It follows that dice rolls / stats in general are reserved for situations the author doesn’t actually care about. This, I think, makes it much harder to gain meaningful choices out of them.
Oh, I’m well aware rand % n slightly favoring smaller values is probably insignificant in the grand scheme for any n likely to be used. Heck, given a suitable seed value, I suspect there are probably mass produced dice with more bias due to manufacturing imperfections, especially for round edged acrylic or resin dice that have undergone the dunk and tumble method of finishing. Still, unless I was specifically simulating physical dice rolls or some other physical randomizer, I’d probably still base my probabilities on having a power of 2 as the denominator when expressed as a fraction.
As for percentages and narrative, in my experience, the type of games most likely to display hit percentages, damage estimates, player stats, etc. or explain their mechanics in-depth are RPGs with turn-based combat and ones where little effort is made to integrate story and gameplay. In my experience, more action oriented games are less likely to give stats in any significant detail, though action games also tend to make hitting a matter of skill rather than chance. Of course, if a game is popular enough, even if it’s stats are completely opaque, players will figure out the minutia of just about every mechanic, if not reverse engineer the game entirely to get the exact values and formulas.
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But we aren’t stuck with powers of two. It’s easy enough to get balanced results regardless of range and using the naive power of two range generators is only for when you don’t care about that imbalance.
That’s what I think. If the player is shown a probability in terms of a percentage, they should get some guidance in how to interpret it. Unless testing their understanding of stats is the point of the game. There’s also the idea of showing the player a probability specifically to give them a chance to practice interpreting probabilities.
But you could also reconsider whether a percentage is even a helpful way to communicate that information. For instance if you’ve put in a hard cap on something randomized, that information is more useful than how exactly it’s randomized. To use Brogue as an example again, it guarantees you’ll find a food ration (or equivalent) every three levels. That’s more useful to know than the prior probability of finding food on a given level.
Brogue guarantees food on at least every fourth level but can be generated more often. There are also a few other important types of items (enchants, life potions, and strength potions) that have some guarantees about how often they are generated. Everything else is just random by some probability per level, regardless of how many of each type has already been generated.
This was always known and the source code is available for anyone interested in the exact numbers.
That the game provides more information than just the to-hit-% is also because that provides some useful information about how much damage is dealt. The game never displays things like numeric remaining hit points or how much damage a weapon or enemy can do, so being told “it can defeat you in 4 hits” or something like that is very useful to the player. It is not only about displaying probabilities.
I am not sure about UFO/XCOM. Even if I bought almost all games in the series I have barely played any. It is a project for… when I retire maybe? Seems time-consuming and there are so many other games to play. And I can’t even remember the names of the old games (released as UFO or XCOM in different countries?). But let’s just say I was thinking about the new XCOM 2 since that seems to be the game everyone agrees about it lying about probabilities. (I thought the very old, original, DOS game did it as well, but I can not find any source for that now.)
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It is an interesting case, because everyone felt like the 2012 game was showing the wrong percentages (“How can a 45 percent shot miss every time?”) so lying about them in the sequel was really about trying to please the audience.
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