If the mongols acquired the blueprints of Hui Hui Pao from the Abbassids, then the Abbassids should also have special trebutchet units, or atleast make then constructable by infantries

Age of Empires IV IV - Discussion
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Hui Hui Pao literally means Muslim Trebutchet.

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By the time Hui Hui Pao was created. There was no Abbasid Empire.
It was fully conquered by the Mongols.
This is why they don’t have it and cannot have it.