WI: Fourth Crusade Gets Off On the Right Footing

The Fourth Crusade is generally regarded as a disaster, since rather than completing its intended objectives, it ended up dramatically weakening and dividing Christendom.

The basic plan of the Crusade went something like this: the Republic of Venice would build a fleet to transport a crusader army of about 33,500. After the crusaders paid the Venetians 85,000 silver marks, the fleet would set sail to Egypt, where they would defeat the Ayyubid Sultanate before marching east and recapturing Jerusalem. However, the crusader army ended up numbering about 12,000 - far fewer than expected - and because of this, they couldn't pay the agreed upon sum. Understandably, the Venetians weren't happy about this, because building the fleet had been extremely expensive. The crusaders and Venetians attempted to find a solution to this dilemma, which kicked off a chain of events that led to them sacking Constantinople and conquering large portions of the Byzantine Empire, irrevocably weakening it and leading to its eventual fall to the Ottomans.

Suppose the crusaders gathered the number of troops expected, and so they could pay the Venetians. Could they defeat the Egyptians and recapture Jerusalem? What would the consequences be for Byzantium?
 
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