As we're already talking about dices and battle rules. I want to bring here something you've explained to me in PW, as it still seems to me strange I'd like others to express their opinions.
According to your equation, result of dice roll shows percent of troops player loses after battle. And that's fine. But it means, that if one player uses, for example 100k troops, while the other only 10k and they both get, lets say, 15 on the dice, then first player looses 15k men, while the other only 1,5k. It means, that having more troops is disadvantage in the battle, as you may lose much more units in single battle. And, a bit hypothetically of course, it would be wiser to send 1 man to the battle and keep 99 999 men as reserve for next battles, than to use whole 100k, as this one man will kill the same amount of enemies as would 100k.
Wouldn't it me more realistic, if result of the roll showed how many of your men achieved to kill one of the enemies? Then player with 100k would kill 15k of enemy men, and player with 10k would kill 1,5k. Equation would be of course changed a bit then, to allow situations where army kills more men that it has itself. Smaller army may still win the battle and force the enemy to fall back and slower their movements by having larger result of dice roll, but even then it would be much less probable to totally destroy bigger army (yet, historically correct, it would still be possible with series of lucky rolls in following battles). What do you guys think about such idea?