In "Hamlet" how does the theme of deception inevitably lead to the death of Hamlet and Claudius?My original thesis was relating deception to the...

Hamlet originally thinks that putting on "an antic disposition" and acting mad will avert suspicion from his investigations in his father's murder. He figures that if he starts snooping around, Claudius will take notice and be alarmed, and possibly cause Hamlet harm.  But, if he's acting mad, people will just dismiss any unusual inquiries or behavior, because it's just the nutty Hamlet being kooky again.  Unfortunately, this plan doesn't work out too well.  Hamlet's strange behavior concerns Ophelia and Polonius, and the Queen, and as a result, they all watch Hamlet even more closely.  The Queen is so concerned that she has Polonius hide in her bedroom during Hamlet's visit, which leads to Polonius's death, which leads in part to Ophelia's madness, which in part leads to Laertes's challenge of Hamlet to a duel, which in part leads to Hamlet's death.  Did you catch the chain reaction there?  Hamlet severely mistreats Ophelia because he knows he's being watched; he's being watched because he's been acting strangely.  His mistreatment of Ophelia in that scene is also part of what leads to her insanity and death, which prompts Laertes to murder also.  So, Hamlet's deceptive behavior leads to people's deaths, which leads to his own.

As far as Claudius goes, if he hadn't murdered his brother, Hamlet would have never sworn revenge against him.  If he hadn't hidden the murder and taken up with King Hamlet's wife, Hamlet Jr. wouldn't have been so vilely angry at him either, and desired to kill him.  Claudius's deception prompts his secretive death warrant on Hamlet given to Rosencrantz and Guildenstern, and it is that action that finally pushes Hamlet over the edge into full-blown revenge mode.  Claudius's deceptive reasons for Laertes challenging Hamlet also indirectly leads to his death.  Claudius's deception about the poisoned wine leads to his wife's death, and alerts Hamlet to his insidious intentions, which then prompts Hamlet to make the final move and kill him.

I hope that all of those connections made sense and helped; good luck!