Let's say you are a student who was pretty sure that no conclusive evidence existed which proved that you had cheated. The optimal strategy might have been to, in writing, state that (1) you had not cheated but (2) had no way to prove your innocence. You cite your concern that, if you do not confess, you could end up with a failing grade or worse. So, as a practical matter, you have decided to falsely claim that you had cheated. After all, the only penalty (other than your professor never speaking to you again) is wasting four hours of your time in an ethics course.

Note that I did not say above whether or not you had actually cheated. Sadly, this fact is irrelevant with regard to strategy!