Why do many people prefer roll-high to roll-under?

The first TTRPGs I played, in 1979, were roll-high, being OD&D and AD&D1e. I was also exposed to roll-under Rune Quest early on, and and several other systems, varying between roll-high and roll-under. Back then, nobody seemed to feel that either mechanism had intrinsic appeal; it was a question of if the game worked as a whole.

This century, I've been encountering increasing numbers of people who feel that roll-high is more emotionally satisfying, or otherwise preferable, and that this is "obvious" to them. I'm baffled by this.

I have a slight preference for roll-under, because it's easier for me to figure out the odds of success. If they're too low, I'll look for some different action to take in the game. But this isn't a "won't play roll high games" thing, just a mild preference. I do see people saying on forums that they don't want to play any roll-under game.

Do players just associate bigger numbers with being "better" in some way? Is there some cultural factor I'm missing? Is this just a way of saying "I don't want to play any game that isn't like D&D"?

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Dirty, realism-hating munchkin powergamer
I’d say yes, more money, bigger house, higher score, I assume it is as simple as that

Mathematically both are the same and I don’t see why it would be easier or harder to know the odds of rolling 5 or less on a d20 vs rolling 15 or higher
You need to do a slight mathematical translation to figure out the odds for roll-high.

If your target number is 15, on roll under the odds are just the number times 5%, assuming that matching the number is a success.

If your target number is 15, on roll over the odds are (21-target) times 5%, assuming that matching the number is a success.

It's the THAC0 issue all over again. Yea, it's simple math, and a trivial near-immediate calculation if you have a decent head for numbers, but it is a slight increase to cognitive load. And it's a load that people who aren't strong with mental calculations notice.

Edgar Ironpelt

One advantage of roll-high, at least in the "roll and add the character's modifier" version, is that the GM can keep the target number secret while letting the player make the roll. With a roll-low system, the GM generally has to make the roll himself if he wants secrecy with regard to the result.

The player knowing how high he rolled, without necessarily knowing if he rolled high enough, creates what I find to be a good balance between player-knowledge and GM-secrecy.

A related advantage is that the quality of the PC's action is given right there by the roll-high result. In a roll-low system, an annoying and game-slowing "how much did he make the roll by" subtraction is called for.


Not your screen monkey (he/him)
It depends on what the goal of the mechanic is and what it represents. Rolling high works well for target numbers that may vary like a defense score and may have a number of modifiers. It also works well if incorporating some open-ended result like exploding dice and damage. Rolling under works well if there are relatively few modifiers to success or if you want the stat to roll under to be an easily represented chance of success.

Do players just associate bigger numbers with being "better" in some way?
Yes, I think that plays a larger role (I would confirm that intuition for myself, too).
The other thing is that with role-under systems you limit the scale on which you can roll. That's fine if we are mostly dealing with human or humanoid opposition, but can get a little tricky if you have human vs. giant or human vs. dragon (there are solutions, but IMO they detract from the simplicity of roll-under systems).
Personally, I still like roll-under, but prefer systems that have a Black Jack mechanic, i.e. roll as high as possible, but under your skill level (at least as an option).


Dirty, realism-hating munchkin powergamer
The biggest advantage to roll-under for a D&D-type system, by far, is that you can the unmodified stat value as a base difficulty for all sorts of checks, which feels very clean and elegant.

Roll-high works better if you have several different bonuses that can stack on a roll, since it will generally let you avoid any sort of subtraction.

I’d say yes, more money, bigger house, higher score, I assume it is as simple as that
That. It's fundamental psychology drilled into us from when we're school children. You don't aim for lower numerical grades, after all. If there was a system that generated alphabetical results rather than numerical people would favor A over F - and I've actually heard people playing Rolemaster complain that A crits are less severe than F crits and that's backward.


Bruce Baugh, Writer of Fortune
It’s very well established in studies of learning and applying what’s learned that almost everyone adds slightly faster than they subtract. (We multiply more quickly than we divide, too.) And then there’s the psychological factor noted above: to many people, trying to roll low feels like sort of aiming to lose even though the success has the same results. Aiming to roll high feels like accumulating victory - not to everyone, of course. I presume none of you are lying about your roll-under enjoyment, and you’re not alone. But the other way taps into common elements way deep in our brain meats.

An oddity of my own: rolling under feels good to me with percentiles but bad or at least not so good with 1d20. Even though it is very much viciously the same math and I have so much experience multiplying a score by 5 or dividing it by 5. What the heck is up with that?

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