Me and my brother had a discussion about a similar subject, which I will raise here rather than in a smaller, less frequented new thread.
The idea is this:
Hypothetical conflict between a Roman(Think
Marian(Late Republican), to
Early Imperial) force of approximately 10,000 men(two medium strength legions), versus a Mongol Tuman(10,000).
The armies are nearly opposites of eachother.
One is a highly mobile force consisting mostly of horse-archers, with a smaller core of a few thousand lancers. I will assume they have no infantry with them, except if some warriors dismount.
The Romans consist mainly of heavy infantry, followed by an insubstantial light infantry force, and then a few hundred equites for scouting & delivering orders.
Keep in mind, the Mongols would have saddles, strirrups, horse armour for the lancers, etc.
Me and Bro figure this would be a complete stalemate unless either side were to make a tactical error.
In the end, we figured that if no significant mistakes were made, then either side would simply redirect their forces somewhere else.
On a plain, grassy field: Romans draw their cohorts into formation, and dig in their position as best as they can.
The Mongols will fan out their light cavalry in a great wave, and fire volleys of arrows into the Romans, who will probably suffer only minor losses, though morale may begin to break.
The Mongols will play this movement out like a charge, then retreat just before they reach the Infantry.
They as well will likely suffer some minor casualties from Roman artillery and throwing spears/slings, or other ranged weapons they may have. Let's say this kills a couple hundred men on either side at most.
By this point, both generals will realize that the enemy force will have to be fooled into wasting their troops.
The Romans would fail by leaving any of their groups open to attack, or stranded, or by following a false Mongol retreat. The Mongols would fail by trying to break the enemy with pure force, probably in the form of a hail of arrows followed by a pincer-movement style lancer charge, both of which would(probably) be completely absorbed by the solid Legions.
Anyone want to add to this?