If I have a reach weapon will the target get a cover with this setup:
T is target
X is me
F is Friend
I feel not, as I can do a straight line from the X square to the target, without crossing the F.
Am I correct?
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The Reach quality is a red herring. It doesn't affect whether or not cover applies. The only thing that it does here is allow the attacker to reach the target. With that in mind we can evaluate whether or not an attack from position 'X' incurs cover from position 'T'.
Walls, trees, creatures, and other obstacles can provide cover during combat, making a target more difficult to harm. A target can benefit from cover only when an attack or other effect originates on the opposite side of the cover...
... A target has half cover if an obstacle blocks at least half of its body. The obstacle might be a ... creature, whether that creature is an enemy or a friend. (emphasis mine)
p.250 and p.251 of the DMG have a chart/description.
To determine whether a target has cover against an attack or other effect on a grid, choose a corner of the attacker's space... trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle (including another creature), the target has half cover....
No matter which corner of the 'X' (I'd use 'A' for attacker, but meh) square you use, you're blocked from 1-2 corners of the 'T' square.
(It's worth noting that this may not be true for all sizes of creatures. If the target is huge, then a medium creature does not "block half of its body", for example)
(to reiterate) The cover description states "attack or other effect originates on the opposite side of the cover".
Let's take the following alternative configuration (Target, Creature, Attacker) and compare it against the raw text.
T - - C - - - - A
I don't know anyone who would say that 'A' invokes "half cover" attacking 'T'. Furthermore you can move 'A' infinitely out to the right and 'T' would still have "half cover" because you can't draw a line from a corner of 'A' to every corner of 'T' without hitting 'C' in the process.
It seems counter-intuitive to imply that a halfling gives the same sort of partial cover as a stone pillar because the smallest section of his "square" is in the way of the enemy "square".
It doesn't make sense that half (or less) of a source of half-cover would still provide half cover.
At my table? The attack does not originate from the opposite side, so it would not be considered.
What I would house-rule is:
If 3+ corners were blocked by a half cover source (i.e. a creature), then you would get half cover. Half cover is the lowest form of cover and since it's only two "lines" from attacker corner to target corners, it would get rounded down to nothing.