Is it arbitrary, and are the players unaware of it?
I think what's missing in this discussion is the idea of WHY the hit points are set to a particular value. When you put a monster into the game world with X hit points, why didn't you give him X+10 hit points or X-2 hit points? What was the criteria upon which you based X? (And don't just say "hit dice, Con mod, and size" because that begs the question; it makes me turn around and say, "Why didn't you give it more hit dice or higher Con mod? Why is that mage a 5th-level caster with 5 HD and not a 6th-level caster with 6 HD?") Some criteria I've seen include: how many hit points would make this monster an appropriate challenge; how many hit points does this monster need to fulfill its role in the story; how many hit points make sense for this monster to have in the game world; and I'm sure there are many other ways to do it.
Whatever criteria you use for assigning hit points, THAT should not change mid-fight. If, according to your criteria, you just made a mistake and got the HP value wrong, then adjust it on-the-fly, like you would fix any other mistake. Tell the players you're doing it, or not, depending on their preferences and expectations and your table's social contract. But it strikes me as weird to think that once a hit point figure is decided upon, it is written in stone and can never be changed mid-play, even if it turns out to be incorrect.
I think what's missing in this discussion is the idea of WHY the hit points are set to a particular value. When you put a monster into the game world with X hit points, why didn't you give him X+10 hit points or X-2 hit points? What was the criteria upon which you based X? (And don't just say "hit dice, Con mod, and size" because that begs the question; it makes me turn around and say, "Why didn't you give it more hit dice or higher Con mod? Why is that mage a 5th-level caster with 5 HD and not a 6th-level caster with 6 HD?") Some criteria I've seen include: how many hit points would make this monster an appropriate challenge; how many hit points does this monster need to fulfill its role in the story; how many hit points make sense for this monster to have in the game world; and I'm sure there are many other ways to do it.
Whatever criteria you use for assigning hit points, THAT should not change mid-fight. If, according to your criteria, you just made a mistake and got the HP value wrong, then adjust it on-the-fly, like you would fix any other mistake. Tell the players you're doing it, or not, depending on their preferences and expectations and your table's social contract. But it strikes me as weird to think that once a hit point figure is decided upon, it is written in stone and can never be changed mid-play, even if it turns out to be incorrect.