I would change WWI to were Germany wins and still have the great Kaiserreich around today
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I was acutally thinking this before I came to your post; I have been pondering the possibilities of a German-victory WWI. Perhaps not so much for the Kaiserreich, but more for the state of affairs afterward. I would enjoy a world with Germany not being everyone's bad-guy, America doesn't develop into a debt-gobbling war machine, and where conservative values are a bit more prevalent.
Besides this, I would change the crusade where...god, am I dusty.
Some Emperor was marching to help in
some crusade- this was before Byzantium was ransacked- and some jack-off fleeing from the battle told him that.... Antioch? had already fallen, so there was no use. This was the final break between the Western and Eastern allies, for the most part; if he had helped, there may have been better relations, and fifty years later
some other emperor would have been able to deal with the divided Turks who had invaded Anatolia, instead of worrying about the West and how little manpower he had, therefore providing a situation where it is not implausible for Byzantium to survive as a major power quite a bit longer, if not completely preventing the rise of the Ottomans in that part of Eurasia. And anything about Byzantium/Rome surviving drives me bonkers, as it just seems so...ancient and cool to me, I guess.