After Gertrude reveals the details of Hamlet's accidental killing of Polonius, Claudius realizes the palpable danger the prince presents. Hamlet nimbly deflects the king's spies, Rosencrantz and Guildenstern, as they vainly attempt to extract the location of the aged counselor's corpse. Since Hamlet is bound for England, the king orders Rosencrantz and Guildenstern to deliver both the troublesome prince and a sealed letter to the king of England, ordering his execution.
Meanwhile, traumatized by the death of her father, Ophelia sinks into madness, wandering the grounds of Elsinore before finally drowning. Laertes, returned from France, is enraged not only by his father's death, but by his sister's suicide.
At sea, Hamlet discovers the sealed letter and replaces it with one making Rosencrantz and Guildenstern its designated victims. After being taken prisoner by a pirate ship, he is able to use his title to negotiate his release.
Informed of his return to Denmark, the king plots with Laertes to kill Hamlet in a rigged duel. After Hamlet and Laertes quarrel over the death of his sister, Hamlet expresses to Horatio his intention to end the reign of Claudius before he learns of the fate of the king's spies.
A duel is arranged, and Hamlet accepts. The nefarious plan of Claudius to dispatch Hamlet goes awry, and not only the prince, but also Claudius, Gertrude, and Laertes, meet their end.
It would seem that Hamlet's possible actions, were one to contemplate alternatives, are severely limited after the death of Polonius. Claudius is now alerted to Hamlet's increasing volatility and possible desire for revenge, making an imminent attempt by the prince a much more precarious enterprise. If Hamlet should attempt to flee, surely the king would order pursuit. His assent to the sea voyage, although among known foes, seems plausible, since he views their inferiority as posing a less dangerous threat than the presence of the wily Claudius.
The lapse into madness and, ultimately, death of the vulnerable Ophelia and the anger of Laertes are predictable collateral damage of their father's demise, but the prince is surprised and then guilt-ridden upon learning of them. This is typical of Hamlet's rare excursions from self-absorbed melancholy, and it's open to debate whether it is this sudden awareness of the suffering of others which leads him to accept a duel sponsored by Claudius, who wishes his extinction. That he does put himself in danger, rather than waiting to seek his revenge from a stronger position, finally renders ambiguous the question of whether or not Hamlet did truly did intend to kill Claudius, as he had said to Horatio.