This is shaping up to be a really good week for people interested in rich dice. For the unfamiliar, "rich dice" is a term used in RPGs when a die roll reveals more than one piece of information. For example, in the One Roll Engine, when you roll a set, the highest number in the set determines how quickly you act, but the size of the set (pair, trio, etc) determines how well you act. Similarly, in Don't Rest Your Head, the dice determine who wins a roll, but the color of a highest die rolled determines which factor "dominates" the outcome.
This is a really robust technology. In addition to allowing more meaningful rolls, it also allows interesting mechanical hooks, such as how Dragon Age handles criticals. This is good stuff. And the unending font of creativity which id Daniel Solis has put forward a very interesting design, Split Decision. Go read it for more detail, but in short, you roll 4d6 of 2 colors, and build a roll out of any two dice. Normally you'd just keep the two highest, but which colors you use also has a mechanical impact, so sometimes you might want to build a less optimal number to get an optimal color combination.
Now, the model used in split decision is usable in a lot of other ways. Any time someone is rolling multiple dice (either to total up or to count successes) you can introduce new colors or dice types to introduce more mechanics or meaning.
The trick that I think is most powerful (and which not all Rich Rolling system supports) is the addition of player choice. If you can create meaningful tradeoffs then you can really give individual dice rolls a lot of potency. Structurally, this is very simple (as split decision demonstrates) - more difficult is figuring out how to implement it in a way which is both meaningful and plays well.
That last can be trickier than you might think. Linneus has a great piece on his four principles of dice games that it's worth thinking about in terms of RPGs, an done point he hits is especially relevant - don't waste a lot of time. You want a meaningful decision, but not one that the player is going to agonize over. You might make an exception if it's the only roll, but even then I'd hesitate - if the decision draws things too far out of the game then it can really move things too far away from play.
That may seem like I kind of abstract consideration, but it actually leads to some very concrete guidelines if looked at the right way. Consider D&D - in a given fight, it is rare that any one thing tips the battle by itself. Usually it's a slow depletion of luck and resources - you don't begrudge a particular hit, you just take it and move on. This is because D&D is nicely structured to spread the big decision (who wins the fight) over lots of little decisions (individual actions). That defines a lot of what makes it playable, and that same logic is worth considering when you think about player choice. A big decision that's either morally very difficult or deeply impactful is going to have a lot more impact than one whose ultimate impact is part of the bigger picture.
Even so, decision paralysis can be a real danger. If I say "Take 5 hit points of damage to get +2 to hit and damage on an attack" then some players will take their time calculating cost-benefit, others will swear and remember they could have done it after they roll, and others will just forget about the option. That's a different sort of choice than the kind you want to be thinking about with rich rolls - specifically, with a rich roll you want a choice to be absolutely necessary. If the character is rolling 5 dice either way, the player needs to decide how many are white and how many are black. Notice the difference - they must make the decision. At worse, they may come up with a default decision (like always going 3w, 2b). Choices that are built directly into the process, rather than layered on top of it (as is the case with, say, "which spell should I cast") tend to be a little bit easier to handle.
All that said, the other factor is where to hook the choice in mechanically. There are some good examples on the Split Decision page of using the decision to fill in a counter that has a mechanical effect when it reaches 10. In the case of Split Decision, this is a solid pacing mechanic, since at 10, some sort of endgame gets triggered, and it's easy to bring that model across to other systems where there are setting-sized decisions to make, such as associating yourself witht he light or the dark side.
The one drawback of this is that you need to make sure the die rolling proceeds narration if you really want things to make sense, and not everyone enjoys that. See, if the dice chosen reflect behavior and that behavior is not reflected in the narration then you can end up with situations where the fiction has you saving kittens bu the dice say you're showing a callous disregard for all life. If making the choice in the dice means making a choice in the fiction, then the fiction needs time to reflect it.
Still, that's not the only path - these choices can have immediate consequences too. This can be a s simple as having the colors of your dice split between offense and defense. To take the split decision model, let's say red is damage and blue is defense. Each red die used in your attack translates into extra damage, Each blue die translates into an increase in your defense value. When the big numbers come up red, do you take the risk and expose yourself to land the big hit?
When you want to design a system like this, it's worth listing the range of outcomes that your secondary information can generate. In the case of split decision, it's something like:
high red, low blue
tied red & blue
low red, high blue
Five apparent outcomes, but that number is not quite as concrete as you might think. There are often ways to compress the list down if there's some other number you're going for. Ties are easy to ignore - you can just say they're player choice, and beyond that you can try to build sets. In this case it's easy to break this down to a list of 4 or three as follows:
high red, low blue
low red, high blue
In this way you can often find the system can end up dovetailing with some specific set of outcomes you're looking to accomplish.
With that in mind, I suggest anyone thinking about these things take a look at Paul Tevis's post on "but" and look at those outcomes and consider how they might map.
1 - If you have the budget to create custom dice, you can do what Warhammer 3rd does, and have things like reckless and cautious dice, where one generates stronger outcomes, but with a greater chance of hurting yourself. Curiously, though, since that decision is made *before* dice are rolled, it's not really rich rolling (though the fact that the WHFRP3E dice track 3 different outcomes is).
2 - It's because of this that this system excels at a meta-level, where the decisions are not necessarily obvious in the outcome. That is to say, in things like magic systems, where there is no external indicator of which Elohim you are now deeper indebted to through that show of power.