Hamlets Hesitation To Kill Claudius

Hamlets intention of having the play put on was in fact to see if Claudius would show any signs of guilt about the death of Hamlets father. During the part of the play when the poison was put into the kings ear it was very obvious that Claudius was sweating a little and was starting to feel the guilt set in and Hamlet could see that. When Claudius ran out and Hamlet followed him to find him praying, I really thought he was going to kill him right then and there and Im kind of wondering why he didnt. I disagree with the fact that he hesitated to kill Claudius and in my opinion he should've done it right than and there. I realize that his punishment would be great and the others already think that hes crazy but he needed to take revenge on his fathers death.