Kenzerco's Hackmaster "penetrating" dice. Like exploding, but at 1 less value.
i.e. 1d6p:
rolling 6, 6, 1 tallies to 11.
6 (face value), 5 (6-less-1), 0 (1-less-1).
I came in here looking for this mechanic as well Me too. I actually discussed this at length with Riley before backing Roll20, since I can't find a single dice roller that supports penetration, and he assured me they would do it. But I expect it's probably on a long list of tasks so I'm playtesting with GURPS 4e while I wait to be able to host my HM 5e campaign here.
One Roll Engine
So a pool of 6d10 that yields 2,2,2,3,5,5 means that you've rolled two sets, 3x2 and 2x5. The first number is the "width" of the set (how many dice are in the set), the second number is the "height" (what the matched number was).
FURPG
[Ask a yes/no question and roll Xd6. X starts as 1, but various things can increase or decrease it.]
Good Outcomes:
6: Yes, and...
4: Yes.
2: Yes, but...
Bad Outcomes:
5: No, but...
3: No.
1: No, and.... I'm quite familiar with FURPG but not ORE, but it strikes me that both are already covered with standard dice rolls. For FURPG, just roll Xd6 and pick the best (or worst, in the case of negative dice) just like you would with real dice.
For ORE, I could see it being useful to have the roll results sorted since I can see most people grouping real dice together. For instance, in your given example, instead of displaying the dice in the order rolled (like this perhaps: 3,2,2,5,3,5), they could be grouped together in ascending order.
That might actually be nice as the standard display unless there there any games where the order in which the dice are rolled matters – I'm not aware of any, but that doesn't disprove their existence. How hard would it be to automatically sort the individual die results before displaying them?