I disagree, I think Littlefinger has been playing the long game with Sansa. Didn't Littlefinger even say "bet on the people you know rather than the people you don't," or something like that? That to me was as much a reveal that he acknowledges this plan is working. Also here is my in show evidence to prove why he thought this would work:Branindain said:The problem with this retooling of the death of Lysa Arryn, however, is that they punctured Littlefinger's aura. The one thing that defines him (aside from obsession with Catelyn Tully Stark) is that he's always, ALWAYS three moves ahead of everyone else and has everything meticulously planned. Littlefinger would never get himself in a situation where only providence ends up saving him, it's just too out of character.
That laugh of Arya's, though... priceless.
1) In general, Lord Baelish, believes the Starks are gullible and trusting. And he doubles down on this idea by telling them "Don't trust anyone," which is a way of saying "everyone else is a liar except me, I have your interest at heart."
2) He manufactured Lysa to be a villain in Sansa's eyes and set the wheels in motion to get Lysa to ride the banana train to crazy town. Lysa doesn't need much of a push, but her gets it working easily. While I don't believe he ever says it on screen, I wouldn't doubt off camera Baelish mentions to Lysa that Sansa is the spitting image of Kat. Even if he didn't Lysa comes to that conclusion. He always seems to show Sansa extra attention when Lysa is around. And icing on the cake he choose to kiss Sansa not in a private room away from prying eyes, but in an open courtyard with lots of places for someone to watch privately. So even if Lysa didn't see it, someone most likely would and tell Lysa.
3) After manufacturing and instigating Lysa v Sansa, Baelish is able to save Sansa for the second time.
4) Not only has Petyr saved Sansa's life twice now, he has avenged Sansa's harrasser, in so much as he was the one that put the wheels in motion to have Joffery killed, and straight up pushed Lysa to her death.
5) Not only has he been filling a Protector/Avenger role for Sansa, Baelish has also been a teacher. He has been leading her to a more savvy way of dealing with people. He has been explaining how he has done this or that to reach these goals to her. Been giving her constructive criticism in how she is a bad liar. He gave her baby steps on how to pretend to be Alayne.
6) Not only that, in this world, it is common knowledge that if you are related or in the service of a traitor, you are seen as one too, Sansa knows this first hand, I don't really think I need to elaborate on that if you know the show.
For these 6 reasons, Baelish has a pretty much sure bet that Sansa has more to gain if not less to lose by siding with him. He had this planned.