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Some role-playing game systems—like Dungeons & Dragon before its third edition—use a combination of roll-over and roll-under mechanics (“roll-over”: high rolls vs. target number are good; “roll-under”: low rolls vs. TN are good).
Does this mixture of mechanics have any design or gameplay benefits that make it superior to using a roll-over only mechanic or a roll-under only mechanic?
I have done some game-design work, mostly in D&D 3.5e-derived settings, which are roll-over. However, some roll-under ideas were considered—albeit briefly—for some of these mechanics, so I’ve given this some thought and discussed these with other designers. I cannot claim as much experience with this question, though, as someone who has done a lot of work with roll-over, roll-under, and mixed systems. But from my perspective,
There is no particular “advantage” to mixing the two; that is pure downside, because it makes the game less consistent and forces players to remember which rolls are which.
But picking one and enforcing consistency has its own downside: there can be advantages to one or the other in certain situations, but if you enforce consistency you cannot use the “better” approach when it would make sense. For examples:
Roll-under has the nice property for percentile rolls that your target number is also your chance of success: if you must roll a 20 or less on a d100, you have a 20% chance of succeeding. For roll-over, the same 20% chance would be a roll above 80—you have to do 100−x to determine your odds each time.
On the other hand, roll-over works much better for unbounded numbers: you can always increase a target number in roll-over, but decreasing a target number in roll-under is somewhat awkward when it gets negative.
In short, by not having the game consistently use one or the other, you are free to pick whichever is appropriate for a given roll, not being constrained by the game using the other type for everything else. The downside is, the freer you are with this—the more you use whatever roll type seems most appropriate for each roll, the harder it’s going to be for players to remember which rolls are which.
I've been a GM and a player in exclusive roll-over systems like Pathfinder and Homebrewed D20 systems with both exclusive roll-under and combined mechanics. This is my experience, it may not be a perfect answer but hopefully it helps.
First a comparison of the aspects that stand out to me about the two systems as a GM.
Roll-over: I've found that the roll-over mechanic is far easier and quicker to fudge when you're putting something together on the fly. I've also found that each individual roll tends to take longer to work out, there's more math involved in getting to the final result, disorganised players make this much worse.
Roll-under: Tends to take more prepwork and is less intuitive when you're setting up, so it's much harder to work on the fly. Once you have the numbers set it's very quick and simple to run for people who are used to it, when you have a group who are either long time players of dedicated roll-over systems or who play dice pool games like Shadowrun getting them into the roll-under habit can be amazingly hard work.
As a player I found the two mechanics to be much the same, I have a target and I get it or I don't, again roll-over takes longer to work out the result for, if there are a lot of bonuses etc... but not that much longer if I'm well organised.
When it comes to combination systems the first system I ever played extensively was a homebrew D20 system that used both under- and over-rolls and at the time I found it reasonably straight forward. A couple of years ago, having played Pathfinder exclusively for several years in the meantime, I went back to it and was amazed by how confusing it was to get back into the habit of most of the game being on over-rolls but having several of the most important mechanics work on a roll-under basis. I ended up having to give the GM my finished roll numbers and trust he had it together, which didn't always work.
In short I don't find that there's a lot to differentiate the two systems but I do find an exclusive system of either roll-under or roll-over more straightforward. Exclusive systems are simpler playing habits to get into they don't have the added complexity of "what kind of roll is this?", all rolls are on the same footing.
I know of a game where roll-over and roll-under mechanics are both used and to great effect.
In Trollbabe, the only numeric component of your sheet is your Target Number, a value between 2 and 9 that never changes during a single adventure.
This way, it is really clear that you can either be good at fighting or at casting spells (Or mediocre at both and a little less bad at social. Trollbabes are not very social women.)
Also, since you can only add or subtract 1 to the Target Number between sessions, it ties the rolls together more easily than "add 1 to this to subtract 1 to that".
Trollbabe has no modifiers to the roll, so the sum/subtract factors that Ash talks about in their answer do not apply.
