I'm not sure what the percentage really shows at this time. When you have a luck bonus you might have 52% whatever while your opponent has 50%, and that's a bit much, isn't it?

"I've won far more 40% auto-resolved battles with a skilled general, than I've lost 60% auto-resolved battles with the Imperial army."

You present two scenarios:
Player 40% using general
AI 40% chance <presumably no general>

Are you saying that you won a larger percentage of your 40% chances than what the computer did, and was that more than 4 victories in 10 battles?

Did you try any 40% battles that were 40% without generals?