Your situation is quite good actually. Plaing HRE is one of the essayist in this game. If you dont install 1.02 you will be swimming in gold (because of the printing press), but even with it you still have banks, so you should be very rich. And you have all the unit types you need to fight the horde- heavy spears and crossbows, and heavy cav, and heavy infantry, all coming out of a fortresses. So if the Mongols are still in Kiev, make sure you grab Iasu, Bran and Sofia fast. These are all by this time citadels, so you will be able to produce huge armies in no time, close to the battlefield. Block the bridges, the passes and garnison these tree citadels to the top, and this is it. Hell, just to tace Iasu and Bran the mongols will have to sacrifice more then 5 full stacks, that is if you decide to fight them in sieges only.
It will be wise to get Thorn and Halych, just to make sure the mongols don't get there. At the end i thing that 3 full stacks at south, and one north will be more then enough to kill the horde, no matter what.
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