Hamlet's Dilemma

At the end of Act 3 Scene 3 Hamlet has found himself in what seems to be the perfect position for him to exact his revenge and kill his Uncle, Claudius, for the murder of his father. However, Claudius is now praying and asking God for forgiveness, which is something that Hamlet's father was not given the chance to do. Now Hamlet is faced with the option to kill him now and risk him going to heaven, or kill him in mid-stroke of a sin.

If you're asking for my opinion on what Hamlet should do, I can only generate one by putting myself in Hamlets shoes. I personally don't believe that Claudius would go to heaven just because he prayed. But then again I'm also not that religious to begin with (that's another story, I'm no story teller). So I have to approach this under Hamlet's state of mind: 

At this time people were very religious and I am sure that Hamlet probably does believe that Claudius has purged and cleansed his soul, now being allowed entry into heaven when the day comes. So with that in mind, I would have done exactly what Hamlet has done. I do not think he should kill him now. He doesn't deserve to go to heaven, especially after Hamlets father was taken without the chance to repent for his sins. Hamlet was smart to wait. The only problem that he might run into is the fact that Claudius may be suspicious of Hamlet's intent. But revenge must be gone about carefully. And what kind of revenge would Hamlet be getting sending Claudius to heaven when his father is still forced to pay for his sins?