[barcadad]

Hmm, I think 50/50 is the worst you could do. What if you put 1 black marble in 1 bag and the other marbles in the other bag. Then even a random choice would get you .5 * 100% + .5 * 4/9 = 72.2%

And also, if you can look at or touch the bag before picking it, then just pick the one the looks like it has only 1 vs. 9 marbles!

[LaserPineapple]

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.

[Rexxar]

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.