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Is all of this true for a 13x13 board? I wonder if gaining territory may be more important than influence on that size?
It is true that on 13x13 is influence is less useful then on larger boards. However Black's influence is so great after the 33 point invasion that even on a 13x13 board white needs careful timing. Imagine if Black starts on 44 and white immediately invades. The result would be good for Black.