How does Rosencrantz and Guildenstern's betrayal affect Hamlet?

Rosencrantz and Guildenstern, Hamlet's school chums, are summoned by Claudius and Gertrude to the Danish court to spy on the student prince. Hamlet's initially glad to see his old pals, but his happiness does not last too long because he soon realizes what they are really up to. Hamlet feels betrayed by them because he thought they were his friends. Their treachery is indicative of the general level of moral corruption ("something rotten in the state of Denmark") that has infected the country since Claudius murdered his way to the throne.
His act of revenge against Rosencrantz and Guildenstern foreshadows his ultimate revenge against his hated stepfather. By sending Claudius's proxies to their death in England, he is indirectly attacking him; Rosencrantz and Guildenstern are collateral damage in Hamlet's battle of wits with Claudius, and they go to their deaths oblivious of Claudius's wicked intentions. In some respects, Hamlet's devious ploy is a substitute for dispatching Claudius with the same degree of ruthless efficiency. There is certainly no procrastination when it comes to getting rid of Rosencrantz and Guildenstern. Perhaps this is a reflection of just how hurt Hamlet felt at his former friends' betrayal. He expected better of them; he never liked Claudius.