Something that I do see as entirely possible in this specific matchup is just an all-in rush, completely balls to the wall, because Order of the Dragon has so few units and many units are good versus few units.
Those units are super expensive though. So if Order of the Dragon ends up losing a few of his land units, it impacts him more than losing one or two Zhuge Nu.
If Order of the Dragon commits heavily to melee infantry, Zhu Xi's Legacy can counter with crossbows, which they can produce quickly using Imperial Official supervision.
Even with lances, you don't run them into Order of the Dragon spearmen — that's a clean counter.
The Fire Lances tech from Zhu Xi's Library adds a fire lance charge attack to spearmen and horsemen, which is very useful up against OOTD cavalry.
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