What is the main conflict in Sleuth by Anthony Shaffer?

When Sleuth made its first appearance on the London stage in February 1970, it saw instant success. Moving to Broadway the following November, it won equal praise, even winning a Tony Award in 1971. In the program, audiences and reviewers were asked not to reveal the plot to anyone who had not yet seen the play, for so much of the enjoyment of the play was derived from its almost constant plot twists. Working on the idea of a whodunit, Shaffer instead created the first of its kind: a whodunwhat.