You have 5 "rolls", and for each roll you can choose to roll a smaller die and know the results, or a larger die with hidden results. Possibly:
- 2d4 visible (min 2, avg 5, max 8)
- 1d10 invisible (min 1, avg 5.5, max 10)
Needs a supporting system where succeeding, and knowing whether you succeeded, are both valuable independently. Maybe a wargame with fog of war (where do you commit additional resources?), or a political/social game where you are trying to sway people to your side (and usually aren't exactly sure where you stand with any individual, and again are deciding where to commit resources based on who you trust).
Possibly a tactics/jrpg "party management" game where you're rolling against characters' confidence levels or relationship levels to see who will do their action well, and who will do it poorly... like you can see if you rolled a miss, hit, or a crit ahead of time, before committing to a plan of action?
I was also thinking of "scouting" or espionage... the result determines how accurate the information you get is (from wildly inaccurate to missing details to perfect). But I think this one requires too much overhead.
The basic mechanics to play with:
Choose some proportion of "weaker visible dice" and "stronger unknown dice" in context of a situation where you want to win your rolls, but where you might reasonably not know whether you won or lost until later, at which point it might be crucial.