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In the description of familiars, it says:

For the purpose of effects related to number of Hit Dice, use the master’s character level or the familiar’s normal HD total, whichever is higher.

The familiar has one-half the master’s total hit points (not including temporary hit points), rounded down, regardless of its actual Hit Dice.

So a wizard with 10 HD and 40 HP will have a familiar with 10 HD and 20 HP. Let's assume this familiar's base creature only has 1 HD.

What happens when the familiar wears an Amulet of Health +6? Should it gains additional health based on its original HD (so +3 maxHP) or the HD granted by being a familiar (so +30 maxHP instead)? Should this be considered as one of the "effects related to number of Hit Dice"?

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The familiars hit points are not calculated as a PC's are, but a change in Constitution will affect them

The familiar has one-half the master’s total hit points (not including temporary hit points), rounded down, regardless of its actual Hit Dice.

This is different from the normal method to calculate hit points, which is described under Constitution:

Apply your constitution modifier to

  • Each roll of a Hit Die (though a penalty can never drop a result below 1—that is, a character always gains at least 1 hit point each time he or she advances in level).

If a character’s Constitution score changes enough to alter his or her Constitution modifier, the character’s hit points also increase or decrease accordingly.

The familiars hit points are calculated from the master's hit points, not by using hit dice and applying a constitution modifier per die when rolling them. You never add a modifier in generating them. In practice, this is irrelevant, as all the standard familiars (Bat, Cat, Hawk, Lizard, Owl, Rat, Raven, Snake, Toad, Weasel) have Con 10 or 11, so a modifier of 0.

The last sentence in the description of Constitution howerver is independent of how hit points are generated. It unconditionally states that a change in Constitution modifier will change the hit points.

This will apply to changes provided by a magic item, such as the amulet, or other sources, like when ability score loss from a monster weakened the familiar.

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    \$\begingroup\$ Does that mean all ability damage/drain towards a familiar's constitution would not affect a familiar's hit point as well, since it is locked in a fixed amount? \$\endgroup\$ Jun 21, 2023 at 22:18
  • \$\begingroup\$ @TerryWindwalker I dug a bit deeper around, and I updated my conclusion. As I originally had answered, yes, that would have been the case. But I think the hp change caused by con change is independent of how hp were generated, and after all will apply. \$\endgroup\$ Jun 22, 2023 at 10:04

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