
Human Fighter |

To determine whether your target has cover from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target's square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the target has cover (+4 to AC).
Here are some examples of situations that I have questions of.
t=target
x=open space
-=wall that isn't a 5ft square, but separates squares
p=player
Example 1:
txxx
- --
pxxx
Example 2:
p------t
xxxxxxxx
Example 3:
xxxxxxt
-x-----
pxxxxxx
As I understand the rules, you take your corner of your square, and then base your sight or whatever to begin drawing lines. If you can get all of the enemies corners, then you don't have cover being an issue.
I need help understanding what is meant in regards to borders.
Example 2, you wouldn't be able to see the target really, but you still touch 2 of their squares.

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Imagine an archer in a 5 foot hallway.
It's technically not possible to not draw a line from any corner of the archer's square to all corners of an enemy's square without passing thru a solid line.
Yet the enemy does not have cover against the archer.
Does that help?
Just to give the next step here: there's a difference between "pass through" and "pass along".

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Can you peak in Pathfinder around corners while in combat, or do you absolutely need to be standing out? Maybe this would settle some of my issues.
The rules do allow you to peak corners.
Consider the example below:
[1]
[ ][ ][ ][ ][ ][2]
If Character2 draws a line from the upper left corner of his square to the upper right corner of Character1's square, he can shoot him. Character2 has cover from Character1, but Character1 does not have cover from Character2
Consider the example below:
[1][ ][ ][ ][ ][2]
Drawing a line from either of the upper corners of Character1 to Character2 shows that the line would pass directly through the edge. In those cases, both shooters would have 100% Cover/Concealment. Some understanding GMs may allow players to peak around the corner and perhaps hold an action to shoot a target that peaks, but Pathfinder does not have rules for that.

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This medium is not exactly the best for drawing pictures. Essentially, you do this:
1) Pick one corner of yours.
2) from that corner draw a line to all of the corners of your target.
3) if any of these lines cross a wall, another creature, or any intervening object, your target has cover.
Note, the line has to CROSS not move along a barrier for it to count.

Human Fighter |

Red, the first example you did has Character2 able to take his upper left, and touch ALL of Character1's corners, and not just their upper right. Character2 could even use his upper right as well.
My example 1 is hard to create, but so people understand I'll do it again and explain in more detail.
(more space because avatar screws things up.)
(more)
txxx
- --
pxxx
in the -'s there is an empty one on the 2nd space. The -'s are not spaces at all, but representing a wall that in in between the 5ft squares. So, one -, then a door, then continuing wall. You take P's upper right corner, and you can draw a line to all of T's corners. Makes sense?

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You take P's upper right corner, and you can draw a line to all of T's corners.
Can you find anything in the cover rules that care about anything else but this statement?
EDIT: But make sure your statement is actually true; if the corner of your square is inside a substantial thickness of wall, that could change whether or not you're truly able to draw a line to all the target's corners.

Jodokai |

Red, the first example you did has Character2 able to take his upper left, and touch ALL of Character1's corners, and not just their upper right. Character2 could even use his upper right as well.
My example 1 is hard to create, but so people understand I'll do it again and explain in more detail.
(more space because avatar screws things up.)
(more)txxx
- --
pxxxin the -'s there is an empty one on the 2nd space. The -'s are not spaces at all, but representing a wall that in in between the 5ft squares. So, one -, then a door, then continuing wall. You take P's upper right corner, and you can draw a line to all of T's corners. Makes sense?
I haven't drawn it on a map yet, but it looks like P's line would hit the left corners of T, the bottom one especially. If I'm wrong with my naked eye ball and you can hit all the corners with straight lines, no cover.

Human Fighter |

I guess I need a better example.
|tD___
|pD
Imagine between t and p is a wall that doesn't take up a 5 ft, but just separates. D are just open spaces but between them is a doorway or an opening. Everything else on the right is just the wall that continues on, and open spaces are above and below.
You would take the top right corner of P, and you can just touch all of the corners of t. It seems weird, but this is to my understanding of the rules.

Blakmane |

Making it even simpler might help to understand:
t-p
- is a border wall. The two characters are adjacent on the grid. Above and below the wall are empty borders. All grid squares are open.
t has no cover against ranged attacks from p, but does against melee attacks. It's a bit odd, but easy enough to handwave.

Claxon |

May I suggest moving to drawing pictures and linking them? Because text sucks to illustrate. I'm having a hard time following.
The verbal explaination is that if any line from a corner of your square to the corner of all your targets squares passes through a solid barrier, they have cover.
Is the picture on this page at all similar to any of your situations?

fretgod99 |

I wouldn't allow the peak around to avoid cover in the case where the archer and the target are standing next to a doorway on opposite sides of a wall that exists on the border between the 5' spaces.
The only reason the claim can be made that no cover exists is because we're treating the wall like a two dimensional object with no depth. The corner of archer's space nearest the door will not cross any boundaries when trying to reach any corners of the target's square, but only because of the limitations of the battle map. There is actual depth to the wall, whether it's accurately represented on the map or not.
Besides, if the archer standing below and to the left of a door can shoot at a target standing above and to the right of the door, without that target getting cover, then the target gets an AoO on the archer if wielding a reach weapon because cover from a reach weapon is determined the same way as cover for ranged weapons. That seems silly to me. They both should get cover because walls in actually have depth, despite the limitations of drawings on a battle map.
YMMV, but I'm using GM discretion here to say cover applies.

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Referring to the links Human fighter posted.
Link#1/Link#3: Sorry, but these are terrible examples. Walls (except for magical effects) almost always have thickness. In most cases, 6 inches is very reasonable...unless you are stating that the walls in your example are made of something like 1/4 inch plate steel.
Link#2: This is the second example I gave above and there are no rules in Pathfinder for this...so RAW, neither shooter can see, let alone target the other. A GM would have to adjudicate this based on what each shooter proposes to do. If it was me, I would let the player describe what he wants to do and then do my best to come up with a ruling that allows him to do it and what modifiers to impose.
Link#1: As with #2, by RAW, neither shooter could target the other.
Link#3: This is a unique situation where the rules fail for the blue creature. An perceptive GM would be able to see that there is a sliver of opening in which blue can fire at yellow, despite the fact that none of the blue's corners can actually connect to any of yellows corners. Of course, yellow has great cover (I would say +8)
Just remember that the rules do not always cover EVERY contingency. GMs need to use their knowledge and rule experience to adjudicate grey areas or corner cases (pun completely intended). While it is nice to have consistent rules to cover every situation, there will be many times when a situation just has to be adjudicated based on it's unique circumstances.
PS: Tell me that those aren't the best minis you have? Please!!!! :)

Human Fighter |

Running published games, they have the map where the walls aren't taking an entire 5ft square, but are just in the middle of two empty spaces.
RedDog, you say by RAW that example #1 won't work, but you'd just take the upper right corner of yellow and draw it to all the other corners of the blue target.
Anyone may feel free to donate me GM supplies. For PFS I use the munchkin colors along with colored note cards so I can have all creatures with separate initiative. It helps players and myself keep track of who is who, and the players notecards are white with numbers associated to a given player at the table. I'm still working to make the game move faster as I continue to GM.
PS
I am the munchkin champion!

wraithstrike |

1 and 2--> If the walls are tall enough to count as total cover then nobody is attacking anyone. If the walls are just low barriers then it should be partial cover.
3. Same as 1 and 2
How tall are the walls? A wall does not have to occupy an entire square to provide cover. It just has to cover all or part of a creature. If the creatures can see each other that normally means partial cover which leads to the +4 AC unless the GM decides otherwise.
PS: I am assuming the walls are there they are, but not tall enough to count as total cover.
PS2: The height of the walls in relation to the creatures is also a factor making this a GM call.
PS3: I am also assuming the arms of the strange creature do not count as the space it occupies. Get a normal mini with the extra parts to make it more clear as to where the creature actually is.

wraithstrike |

The walls connect to the ceiling, and each mini occupies a 5ft square which they're stationed in.
Again, this is trying to address the cover rules on taking corners, and connecting them to the corners of your target.
I understand what you are trying to do. Basically if the line passes through the object(wall or otherwise) then there is cover.
If this wall also goes from one side of the square to the other side then the only thing left to address is how much space that creature actually takes up.
If the creature takes up a 10 foot area in scenario 3 then then it is possible to take a shot without cover for the yellow figure, but from what I see the blue creature does not get a clear shot assuming it even has a ranged attack.
Below is your pic showing how the yellow archer gets his attack without cover since he can draw a line from the corner of his square to all corners of the enemy's square without anything blocking the lines.

Human Fighter |

The blue mini isn't in that square that you marked the corners to hit, but adjacent to the wall. It's only taking up a 5 ft square, and is not a large size creature. I do understand that someone with range can choose any of the squares a creature takes to determine if there is cover or not.
To me, it seems like example 1 and 3 you can shoot without cover, but example 2 is really weird stuff, because technically, you can touch two of their corners.

fretgod99 |

Technically (if we use a depth-less wall), there is no cover in the first image. The top right corner of the Munchkin can reach every corner of of the Finger Puppet. It passes along the adjacent wall to the bottom to corners and is otherwise unimpeded to the top two corners.
The same process works for image 3. Munchkin can attack Finger Puppet with no cover because the line from the top right corner passes along the wall, but never crosses it.
This is the issue I was discussing in my post earlier. This works if you assume the wall has no depth. If the wall has any depth and isn't simply a two dimensional object, then no line from the top right corner of Munchkin's square can reach the left corners of Finger Puppet's square in image 1. Either there is total cover or at the very least improved cover. Arguably one or two corners could be reached (depending on depth) in image 3, but lines to the two corners flush to wall would pass through the wall. So at least cover if not improved cover.
So perhaps RAW might suggest that there is no cover in 1 & 3, but that's only if we assume no depth to the intervening wall. So my decision would determine cover based upon the existence of a three dimensional wall.
At best, we're looking at improved cover for image 2. In all likelihood, I probably would adjudicate that as being total cover in my own games.