Would you consider Chess a "casual" game?
It needs the right amount of complexities. Chess weakness is not the amount of rules you need to know, it is that it requires thinking several moves ahead, luring your enemy in a trap while avoiding his. That requires a lot of continual mental effort, and you have little tools to help you think through it.
I like to distinguish between "complex" and "complicated".
In this context. Complicated is if you have to run through a lot of steps to achieve your goals. Complex is if you have a lot of possible things to do.
For example: There are tons of feats in D&D 3E and 4E. But that doesn't make the game complicated, just complex. Complicated is a feat that does give you a +2 bonus instead of a +1 bonus to attacks when you charge an enemy you have marked that has hit you on his last turn. The bonus increases to +4 if the enemy hasn't moved since his last turn. (This feat doesn't exist, as far as I know.
) Try to figure out when you can use this feat and what benefit you get!