In Shakespeare's classic play Hamlet, many people look at it from two very different point of views. Each of them changes the outcome of the story. Hamlet mentions many times in the play that he is not crazy but only acting crazy to avenge his father's death.
The way that people look at the situation makes the outcome very important. Now from the beginning of the play Hamlet is debating on how to handle the revenge of his Dads death.

The plan that he goes with first is to act like he is crazy or Hamlets words "As perchance to put on antic disposition." That is the first big clue that he is just acting.
Now the reasoning for acting crazy in his plan for revenge is for everybody to think that he killed Claudius at the spur of the moment and not a pre meditated deal. In the end to maybe save his life from the punishment of Murder. Hamlet contemplates many times throughout the play on the value of human life and if he could actually take someone's life. So he keeps doing weird stuff convincing people that he really is crazy.

In Act 3 Scene 4 his Mom the Queen says "Alas he is Mad." This shows that his plan is working out so far.
During Hamlet's act of playing crazy and planning to kill Claudius it has helped him find the real value of human life. In Hamlets "To Be or not to Be" speech he ponders the value the value of his own life and the value of Claudius life in retrospective to his own life. He wonders does one murder really warrant another person to die. Now If Hamlet was truly crazy he would not of spent all on this careful planning and thought.

He would have killed him a few hours after seeing the ghost of his Dad. Hamlet has reasoning and morels enough not just to run out and kill someone.
During Hamlet's debate on what to do about his Fathers death, many other big events happen. First he kills Polonaise thinking that he was the king hiding behind the curtains.

To Hamlet that is a big event because it proves to himself that if he had to do it he could. He could kill someone that he doesn't care for too much. But when Ophelia dies he has to deal with loosing another loved one from the chain reaction that started from his Dads death. So this makes hi even angrier about his fathers death.
"With heated visage as against the doom is thought sick in the act.

" Now does a crazy man plan a murder with such thought? After looking at all of the details it all comes down to your personal interpretation of the situations. Hamlet mentions many times in the play that he is not crazy but only acting crazy to avenge his father's death