Come, Hamlet, come, and take this hand from me.
I've never understood what's in their heads as they face each other before that duel begins.
Claudius: How the hell did you escape my plot to have you killed? If you're here, and Rosencrantz and Guildenstern aren't, then something's radically wrong. What do you know?
Hamlet: Why are you smiling at me? You know that I know what you know: you tried to have me killed. (I bet you're wondering where your accomplices are.) And I still know damn well you killed my father. I don't know what you're up to here, but I've already thought about dying.
With a subtext like that, the fact that those two would choose a public event for their first meeting after Hamlet's departure for England baffles me. Hamlet maybe -- he's got the upper hand. But Claudius? Is he riding on the crazy hope that Hamlet somehow escaped R&G without discovering his own murder plot? Why didn't he simply show Laertes the way to Hamlet's chamber?