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The Fourth Crusade somehow doesn't get diverted to Constantinople.
Instead they land in Egypt as planned. This was to be a precursor to an invasion of Palestine. I think the army was about 20-25,000 strong. I am assuming they could take a coastal port like Damietta. Could they take Cairo?
I am guessing that after conquering Egypt they wouldn't have the strength to effectively challenge the Arab forces in Palestine/Syria. Therefore I think they will stay in Egypt and found a Latin Empire there.