How does shield guardian damage get transferred along a chain?

Question

Related to this question about the Shield Guardian's damage transferrance:

If the guardian is within 60 feet of the amulet's wearer, half of any damage the wearer takes (rounded up) is transferred to the guardian.

If a line of shield guardians each wear the amulet of the one next in line and the first one takes damage, what happens?

My assumption is that each takes half of the damage from the previous one until a shield guardian takes only 1 damage which would then get transferred down to the last shield guardian. Is this correct?

Answer 1

The important line is:

half of any damage the wearer takes (rounded up) is transferred to the guardian.

The three things to note are:

1. Transferred damage is always half
2. Transferred damage is always rounded up (contrary to the general rule)
3. Transferred damage is rounded before being taken from what's to be left behind, since it's explicitly a transfer

This means that odd numbers that result in fractional damage will distribute X to “sender” and X+1 to the “receiver”, where X and X+1 total to the original amount the “sender” suffered. So a Guardian receiving 5 damage will transfer 3 (2.5 rounded up) to the next Guardian, leaving only 2 for it to absorb.

This further means that if there's 1 point of damage to divide, half-rounded-up is 1, and so 1 damage is transferred, leaving behind zero damage to stay with the “sender”.

We can look at this as a branching tree, with each layer representing one step of cascading damage-assignment procedure. The first layer looks at just the damage on the first Shield Guardian; the second looks at how that gets distributed among the first and second Guardians; the third line looks at how it gets distributed among the first, second, and third Guardians; and so on until N Guardians. Only the last line represents the final distribution of damage; the intermediary lines are just to help us visualise the cascading divisions working down the chain and accurately arrive at the last line.

Guardian #   1 2  3  4  5  6  7  …  N

            14
            | \
            7  7
            |  | \
            7  3  4
            |  |  | \
            7  3  2  2
            |  |  |  | \
            7  3  2  1  1
            |  |  |  |  | \
            7  3  2  1  0  1
            |  |  |  |  |  | \
            7  3  2  1  0  0  1
            |  |  |  |  |  |  |  …
            |  |  |  |  |  |  |  … \
            7  3  2  1  0  0  0  …  1

As you can see, your intuition is correct: as soon as the transferred damage reaches 1 point, that Guardian's amulet will divide it, give 0.5 to that Guardian (rounded down, per normal rules) and then transfer 1 point (that is, 0.5 rounded up) to the next Guardian in the chain. That will continue for every following guardian, resulting in the last point of damage being allocated all the way down the chain to the last Guardian.

---

The net effect being relatively pointless is worth noting though: the first wearer of the amulet will still take the same amount of damage as if there was no chain of Guardians.

The only effect this has is to spread out the damage on the Guardian chain, ensuring individual Guardians survive longer. In effect, it will only help the Guardian Chain survive the demise of the owner, which has questionable benefit for said owner.

Answer 2

This wouldn't work as it is against the nature of Guardians

Understanding how damage transfer works RAW is a worthwhile exercise; this question and its current answer are valuable efforts. But I am going to frame-challenge here and assert that RAI, a Shield Guardian cannot wear the amulet of another Shield Guardian in any meaningful sense. Thus, this particular scenario, a 'shield guardian chain' cannot happen.

In making my point here I am fully aware that I can't prove most of my statements with the same level of rigor as I normally would seek to for a RAW answer. I ask that the reader bear in mind that this is coming from a good-faith RAI perspective.

Shield Guardians have masters

The shield guardian is a construct, made to serve. It might be sentient, but it is not free-willed. The question quotes the line in the stat block of the creature, "If the guardian is within 60 feet of the amulet's wearer, half of any damage the wearer takes (rounded up) is transferred to the guardian." However, in doing so, it ignores everything that is implied about the amulet's wearer which is explained in the 'lore' part of its entry in the Monster Manual:

A shield guardian treads beside its master, absorbing damage to keep its master alive as long as possible.
Master's Amulet. Every shield guardian has an amulet magically linked to it. A shield guardian can have only one corresponding amulet, and if that amulet is destroyed, the shield guardian is incapacitated until a replacement amulet is created...A shield guardian's solitary focus is to protect the amulet's wearer. The amulet's wearer can command the guardian to attack its enemies or to guard the wielder against attack.

The nature of the amulet, amulet wearer, and Shield Guardian is such that the wearer of the amulet is the master of the Guardian and commands it. To my reading, a Shield Guardian cannot be the master of another Shield Guardian because by its very nature it lacks the ability to command. Perhaps with a free-willed creature at the head of the chain orders might be passed along, much like a free-willed vampire lord might dominate greater but subservient undead which in turn dominate lesser mindless undead. Even this, however, goes against the RAI nature of the Guardians.

Note that destroying an amulet does not free the Guardian; the amulet is not some means of binding the will of the Guardian to that of its master. Rather, destroying the amulet renders the Guardian incapacitated; without a means for the master to communicate its will, the Guardian itself is inherently will-less and does nothing. Placing such a will-less individual in 'command' of another Guardian should not be any more possible than placing a guardian's own amulet on its person convert it into a free-willed creature serving itself.

Shield Guardians cannot issue commands

Further evidence that Guardians are not meant to command other Guardians can be seen in its stat block:

Languages understands commands given in any language but can't speak

Aside from the simple command 'come to the amulet's location' which can be delivered telepathically, all other commands to a Shield Guardian are made verbally. The Guardian hears and obeys. However, because the Guardian itself cannot speak, it is incapable of delivering its own commands, even if it could wear the amulet of another Guardian.

Shield Guardians might not be able to wear amulets

Consider what is implied by the phrase 'wearing' a magic item (emphases mine):

Using a magic item's properties might mean wearing or wielding it. A magic item meant to be worn must be donned in the intended fashion: boots go on the feet, gloves on the hands, hats and helmets on the head, and rings on the finger...In most cases, a magic item that's meant to be worn can fit a creature regardless of size or build. Many magic garments are made to be easily adjustable, or they magically adjust themselves to the wearer. Rare exceptions exist. If the story suggests a good reason for an item to fit only creatures of a certain size or shape, you can rule that it doesn't adjust...When a nonhumanoid tries to wear an item, use your discretion as to whether the item functions as intended. A ring placed on a tentacle might work, but a creature with a snakelike tail instead of legs can't wear boots.

This passage is focused primarily on whether an item can physically fit a body type or not. Shield Guardians are in fact not Humanoids, they are Constructs, and they are Large. Since amulets are typically made for Medium wizards, as well as "princes, nobles, and crime lords", we can just assume that the amulets are an example of a magic item that does not change its size for the wearer - anything that would comfortably fit a Medium wizard will simply not fit around the neck of a Large Guardian.

More metaphorically and admittedly speculatively, we can assert that a Guardian cannot wear an amulet "in the intended fashion", if the intended fashion is to wear it in such a way so as to command another Shield Guardian. The Guardian simply has no intent to command. Put this way, while it can carry the amulet of another Guardian, it cannot 'wear' it because it lacks the intent to do so.

Looking at the array of information presented beyond the passage about damage transfer, I would rule that placing the amulet for one guardian on another has neither given the Guardian a true master nor created the "bound" connection that makes the damage transfer possible.