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human
[Game of Thrones] What was Littlefinger's plan if Jaime Lannister didn't push Bran?

SPOILERS: Littlefinger had John Arryn poisoned and was able to start a feud between the Starks and Lannisters, but I realized last night this relies on framing Tyrion as the one who attempted to kill Bran. If Bran never caught Cersei and Jamie and was never pushed from the tower, it seems like Littlefinger's plan wouldn't have gotten very far. He probably had a backup plan, but what was it?

Rather, it seems like he had a plan and was able to change it to capitalize on the situation, but what was his plan if the events of the first episode had happened differently.
gpt
If Bran hadn't "fallen", one of two things would have happened.

1) Ned Stark would have become Hand of the King. In King's Landing, Littlefinger would have steered him into discovering Joffrey's illegitimacy, thereby setting the Starks and the Lannisters at odds, creating chaos and giving him an opportunity to rise.

2) Ned Stark says no. Somebody else - probably Tywin Lannister - would have become Hand of the King. Littlefinger cancels that plan and looks for a different way to create chaos.