‘How now! a rat? Dead, for a ducat, dead!’

A ducat was a gold coin, so the line is a bet thrown out mid-lunge: a ducat says I’ve killed it. Hamlet hears a voice cry for help behind the arras, the hanging tapestry on his mother’s wall. He calls it a rat and stabs through the cloth.

Behind the curtain is Polonius, who hid there to eavesdrop on Hamlet and his mother. Hamlet’s next words show who he hoped it was. Lifting the tapestry, he says: ‘Thou wretched, rash, intruding fool, farewell! / I took thee for thy better.’ He thought he was killing the king.

For a man famous for delay, the speed is the shock. Hamlet spends two acts unable to kill Claudius deliberately, then kills the wrong man in half a second on a noise.

This is the closet scene, Act 3 Scene 4. A closet here means a private room, not a wardrobe: Hamlet has come to confront Gertrude in her own chamber, and Polonius has hidden himself to listen.

Polonius’s death is the hinge of the play’s second half. It hands Claudius his excuse to ship Hamlet to England, and it leaves Laertes an avenger with a murdered father, which is exactly what Hamlet is. From here the play drives straight to the poisoned fencing match.