How to resolve multiple sources of cover when using a grid?

Question

The cover rules in the PHB say:

There are three degrees of cover. If a target is behind multiple sources of cover, only the most protective degree of cover applies; the degrees aren't added together. For example, if a target is behind a creature that gives half cover and a tree trunk that gives three-quarters cover, the target has three-quarters cover.

However the DMG (250/251) appears to have an alternate method for resolving multiple sources of cover:

To determine whether a target has cover against an attack or other effect on a grid, choose a corner of the attacker’s space or the point of origin of an area of effect. Then 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. If three or four of those lines are blocked but the attack can still reach the target (such as when the target is behind an arrow slit), the target has three-quarters cover.

The only case I can think where these might collide is something like the following:

Individually T would not get cover from D1 or D3 and only get half cover from D2. The DMG seems to indicate T might get full cover since all 4 lines would be blocked. However if you use the guidance from the PHB (as shown above) T would only have half cover.

Seems to me it's just a judgement call which interpretation is correct. Anyone know of any rules that clarify this other than a judgement call?

EDIT: assume D1, D2, and D3 are separate obstacles or monsters.

Maybe this makes it more clear:

Answer 1

It's a judgement call, but be consistent

You are right, those two methods are incompatible. It's a judgment call, it's up to you to choose which one makes the most sense.

Whatever you choose, you need to be consistent about applying it. You don't want to make uncertainty for your players, they need to know what is going to happen when they try to use cover, or fight enemies who are in cover. Otherwise, they can't make plans, and if you can't make plans you loose player agency.

In my experience, the PHB method works best until you run into a strange situation. The DMG method feels very gamey and I don't find it enjoyable. I use a hybrid method detailed below.

PHB

For each obstacle, consider what percentage of the creature's body is covered. Only the obstacle that covers the most percentage of the creature's body has an effect.

Pros: Usually it's obvious which cover is best. Takes into account how the creature is standing or what they are doing (eg crouching behind a box).

Cons: Not all that realistic, the creature's body may be 100% covered but the creature only gets half cover.

DMG

For each corner of the creature, consider if that corner is obstructed by any obstacle. The more corners are obstructed, the better the cover.

Pros: Very cut and dry, just draw the lines and there's no discussion needed.

Cons: Not all that realistic, the creature's body may be nearly 100% visible but the creature has total cover. Doesn't take into account what the creature is doing, doesn't take into account the visibility of a creature over an obstacle.

My Method

From the perspective of the attacker, consider what percentage of the creature's body is visible. Use this percentage to calculate what cover the creature should have.

Pros: More realistic, forces players to look through their character's eyes. Encourages players to describe what their character is doing and interacting with the environment.

Cons: Much more room for debate about where the target is, what they are doing, what the attacker can see. Could slow down gameplay if you aren't comfortable making decisive rulings. Encourages players to min-max their turn ("I stand flat behind the cactus with my arms going left/right matching the branches so I can't be seen").

Answer 2

It Depends on How Your Combat Is Represented

If You're Using Grids

Use the Dungeon Master Guide's rules found on page 250.

These rules are under the section Using Miniatures and reads:

The Player's Handbook offers simple rules for depicting combat using miniature figures on a grid. This section expands on that material.

The Player's Handbook rules for playing on a grid, on page 192, have new rules, such as for Squares, Entering a Square, and Corners. However, it also lists existing rules that are replaced with these specific grid based rules, ex. Speed and Ranges.

I think it's safe to make the leap that the DMG grid rules are applied in the same manner: they add additional rules where they didn't exist, such as Tactical Maps and Creature Size on Squares and Hexes, and replace rules that exist already, such as Line of Sight and Cover.

If You're Using Theater of the Mind

Use the Player's Handbook's rules found on page 196.

These are simple rules that are meant to be used when not using grids.

Do Not Combine These Rules

As you state in your post, these two rules are in conflict with each other and cannot, or should not, be used in tandem.