How many Cannaes would Hannibal have to win to break rome

We can't know for certain what Hannibal's original plans and intentions were, but I've seen it argued that Hannibal's invasion of Italy was supposed to be a "Pearl Harbor" of sorts whereby the audacity, shock, and speed of the campaign would intimidate the Romans into capitulating (or at least backing down from a wider war). Only after that failed, did he eventually switch to a strategy of divide and conquer by playing off the different loyalties of the Italian socii. If that’s true, then Hannibal's goal was never to "break" Rome to begin with, since doing so was likely beyond the scope of his logistical and diplomatic capacity. In my opinion, the only feasible way to achieve this would be to divide the Italian aristocracy among itself (which is how the Western Empire finally collapsed IOTL)
 
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