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Let's assume we have some PCs moving along infinitely flat plains. In the air (some distance away) is a large creature with a rider that can cast spells. In optimal conditions (so there's normal daylight and no obstructions), how far from the PCs can the rider be and still see them?

Note that I've certainly seen the Light Sources and Illumination table, but that's not helpful. We're talking about natural light sources under optimal conditions; is there an official Pathfinder rule for how far PCs and NPCs can see?

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*waves hands* GM's discretion –  okeefe Jan 26 at 21:23
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@KRyan Spelling it out is helpful, but not necessary. We do expect people to read the tags: if someone replies with a 3.5e-based answer, they are in the wrong for not reading the tags, not the asker for not redundantly saying "Pathfinder" in the question. –  SevenSidedDie Jan 26 at 21:52
    
@SevenSidedDie Huh, for some reason I’d misunderstood the policy. I’ll admit that a lot of the theory around tags strike me as arcane and I don’t know it all that well. –  KRyan Jan 27 at 0:22

4 Answers 4

There is a +1 to the DC for perception when trying to see something for every 10 feet away it is from you. Therefore, you have a chance to see things that are less than 200 + 10*perception modifier feet away; if things are more than 100+10*perception feet away, you can't see them by taking 10, so that's about when I'd be rolling to see things. Of course, that assumes the object to be seen is average sized and there's neither favorable or unfavorable conditions. Darkness, objects in between, and so on will reduce visibility.

Of course, this is a bit silly: If a visible medium-sized creature (base DC 0, as per the "notice a visible creature" line; this creature is not attempting to use Stealth) stood at one goal-line of a football field and you stand at the other goal-line (300 feet away), you could only see him on a roll of 20 with a +10 to perception. Take ten and you have no idea he's there.

(It might not be as silly as it seems: Atomic Think Tank, the Mutants and Masterminds message board, found that, based on the known data for 20/20 vision in terms of spotting a human being not trying to hide, and distinguish some small number of details, the maximum distance is approximately 1 km. This neatly works out to the distance penalty for vision being +1/100 feet if you assume Taking 10 and a +0 to your Notice check.)

For ultimate silliness, @DuckTapeal points out that "the penalty to see the sun at noon is roughly -42 million". Of course, the size penalty for spotting a creature 30' by 30' is +8, and it goes up for each size category above that, so... What size category is the sun?

As @KRyan points out, by RAW, “The sun is colossal, because there is no size category larger than that. Colossal covers everything that is ‘64 ft. or more.’ That said, each size category is twice the size of the previous category, so we can extrapolate larger categories; if we do, the sun is about 232 ft. in diameter, or 26 size categories above colossal. However, the size penalty is just −4 per size category, so it would be −116 for 26 size categories above colossal.”

In short: The party can see as far as you want them to be able to see, unless the range is under about 50ft or so, at which point the rules make sense again.

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@KRyan That isn't correct. There are two different entries on the Perception table, one for "Notice a visible creature" at DC 0, and a different one for "Notice a creature using Stealth" at "Opposed by Stealth". It still, technically, takes a Perception roll to see something that isn't using stealth, if there are enough penalties involved. –  DuckTapeAl Jan 27 at 0:25
    
Please flag obsolete comments, as this seemed to be useful clarification. –  Brian Ballsun-Stanton Jan 27 at 4:02
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Personally, I interpret that table as the ability to actually notice something about the person... So it's more like "Can you see his facial features from the other side of a football field?" than "Can you see him at all?" But that's just my interpretation, not RAW. –  Bobson Jan 27 at 4:36
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Note that this same thing happens pretty much anywhere an inverse square law, or any other function with a non-one exponent, for that matter, is involved. Games designers, whether in D&D or other RPGs, or CCGs, arcade shooters, or any other type of game, tend to shoe-horn linear functions into anything non-linear. This works fine within a small enough scope (zoom in tight enough on any curve, and it will always eventually look straight), but tends to make things go flaky (at best) if you exceed the intended scale, or in many cases even if you just spend too much time in its extremes. –  Matthew Najmon Jan 28 at 20:00
    
When we discussed this on the Atomic Think Tank (Mutants and Masterminds message board), we found that, based on the known data for 20/20 vision in terms of spotting a human being not trying to hide, and distinguish some small number of details, the maximum distance is approximately 1 km. This neatly works out to the distance penalty for vision being +1/100 feet if you assume Taking 10 and a +0 to your Notice check. That may accommodate some of the issues with "why can't I see this person on the other side of the field". –  Sean Duggan Apr 18 at 13:21

There are distance limitations on Perception checks in the rules, establishing that sight is not limited only by cover or lack of light. The limitation doesn't appear to be an abstraction of cover since the likelihood of nearby cover is also mentioned apart from the distance limit. Based on the reasoning given in the various terrains, it appears that distance limitation represents an abstract combination of terrain folds, vegetation, distortions in the air, and simply the inability for an observer to distinguish an object from the background on which it visually sits. (See the part about visibility in mountains being both a very short number and alternatively very far as determined by the DM's map of ridgelines, and the visibility in the desert being limited in part by heat shimmers in the air.) Furthermore, these limitations are mentioned in addition to limitations caused by obstructions to light of sight, making these limitations explicitly apply even when you have line of sight and the target is not in cover:

In plains terrain, the maximum distance at which a Perception check for detecting the nearby presence of others can succeed is 6d6 × 40 feet, although the specifics of your map might restrict line of sight. Cover and concealment are not uncommon, so a good place of refuge is often nearby, if not right at hand.

Unfortunately, in the set of terrains they failed to include an aerial "terrain" or even an above-water terrain, so there are no rules-as-written distance limitations for flying creatures outside of terrain like forest (where the canopy would restrict vision between creatures on foot and in the air). The limitation in plains terrain is 6d6×40 feet, but I don't think anyone could convincingly argue that this applies to flying creatures, given the rules-as-written distance limitations in mountains (as mentioned above).

However, the precedents in RAW strongly imply that there is a limitation based solely on the fact that air can obstruct vision optically, but the DM is on their own to figure out what it should be. There is no RAW answer. Personally I would either try to develop a table based on real-world principles of visibility, or I would build something more game-able like "1 mile per size category" or something to that effect.

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On a clear day, the human eye can make out airplanes flying five miles above them. On a clear night, it can pick out a candle flame at comparable distances.

Generally speaking, Perception checks shouldn't be used at all for something that shouldn't be tricky to spot. If you want to make a check, you need some factor to make it tricky. Maybe it's dark or foggy. Maybe the object is camouflaged as something the characters would normally ignore. Maybe it's just not in a place they'd normally think to look.

For your specific example, I wouldn't assign a very high DC. There's no fog or cloud cover; the only thing the PCs really have to do is think to look up at the right time. I'm not sure I could justify a DC higher than 10 or so, if that's the only complicating factor.

If you want to make it harder, I can think of a few tricks that might up the DC some. Maybe the rider keeps himself between the sun and the PCs, so that the sun is in their eyes if they look his way; that ought to be worth a good +5. Or maybe he uses a minor illusion to turn himself and his mount blue, making them harder to spot; that could be another +5. With a couple of tricks like this, you could up the DC quite a bit.

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Definitely not fond of the idea of all the calculus that would be needed to figure out how far out diminishing perspective makes them appear as a fine object or larger and thus get (technical) size modifiers to the roll. –  CatLord Jan 28 at 17:45

Checks are only made if there is actually a challenge to the task, that is: if the player can fail.

So in your case one must assume that the target is actually trying to cover itself, which seems like a very challenging task for a rider in an infinite flat plain. So the difficulty to see that target should first be based on the success of the attempt to hide. If this is a flat failure and there are no other circumstances, the players will see the target.

One other circumstance could be the distance to the target (as you mentioned), which can become a challenge based on the resolution of the eye or the mirage-effect of the sun at certain weather conditions. As far as I am aware, there are no rules for either of those circumstances, so it boils down to a GM decision whether to take real-life values or just make a sophisticated guess.

Mathematically the projected size of a creature at a certain distance can be calculated using trigonometric functions, where the resulting size can then act as a size difficulty for the check.

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