[RPG] What happens to HP when Constitution decreases

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WotC recently released the Basic Rules for the DM, and with it came a few items like the Amulet of Health:

Wondrous item, uncommon (requires attunement)

Your Constitution is 19 while you wear this amulet. The amulet has no
effect on you if your Constitution is already 19 or higher.

The Basic Rules state at the end of Chapter 1, under "Beyond 1st Level":

When your Constitution modifier increases by 1, your hit point maximum
increases by 1 for each level you have attained. For example, when
Bruenor reaches 8th level as a fighter, he increases his Constitution
score from 17 to 18, thus increasing his Constitution modifier from +3
to +4. His hit point maximum then increases by 8.

But it doesn't explain what happens when the Constitution modifier decreases!

My players will soon get the Amulet as a reward, and I fear that they will just pass the item around to increase everyone's max HP; I want to prevent that. Are the HP lost when a character is no longer attuned to the Amulet?

Best Answer

PHB Chapter 7 says this about hit points under the "Constitution" subheading (p. 177):

If your Constitution modifier changes, your hit point maximum changes as well, as though you had the new modifier from 1st level. For example, [...] if you are 7th level and some effect lowers your Constitution score so as to reduce your Constitution modifier by 1, your hit point maximum is reduced by 7.

When your Con modifier somehow decreases by X, your Max Hit Points are decreased by an amount equal to X*Level.

What happens to HP when Constitution decreases? / Are the HP lost when a character is no longer attuned to the Amulet ?

If your Con modifier decreases, your Max Hit Points decrease; any current HP over your new Max HP are lost, too.

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