When I played the Hôjô I was rather lucky because my foes crushed themselves, leaving me a rather plain path to advance. My route was 1. Suruga, 2. Musashi, 3. Shinano. I did this with 3 major armies, if I recall right, but I am sure that I did not have such a strong Imagawa against me, I think Oda kicked him badly rather early, while Uesugi had it on with 2 times reemerging Takeda and half his provinces in rebellion. I would move to Uesugis backland with Shinobi to force him split his main battle forces.
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