mqstout: Only tangentially related to the thread, but Guild Wars had numerous builds (especially early in its life cycle) that having the lowest max HP possible were best. (Because a certain skill prevents you from losing max than a maximum percentage of your maximum HP per hit.) Of course, that game's HP growth were very much fixed, within a very narrow range of gear. One particular trash quest reward you get early in the game (during the training/tutorial area) has larger than normal HP penalty associated with it, and that's the only time you can get it. If you sell it, you can't get another.
Reminds me of the HP situation in Dragon Wars. What's worth noting about it is the following:
* Health is expensive; one HP costs 2 skill points, which is a full level's worth. (Combat and magic skills have the same cost (except fistfighting, which is 1, and learning a new magic skill, which is 5 or 10.)
* Bandage (2 SP per point, just like Health) can heal a character, but only up to 10 + its level (so Bandage 2 heals you up to 12).
* Then there's stun, which starts each battle at the character's max health. Attacks that do health damage do double that to stun.
* A character with 0 stun is stunned; said characters can't act, but can be revived with a healing spell or the end of combat. While stunned, the character won't be targeted by enemies and will be immune to all damage.
* A character with 0 health is dead, which can only be cured by going to a specific out-of-the-way location. (Usually, a death means a reload in this game.)
* As a result, a character with higher max health but the same current health is more likely to run out of health before stun, and that's not good, as death is more severe than stunning. Hence, higher max health is not good, as it puts the character at risk unless you use healing magic (as opposed to just Bandage).
I could also mention the original Zelda, which has this quirk:
* At full health, you can shoot sword beams, which allows you to hit enemies on the other side of the screen with your sword. (Otherwise, the sword's range is only about 1 tile.)
* You start the game with 3 hearths of life, both current and maximum. This gives you sword beams right away.
* If you continue after death or reload a save, you start with only 3 hearts of current health. If you've collected at least one heart container, then you do not get sword beams.
(Another interesting case is Undertale, where higher current HP means you take more damage, though higher max HP isn't strictly bad in and of itself.)