I've been reading a book about this period (I really should finish more books), and my memory isn't 100% on this so I won't go into depth, but I recall that during Henry II's reign, his children's placement in control of land was like playing chess against multiple opponents, where his children were both the chess pieces and the opponents.
Henry's children were naturally rebellious - it didn't help that Henry's wife, Eleanor of Aquitaine, encouraged their rebelliousness. He was unwilling to have one child take the whole inheritance, as the natural idea to Henry, a product of the age and his reasoning, was the idea of having a sort of "federal England" (and that's a direct quote from my book) with his eldest child being King of England and the head of this state, and his other children forming dynasties to rule over the individual parts as vassals to England. The fact that several of his children died, reducing the inheritance, was simultaneously troubling to his vision, and probably the thing which held England's control of continental land together. But John Lackland was called Lackland for a reason - he was his father's least favourite son, and Henry laughed in John's face publicly that he had no land. Depriving him of land wasn't a sick joke, of course, though his treatment of John was quite cruel, but Henry only saw his Empire as being divisible into three portions. He had to actually create Ireland as a Lordship to make a fourth portion for John later on, when he decided that John needed land. And as Henry the Young King and Geoffrey died off, these weren't expected deaths. John didn't sit back hoping to inherit over his brothers' dead bodies. Though there was some chafing at each others' power, and some rivalry when war broke out amongst father and sons, by and large there wasn't any attempts at brother dethroning brother. Certainly not in England. The only political playing was trying to usurp Henry II's authority (his sons wanted to force him to resign his thrones so that they could run amok themselves). John had no inkling that he'd ever take England's throne - especially when Richard became sovereign. His death was a shock. So John isn't going to sit around waiting for his chance, he'll go for Savoy. In fact he'll probably go there early, even before he has inherited, in order to feel like he is in his own province.
What is more interesting to me is what John will do while Richard is King, and whether by posing an addition threat from another angle, England could stave off France's invasions to hold the Angevin Empire together a little longer - at least until a more militarily competant king comes along...though with Henry III next, maybe not...
