The weak center effect makes sense. I've long used the approach of keeping weaker units in the center. Great generals sometimes did this with weak or unreliable units (Hannibal for instance.) It boosts their morale because they are near the best officers, they are supported on the wings, and they can't very easily run away. No wonder the AI is always charging my center with all its captains and generals.
I'm glad to see CA's explanation, but I still can't understand why they didn't opt for pushing other strong units against the weak point, rather than the general's cav. He really should have been used primarily as a heavy reserve.
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