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Had an interesting idea lately: Lets say that the Mamluks decide to intervene in Mesopotamia during Timur's invasion of the place, leading him to invade Egypt instead of Anatolia. Further more, lets say he dies while campaigning there, while still giving the Egyptians a thrashing.

At the same, with no distractions at hand, the Third Ottoman siege of Constantinople succeeds, and the city falls in 1402. So the Ottomans have a 50 year head start.

What happens next? How big can the Ottomans get?

Its worth noting that most of the powers that can fight them have been weakened by recent conflicts (Egypt and Persia by Timur, Venice by Chioggia) or are currently embroiled in their own issues (The Hundred Years war).
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