First, to adress you absurd misreading about the dungeon complex. If you kill off every enemy that is engaged in combat with you before more reinforcements arive (which odds are you will unless your DM hates you) then you will be rolling initiative again when the next wave of reinforcements find you (which you could potentially avoid by moving to a different location between combat encounters. The act of rolling initiative is done at the begining of each combat encounter. The whole dungeon being alerted will not circumvent this unless you are unlucky enough to have new waves of reinforcements constantly arive before you kill the last enemy (or your DM hates you).
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Typically your going to clear the first wave of reinforcements before the next wave arrives. In a properly structured dungeon you will begin a new encounter with each new wave of reinforcements after the first if you managed to alarm the whole dungeon. You should find yourself with on average 2-3 rounds of actions between each wave, which may be enough time to move to a different room, depending on how your party moves you could even extend thhe time between waves or successfully hide from the enemies fooling them into beliving that you may have fled the dungeon. If you find yourself facing seemingly endless waves with no break between them, then you should take the que to flee, in a situation like that the Factotum is not the only one screwed over, ANY CLASS would be screwed over for resources in that situation.
Or you know, if the Dungeon is properly designed, and the enemies are alerted, then whether or not they zerg rush you or build a barricade is their choice, and if they zerg rush you there is no reason to expect you to be able to kill everything before anything else can get there.
But hey, and class would be screwed under those circumstances! Except classes with at will abilities like Rogues, and classes with daily abilities like Wizards and Clerics and Druids and Beguilers and Dread Necros, and classes with encounter abilities that resetable with some kind of action like Warblades and Swordsages... So yeah, just everyone except Barbarians and Factotums is just fine.
As for your IP refilling per encounter... this is a RAW vs RAI argument. RAW you add to your remaining pool, RAI you REFILL your pool. If Factotum added IP to their remaining pool at the start of every encounter with no cap, then the class would be banned at nearly every DnD table. Many of the mistakes in RAW have pretty basic common sense RAI corrections. Take some time to browse boards and guides about the Factotum, you'll find that the common sence RAI interpretation is indeed REFILL IP.
So what you are saying is "The rule is obviously terrible, so obviously terrible that everyone knows you have to houserule it, and that's why it's a perfect rule that doesn't need houseruling!" Well I agree with some of that, specifically everything before the comma. And nothing after it. Again, if the rule is so garbage that it is not functional without houserule, then I'm right when I say that it's garbage you have to houserule.
Starting the day with a full pool of IP is not a houserule, name one resource (besides health) that you do not begin the day with a full pool of after a full 8 hours rest. There are none. Additionally your morning routine can be defined as a Miscelaneous Encounter.
Inspiration Points!
Beginning the day doesn't give you full of any resources except Barbarian Rage and Paladin Remove Disease. You don't have full spells when you wake up, you have the ability to prepare spells under the spell rules for your class. You don't have full Warblade manuevers, you have the ability to prepare manuevers under the Warblade rules. When you wake up in the morning as a Factotum you have the ability to gain IP as per the Factotum Rules, which is to say, when you have an encounter.
Look, I agree that the Factotum would be a much better class if they could just take 3 full round actions to restore their IP to whatever their max was (and their max was some much larger number, and they had any non shit class abilities) but that doesn't mean that they actually can.
The DM determining if your action counts as triggering an encounter or the first action of an encounter is not a houserule by any stretch of the mind. That is blatently an open rules interpretation, when the rules do not properly define something it is the DMs responsibility to make a call on how to proceed. If you take the time to read you DMG you'll find this is spelled out to you in black and white.
"also Houserule 2" means both go back to houserule 2, and that it is a different statement separate from the thing before also. I'm not calling DMs deciding what are encounter a houserule, but I am pointing out, (in the first part, before the "also") that if the answer to the question "is this and encounter" is "Yes and No, Both Neither, Whatever the DM decides" that the rules are vague and unhelpful, and you could totally write better rules by just not being an idiot, like this:
"A Factotum can refresh his IP pool to his maximum based on level by spending 3 consecutive full round actions doing nothing else." Then the answer is never yesno, it's just yes or no.
Are you seriously trying to call rolling initiative at the start of a combat encounter a houserule now? How dense can you be to belive that one? When you enter combat, you roll initiative and the encounter begins... look at that an enounter began so YES your IP refills to full. You encountered a monster, you began an encounter at that moment weither the combat started that turn or 2-3 turns later you began the combat encounter when you ENCOUNTERED the foe.
Look, if you can't read, that's really not my fault, take it up with your elementary school teachers. I never claimed that rolling init was a houserule, I said "Houserule 2 again" Which even if the fact that I'm specifically numbering the houserules didn't tell you that I was referring to the same houserule I had already labeled as 2, the part where I said "again" should have triggered some basic level of reading competence to figure out that I was referring to something I had previously called a houserule.
upon entering your first encounter your IP will reset to 10 (it won't add 10 to your remaining IP, you have a MAX on your IP pool defined by your level and the FoI feat). You will NOT stack you iP into 9000. If IP stacked the way you claim it does then the factotum would be absurldy over powered, especially if you misdefined encounters the way you seem to be.
So you are making up a houserules because the IP rules are dumb. Okay, and this leads you to claim that no houserules are needed why exactly?
No need. That clarification appears in the FAQ.
D&D® Frequently Asked Questions
Version 3.5: Date Updated 3/14/08
page 17
When playing a factotum (Dungeonscape, page 14), what
happens to inspiration points unspent at the end of the
encounter?
Unspent inspiration points are replaced when the factotum
returns to his full number of points once an encounter ends.
Yes, yes, I know that's not RAW in the book, or "official" errata, and what not, but it is actually not "just" someone's houserule, unlike your issues with defining "encounters".
So the rules are so bad that the designers had to pretend errata because they refuse to ever correct anything with errata and this means the rules are perfect? Yeah, spoiler alert, that means the rules are garbage and need to be houseruled.
"I can totally go online and find a non rules sources that tells me to ignore all the actual rules and use something else because the rules are ass, therefore the rules are perfect" wasn't true the last 400 times people pulled out WotC dumb attempts at stealth errata in the FAQ to defend the rules in the books, why would it now?