here is a battle example: player 1 attacks with 3 infantry, 2 tanks, 1 fighter. Player 2 is defending with 3 infantry, 2 artillery.
player 1 rolls:3,6,4,3,2,5 the 2 tanks both got hits 3 or less so score hits, the first is 3 hp so kills an infantry, the second is 2 hp which also kills an infantry.
player 2 rolls:4,2,1,2,5 one of the infantry rolled a 1 so player one moves an infantry down to 1 hp, one artillery rolled a 2 so another infantry is killed.
player 1 has 1 dead infantry, 1 infantry on 1hp, 1 infantry on 2hp, 2 tanks, 1 fighter
player 2 has 2 dead infantry, 1 infantry on 2 hp, 2 artillery on 2 hp
player 1 rolls:5,2,1,3,5,2 one infantry rolled a 1 so player 2 moves an infantry to 1hp, one tank rolled a 3 so player 2 losses an artillery, the fighter got a 2 so player 2 has to remove the artillery to do the maximum damage.
player 2 rolls:2,3,2 an artillery rolled a 2 so player 1 moves a fighter down to 2 hp
player 1 has 1 infantry on 1hp, 1 infantry on 2hp, 2 tanks, 1 fighter on 2 hp
player 2 has 1 infantry on 1 hp, 2 dead artillery
player 1 rolls:2,5,6,6,2 the fighter rolled a 2 so player 2 removes the last infantry
player 2 rolls:2,3,2 an artillery rolled a 2 so player 1 brings a tank down to 1hp
player 1 has 2 infantry, 2 tanks, 1 fighter - the troops automatically heal at the end of battle and have full hp when they go into battle again.