Ive just found the start of it really slow. Practise jumping. Right now go here, ok now go there... and the only weapons i have so far are metal poles of one kind or another and my guy can only swing them like 3 times before he gets tired and has to back off.
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I think that's the point of the game. You're supposed to be weak and you have to pick your battles. As you level up you get better stuff, but even then you don't want to waste your katana killing tons of zombies with no purpose.