I like doing brute force analysis of this sort of stuff. It's easier than stats, although you do need to use stats to validate at least a couple test runs too. It may be a few days before I could start on it (RL stuff), but if you can link me to a good explanation of the system I can write a light-weight java program or something that would do it.

I presume that the S dice are d12, yes? Your post says d6 but the table you give has 12 entries.