Pitati Archer (Nubia): 12 (15 - 3) - some cheap math
War Cart (Sumeria): 25 (24+1) - some cheap math
Pitati Archer = 30/17
War-Cart = 30
Damage = 30 * 1.041^(Difference in Strength)*(Random modifier)
I can't find anything specific in my quick search, but I see an approximation that says -10 health means -1 strength, which matches my vague recollection, so I'm going to use that for now, as though every 10 is a strength point lost (80 is 1 weaker than 90-81). Please feel free to re-do this with more accurate calculations.
Also, because we cannot assume random numbers will benefit either side, I'm going to ignore them, with the vague idea that an infinite number of tests would roughly ignore it when averaged together. (I haven't done stats in years, leave me alone).
Pitati first:
Pitati 100, War-Cart 70
Pitati 55.2, War-Cart 50
Pitati 55.2, War-Cart 18.8
Pitati 12, War-Cart -2 (Dead)
War-Cart first:
War-Cart 82.2, Pitati 49.4
War-Cart 56.7, Pitati 49.4
War-Cart 39.6, Pitati -3.2 (Dead)
Survivors- Pitati First:
Pitati 12, War-Cart 11
Pitati -38 (Dead), -6 (Dead)
Survivors- War-Cart First:
War-Cart 23.2, Pitati -42.8 (Dead)
Bonus Round - War-Cart (23.2) v additional damaged Pitati (12):
Pitati First
Pitati 12, War-Cart -5.6 (Dead)
War-Cart First
War-Cart 6.1, Pitati -40.6 (Dead)
Essentially, in head to head combat, the War-Cart will win, but barely enough to make a difference. So, I'm giving them points for that. But, you can take that with a grain of salt for several reasons. First, War-Carts are available sooner, but Pitati are I believe slightly cheaper with Nubian bonuses. Second, Pitati’s can use city and encampment covers for protection when attacking, War-Carts can capture cities. Third, War-Carts turn into the powerful knight unit, but that will need iron. Pitati turn into the respectable crossbow units, no resources needed.
