There's an android game called Elder Signs: Omens that is based on a board game, and uses a nice dice-based system. But it doesn't look like dice... It's only by knowing how many board games work that I realised it was using dice. Maybe give it a check...
Another system to use is a fruit machine spinner thing. You see exactly what all the possibilities are, how they're spread, etc, in the brief animation. You get a sense of the randomness and the chances of good and bad, and potentially something visual for any effects like a curse causing extra possibilities to miss.