Hamlet spared his life because he thought Claudius was praying.
On the night of the play's performance, Hamlet charges Horatio with determining Claudius' response to the murder scene. Hamlet acts outraged once more as the courtiers gather to watch, taunting Ophelia with a variety of lewd remarks.
As the play opens, Hamlet pays close attention to Claudius. Indeed, when the play's imaginary king is assassinated in a manner similar to how Hamlet's father was, Claudius departs, plainly alarmed. Horatio supports Hamlet's impression, who is overjoyed to have conclusive evidence that Claudius killed his father.
Hamlet is informed by Rosencrantz and Guildenstern that Gertrude needs to see him right away when they arrive. He promises to be cruel but will work hard to control his rage when he leaves to visit his mother.
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