Hamlet gives extremely detailed instructions to the players on how they should be performing the play.  Horatio enters and Hamlet lauds his friendship:

He entreats Horatio to watch Claudius’ reaction during the murder scene of the play to determine if he is guilty; if he does not react, the ghost that they saw may have only been a figment of their imaginations.  Horatio promises that nothing will get by him.

All enter and sit for the play, Gertrude entreating Hamlet to sit next to her.  He chooses to sit next to Ophelia instead, bantering with her about sex, and then the death of his father.

The players begin their performance, bringing to light the death of the king and having the queen renounce remarriage on the grounds that it’s a confession of murder of the first king.  The play continues and when the murderer pours poison into the king’s ear, Claudius calls for lights and the performance is ended.

Rosencrantz approaches Hamlet at his mother’s bidding to ask his audience in her chamber, then he begs Hamlet to tell him what is bothering him. Guildenstern gets somewhat impatient with Hamlet’s prevaricating and Hamlet responses in anger, accusing him of trying to play him, as he would play a recorder.  Polonius enters and Hamlet spews more nonsense before agreeing to see his mother.  To himself, he promises to be “cruel, but not inhuman,” referring to Nero, who carved out his mother’s womb to see where he had lived before his birth. 

The Play Scene from “Hamlet” (1841) Daniel Maclise source Wikimedia Commons

Hamlet’s advice to the players and his careful attention to detail, highlights the importance of the play to him.  It requires a detailed structure and a believable reality to make it highly effective.

Hamlet admires Horatio for mastering his passions, which is curious because Hamlet has so far shown all throughout the play that he has little control over his.  He is admiring what he is not.

With regard to Hamlet’s confession that if Claudius does not show guilt, that the ghost might not have been real, highlights that he is still unsure of his position.  This uncertainly perhaps explains his inaction so far in the play.

As for Claudius and his guilt, Hamlet, in effect, supplies a one man jury, which I suppose is better than nothing, as he is wanting confirmation from someone, other than himself, of the culpability of Claudius.

Why Hamlet concludes Claudius’ ire over the play confirms his guilt, is uncertain.  Claudius could be innocent and simply be angry that Hamlet is obviously accusing him of the first king’s death.  However, the fact that Guildenstern is still asking Hamlet what is the matter with him is suspect.  After the performance, it was blatantly obvious what was on Hamlet’s mind.  That fact indicates that Guildenstern, instead of being concerned about Hamlet, is, in fact, prodding him to confess.  His motives are suspect and Hamlet is certainly justified in his suspicion.