I wish that was the case. In three years of playing AGoT I've never found a satisfactory 2-player game. Whoever gets off first wins 9 times out of 10. I've seen that against people with great decks and experience who should have one but because their opponent got going first they won.
Well, our experiences differ then. Certainly, a fast start is highly advantageous in this game, and games can be virtually decided in the first round, so one's deckbuilding should reflect that. There are mechanisms that can turn a game around, though, to an extent. Of course, a good player with a good deck and a lucky starting hand will probably not lose against an equally good player with an equally good deck and an unlucky starting hand. Luck of draw is necessarily a part of every card game, and I don't feel it plays an unduly big role in this one.
I've played roughly a hundred 2-player games since I got the game. There were games with and against any of the houses, with and against all kinds of deck types. Some games were short, some were long. Some were tight, some were lopsided. Some were virtually decided early on, some had a swing. Some were a tad predictable, some were full of surprises, and some were downright epic. But I can safely claim that not one of them has been anything less than satisfactory. Well, except the one that I had to concede early on because I realized I had foolishly forgotten to include one vital plot card. I still take that record anytime, although your and anybody else's mileage may vary, of course.