A discussion for all my history geeks

I love history, from early humans, Mesopotamia, Rome, WWII, revolutions, all of it fascinates me. However, I always tend to go into the darkest periods of our human history. I feel it's where we can learn the most from our nature, but that's just me.

Listening to Dan Carlin always brings up the question what if so and so army faced this army, who would win?

One question that I ponder is, what if the Greek Legions under Alexander the Great faced the Mongolians under Genghis Khan and his sons? Would Khan ultimately win? Maybe?

I don't know how well the roman legions would battle against the Mongol horde. The Mongol soldiers are quick, can fire arrows from horseback, and are able to ambush and disappear within mins. However, we got the highly efficient and tactically gifted Greeks, who can build a fort overnight and defend it as if they were fighting in home soil. And the long list of mercenaries that came with the Greek army.

I like to think the Mongol Horde is simply too much for the Romans, and can only be simulated in Total War melees.

A great what if and would love to hear what you guys think would happen or other scenarios you've played out in your heads.