You can definitely do worse than 50/50: just flip your solution and put a single white marble in one of the bags. By the way, your solution--single black marble in one bag, all other marbles in the other bag--is optimal; do you know of a way to prove it? Besides just exhaustive enumeration, that is.
Exhaustive enumeration is a proof even if it's not very satisfying :-). For example, a big part of the Four colour theorem is a big enumeration of all configurations.
