Search your library for a card put that card into your hand. If Increasing Ambition was cast from a graveyard, instead search your library for two cards and put those cards into your hand. Then shuffle your library.
It's pricey, but there's no denying the power of its ability. I don't really know what to say. It's a tutor and tutors are good. At the same time, it looks like Wizards also knows how good tutors have been in the past and intentionally over costed Increasing Ambition just to make damn sure that it doesn't break the format. Because of this, I'm going to go ahead and say this is the weakest of the four spoiled Increasing cards thus far. I know that might be heresy to say such a thing about a straight up, nonconditional tutor. But it just seems so slow to me, to the point that it becomes reduced to a "win more" card.
Okay, I admit that if you hard cast it for 5 mana and get the answer you need, it's still very, very good. But the effect of that answer only comes 1 turn later. In a non-combo deck, I just feel like in most situation I'd rather have the power of the instant speed, 3cc Forbidden Alchemy. On the other hand, who says you can't have both?
Despite all my crying in the two paragraphs above, I think a single copy of Increasing Ambition might have a place in Burning Vengeance decks. It's hard to say how viable they'll be once the dust settles from Grafdigger's Cage. But if Burning Vengeance decks are still played, Increasing Ambition wants to be in that deck.
There's something to be said about the risk of self-milling (through Dream Twist) or random Discard (through Desperate Ravings) all 4 copies of Burning Vengeance in your Burning Vengeance Deck. A tutor will certainly alleviate this problem.