write out crib notes on one sheet of paper.  This turns studying into pure rent-seeking.  All students will predict which are the essential concepts from the book and will write them down and, predicting this, the Professor will not ask questions about those topics.  In the end the outcome is just like open-book except the poor students lose valuable studying time while they squeeze the book onto a sheet of paper.

(To my PhD students and undergrads taking exams today:  aren’t you glad the exams are closed book?  Oh and good luck!)