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.