Here is the problem. Turn one, you could use
Saved From the Fire (three cards) and
Birthday Present (one card) once.
So this would have to survive at least one turn and even then, the next turn you could use
Birthday Present a maximum of four times...then another turn, another four times...you get the idea.
I will be smearing the hobbits' faces into the dirt at site three before you cycle all the way through your deck.
Of course, for statistically better odds, why not take out
Sting and the three Hobbit Swords and run four copies of
Practically Everyone Was Invited? That doesn't count against the rule of four...
-wtk