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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?

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    \$\begingroup\$ I'm suddenly imagining an old soldier with the constitution of a mountain, who has no idea why... the only constant is he takes off his amulet every night to sleep, and puts it back on the next day, like he's done every night for decades. \$\endgroup\$ – doppelgreener Aug 25 '14 at 13:56
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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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    \$\begingroup\$ Note, it does not discuss current hit points reducing, but if your current ends up higher than your max because your max was reduced, your current goes down to your new maximum. \$\endgroup\$ – Aviose Aug 27 '14 at 16:17
  • \$\begingroup\$ "any current HP over your new Max HP are lost, too." That seems logical, but where is it explicitly stated? I couldn't find it. \$\endgroup\$ – GrandOpener Jan 6 at 15:43
  • \$\begingroup\$ @GrandOpener not being able to exceed the maximum is it's definition. It's the upper limit. Related are temporary hit points, which are a separate pool not related to your maximum hp. \$\endgroup\$ – GcL Jan 9 at 20:17
  • \$\begingroup\$ @GcL I'll grant that you cannot have more current hp than maximum. That's what the word means. But as far as I can search, there is no mention of what happens when an effect would otherwise violate that restriction. Just for the sake of example, some theoretical resolutions: excess current hp is lost, excess current hp is converted to temporary, max hp change does not take effect because it would be invalid, etc. There are tons of ways it could be ruled. The ruling that current hp are lost is intuitive and logical, but thus far I cannot find any source where it is explicit in RAW. \$\endgroup\$ – GrandOpener Jan 9 at 20:24
  • \$\begingroup\$ @GrandOpener awarding temporary hit points is a reasonable approach, but that would be a house rule. The rules state that the maximum hp change down. Since you can't exceed the maximum, you end up with fewer hit points. There is no provision for hp max only changes if it doesn't invalidate current hit points. As written, rules uses maximum to mean maximum and state what happens to that limit. Anything over that limit is disallowed by definition. \$\endgroup\$ – GcL Jan 9 at 20:36
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There are actually clear guidelines on this. (Thanks to GMNoob and Crico)

The next sentence in Basic is

Or if you’re 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

So if you put this on, and you had A Con score of 15 and you're, say L12. Then you'd gain 24 HP. If you take it off, and you still had a Con score of 15, then you'd lose those 24HP.

Something I had missed was that putting it on, gives you all of the HP as if your CON mod had always been 19. Which is cool (and a huge boon if you boost CON as a stat increase). So taking if off removing all of it's benefits makes sense.

Some things worth talking about though:

  • Obviously this pretty much eliminates any silly business with passing the item around. There's no benefit at all to putting it on and then taking it off.
  • Attunement should always be enforced with items like this. So if a PC finds that they aren't using the bonus HP regularly and their buddy is getting beat down, and they want to pass it on, you need to make sure they spend 2 short rests doing it, and that the newly attuned character doesn't already have 3 attuned items.
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    \$\begingroup\$ Note for future readers: Con mod changes only affect your max HP, not your current HP - unless your your current HP would be greater than your new max HP (in which case your current HP is reduced to your new max HP). \$\endgroup\$ – V2Blast Jan 6 at 8:22
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Answering the second, more specific part of your question...

(...) I fear that they will just pass the item around to increase everyone's max HP. how can I prevent that?

Attunement exists precisely to prevent this kind of abuse.

This is pre-prevented by the fact the amulet requires attunement. Changing who in the party is attuned to the item generally requires two short rests, one to voluntarily end one character's attunement, and another for another to attune.

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