using your battle, a person will never defend when they can attack, because there is a high chance that they will fail/partially fail when defending. take in mind that if one keeps defending, they will never win
a better calculation is that when one defends, there is a chance that they will (1)miss at defending, (2)defend all of the damage, or (3)take half damage and inflict the other half back at the attacker. this way, there is a more equal chance for the defender to win.