I used to be very uneasy around dice, but the last campaign I ran had me thinking that the dice largely served to mean that characters could randomly fail at something that was meant to be the core purpose of their character. Being lousy in combat is fine when that's not your gig, and fights should always be a little unpredictable... but it's when the scholar flubs a knowledge role, or the socialite fails to be persuasive...
I seldom have that problem because I don't require skill rolls if I think the character should automatically succeed at the task he is attempting. Or I just use the skill roll to decide how well the task succeeds. Of course, I started playing RPGs back before there were skills (D&D, early CD&D, and AD&D 1E really did not have them) so I am used to making GM decisions rather than having the dice decide everything.
My basic idea is going to be that the characters are unknown children of Amberites from previous dalliances (ie: the kid you never knew you had) who have been dug up by someone who'd like to throw the succession back into debate.
Perfect setup for a good game -- at least with the right players.