I figured it out!
The cards you get depend on both the difficulty of the enemy and your current level of power. I just faced off against a guy who used Yetis, Dark Armors, Succubi, and really powerful other units with goblins, taurus troops, and Meteor, and when i won i got three cards. :D
It would be good if every 10 seconds I didn't lag, which causes my character to totally spazz. Or if there WASN'T a horrible glitch that makes your guided missles lock on to YOU.
3.5/5 (bugfix necessary for a 4)
 "Epic War 3"){kind=icon}
 "Bubble Tanks 2"){kind=icon}
 "SHIFT 3"){kind=icon}
 "Chaos Faction"){kind=icon}