In Pathfinder and other d20, the higher the better. In WFRP, when it uses percentiles, the lower the better, the opposite for other dices such as damage and player's call for other rolls such as testing luck, using odd or even.
So it all depends on the system.
I do not recall any rolls that could pass or fail using the percentile dice in Pathfinder. Could you please provide an example?
Got one. Spell failure from armour.
You roll to check whether something happens so the low range is the occurrence of the event.
But why? If you have a 15% chance arcane spell failure, that could be 1-15 or 86-100.
How about a greater cloak of displacement, or simply full concealment. 50% either way.
I don't recall a hard and fast rule, but does it matter? Just set the standard at your table(s). Decide which end of the spectrum the event occurs on, or (if you want to complicate things) which end is "good" and "bad" for the player. Not sure if I like that, though; if you want your opponent both have concealment, your concealment works (he misses) on 81-100, but your attack hits (his concealment doesn't work) on 1-80... that feels weird and confusing to me.
Honestly it doesn't really matter. As long as you decide before the roll is made the odds are the same.
The general rule for pathfinder is the High is a pass and low is a fail, but as Agénor said in other systems it works the opposite way (notably in systems that are based around a d% roll - instead of a d20 roll - the lower roll is usually a pass).
The GMs saying "High or Low" is them giving the players a little more agency without really changing the odds (which I always think is a good thing).
Personally... I'd keep it simple. If a binary percentage is given, such as:
- caster_level% chance that Mage's Disjunction forces an artifact to save
- 95% chance that some powerful entity is going to be CHEESED OFF that you just smashed its artifact with Mage's Disjunction
- 20% miss chance from concealment
- 25% arcane spell failure chance
Then the thing happens on the low roll. That way, you always know that an n% chance occurs on {1...n} rather than {(101-n)...100}.
But why? If you have a 15% chance arcane spell failure, that could be 1-15 or 86-100.
To keep positive modifiers positive. If an event has p probability of happening and a circumstance gives an extra n% then the new odds are p+n.
You could play with 100-p-n. It isn't how the rest of the system goes anymore but once upon a time, there was something called THAC0^^
If you have a 15% chance of something happening I'd use 01-15 just to avoid requiring an extra step of mental arithmetic. Like Agénor said above though, the simplest way hasn't always been the rules-as-written way in the past.
it doesn't matter really, but I &$*#&%*( hate it when people "go high"
There isn't a solid rule for it, it's totally personal preference.
As a GM, if it's a percentage chance that isn't 50/50 then it's low. Because, yes, 20% chance can mean 81-100 on the die, but every time someone rolls an 80 someone in any group is going to stop and think about it for too long.
Never mind if there's somehow a 37% chance of something happening.
Oh, and when it's a 50/50 chance I'll ask for high or low and grab any random die I have and roll it rather than percentile.
On 50/50, I generally just grab a die and call "Even" [such that rolling the maximum number is always good] and about half the time it works ;)
The real issue that comes up around this is when doing a play-by-post format, where the number gets locked in, but the rest of the post doesn't. Players can do a preview of their die roll, then edit the post and call high/low based on what the die roll is. If you are playing in that kind of format, as a GM insist on a specific standard.
For what it's worth: PF2 appearantly uses "flat checks" with a d20 where higher is better. I found only a single application for the d% in the entire PF2 CRB: The rod of wonder, with its really fine-grained probabilities for different effects.
And, honestly, most cases can be covered with a d10 (if there are 10% steps) or a d20 (for 5% ones). 50/50 can be done with any dice, but that was already mentioned. Personally I prefer "you need 3+ on d10 to beat concealment" over dealing with a d%.