GMs are not like time-travelers, desperately trying to not impact the future. Fudging may impact the trajectory of play, yes. But so does every other ruling or rules-decision made by the GM. Not to mention how the adventure-design and encounter-design decisions by the GM impact play. The whole idea that somehow the GM needs to avoid changing trajectory of play is kind of illogical.
For some approaches to RPGing, there are categories of GM decision-making which serve different functions, and are subject to different constraints.
Some systems state these differences expressly (typically, more modern systems using a developed vocabulary). Others make them implicit (eg Gygax's DMG, now more than 35 years old).
For my purposes, I can divide GM decision-making into at least three different categories: (1) rules adjudication; (2) action resolution; (3) fictional content introduction (eg drawing maps, writing up keys, framing encounters etc).
In relation to (1) I prefer to be overt and consensual, but I do expect my players to defer to me if consensus is hard to reach, especially when they have an interest (in terms of PC power) in the outcome.
In relation to (2) I am overt. My players can see my dice. I explain what the outcomes of action resolution are. If the players are confused or uncertain, I clarify. If I forget something that is relevant, my players hold me to account.
Sometimes (1) and (2) can run together, in the context of a complex action declaration at the margin of the rules. In a good rules system, that doesn't happen too often. (Or perhaps I should say - one of my markers for a good rules system is that this doesn't happen too often.)
On (3), I assert full authority as a GM, including the authority to depart from pre-prepared notes if I think it will serve the purposes of the game. (If I was running Gygaxian dungeoncrawls then I would not depart, because that would undermine the purpose of the game, which is prudent exploration. But I don't run a Gygaxian game.)
Which leads to:
You're saying changing a monsters hit points is cheating, but having more monsters simply show up is perfectly valid?
I already discussed this upthread, I think in reply to you.
Changing hit points is a
covert manipulation of the action resolution mechanics. Having more monsters show up is an
overt introduction of new fictional content.
The difference between the two mightn't matter to everyone, or even to many, but it matters to some, including me. Here are three reasons: first, introducing new content is
overt. The players can see what I (as GM) am doing. They can respond to it (with groans, with wry smiles, with complaints, as seems appropriate). That contributes to the social aspect of play, and also helps me (as GM) understand the effects that my decisions are having on play.
Second, new monsters are
new fiction. They mean a change not just in mechanical difficulty, but in the fictional positioning of the PCs. The players can respond to this (via their PCs). It helps determine the shape the game takes.
Here is an example of what I mean.
Third, new monsters (at least in some systems, such as 4e) which change the balance of the encounter do so in a way that feeds transparently into other aspects of the game (eg in 4e, the XP and milestone systems).
That's not to say that introducing new monsters is acceptable all the time or at all tables. In Gygaxian play, which is based around skillful planning and the deployment of limited resources, introducing new monsters can be as bad as fudging, because it undermines the players' earlier choices (about resource use, for instance). 4e is very different in this respect - while it does involve resource play, it doesn't have anything really analogous to a classic nova round or gank round. The players can't burn all their resources at once, and so bringing in new opponents might require them to dig deeper, but generally isn't in danger of invalidating/undermining earlier choices.
As I already, said, these differences obviously aren't salient to everyone. But I've tried to set out the context in which they are salient to me.
the difference between you and someone who modifies hit points on the fly is really just a matter of the scale at which modification happens.
I don't see anything to do with
scale. It's about transparency vs secrecy, and the difference between action resolution and introducing new content into the shared fiction.
unless you show your players all "DM only stuff "at all times, they can't be sure you're not fudging.
I'm not sure this follows.
For instance, a GM might say to his/her group "I don't fudge." If the group know that the GM is in general a truth-telling person, then they can be sure s/he's not fudging without scrutinising him/her at every moment.
I'm curious, do you allow the players to look at the monster stats while you're playing? Do you tell them how many HP the monsters are currently at? Do you tell them the DCs of all checks before they roll? Do you let them read your notes for the game?
I find that very interesting, and to me not D&D at all.
In my 4e game, monster stats are knowable via skill checks (but these don't reveal hit points, although the players have got a pretty robust sense of rough hit point totals for the creatures their PCs face).
Whether or not I reveal hit point totals in the course of play I decide on a case-by-case basis. I do reveal when a monster becomes bloodied - that's a rule in 4e - but whether I reveal anything more detailed depends on whether I think it will improve the mood and "vibe" of the game. Sometimes if a monster is left on 1 hp it is fun to taunt the players!
When Lolth had 307 hp left and the PCs had to reduce her to zero at interrupt speed before she discorporated, I let the players have a running total of her hit points because it added to the tension/suspense - would they hurt her enough?
On the DCs of checks, generally I tell them because they need to know whether or not they want to deploy resources to buff themselves.
No, I don't let the players read my notes. That would spoil the big reveals.
As to whether or not what I've described is D&D to you, it is D&D to me. People approach the game in different ways. That is why blanket claims can misfire, like the blanket claim that fudging dice, or hit points, is just another tool in the GM's toolbox.