The spell Time Stop allows you take take extra rounds of action during your turn. For the purpose of effects that have the duration of "End of Turn", would buffing yourself with something that lasted till the End of Turn be gone in 1 round of Time Stop? Cite sources if possible, please.
[RPG] How does Time Stop interact with “End of Turn” durations
combatpathfinder-1espellstime
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All effects with a fixed duration measurable in rounds end just before the beginning of one of your turns. (Otherwise, their duration would be too short to be a full round, or a full 2 rounds, etc.)
We can see this by looking at a duration of 1 round, and applying the same logic to the case of 10 rounds.
A duration of 1 round, measured in turns, is “each participant in a battle takes a turn” (PHB, p. 189) — or put another way, one turn each for you and everyone else. Since you enjoy the benefits of an effect like Rage on the turn you activate it, that's one turn of effect for you; everyone afterward also “enjoys” the effect for their turn after you, until the end of the turn of the creature just before your next turn. When your next turn begins, you would be enjoying the effect for a second turn, therefore the 2nd round of the effect begins as your 2nd turn begins.
Thus the dividing line between the rounds, for an effect you enjoy on its first turn of activation, is just as/before one of your turns begins.
(There are a few exceptions, but these explicitly say when they end in relation to your turn. Most are single-round spells that alter your next action, which explicitly extend to the end of you next round so that they're not useless — you can think of effects like that as beginning to be “enjoyed” by you and everyone else only after the end of your 1st turn.)
Now we can extend this out to 10 turns, to see that Rage ends just before your 11th turn begins. For simplicity, we'll call the turn an effect starts “your 1st turn”, no matter how long combat has been.
A duration of 1 round begins on your 1st turn and ends just before the beginning of your 2nd (next) turn. Otherwise, it would not be a full round long.
A duration of 2 rounds begins on your 1st turn and ends just before the beginning of your 3rd turn. Otherwise, it would not be a full 2 rounds long.
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A duration of 10 rounds begins on your 1st turn and ends just before the beginning of your 11th turn. Otherwise, it would not be a full 10 rounds long.
So in the case of rage, it ends just before you take your 11th turn, preventing you from enjoying 11 rounds of rage but allowing you to enjoy the full 10th round of your rage, including during everyone else's turns.
The bless spell is not interrupted
The key to the answer is:
You briefly stop the flow of time for everyone but yourself.
For everyone else, delta t is zero.
No time passes for other creatures
Turns / rounds each last six seconds -- six seconds elapse from the beginning of someone's turn and the beginning of their next turn. From this game mechanic, we can say that the usual delta t from round to round is six seconds. Spells with duration of a minute can be modeled as being on a counter in this case: you count down one for each turn/round elapsed.
For everyone who is not the archmage, their time / turn / round counter remains where it was when time stop went into effect. Since no time is passing for them, the durations of their spells are, compared to the archmage's frame of reference, extended. The archmage's delta t keeps moving. For the other characters, they don't notice a difference since for them time stopped.
The bless spell's duration depends on the caster
In the case of bless, a concentration spell, the duration is keyed to the character who cast it, which is also the character who is concentrating on it. If it is a character who is not the archmage, their delta t is zero so their duration counter resumes on their next turn. (That is after time stop ends). Their spell still lasts a minute for them because time (and the counter) stopped for everyone but the archmage. That would provide the archmage with a few extra rounds / turns of the bless spell's magical effects.
If the archmage cast bless (from a ring of spell storing) it's duration would keep decreasing since time/turns are ticking away for the archmage.
@Medix2 asked for clarification in a comment:
If bless were cast by somebody else, but cast on the Archmage, would they benefit from it?
The answer is: yes. Nothing in the time stop spell says that it stops the effects of other spells. Bless, once it takes effect, keeps on taking effect until the spell ends (or concentration ends). Nothing in its text says otherwise.
Concentration
Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends. (Basic Rules p. 79)
In plain English, you in those two sentences is the caster of a spell requiring concentration. Unless you lose concentration, the spell does not end.
Best Answer
Yes, even during the spell time stop an effect that ends at the conclusion of the casting creature's turn still ends at the conclusion the casting creature's turn
The 9th-level Sor/Wiz spell time stop says
In defining a round the game says that
In defining a turn the game says that
Thus the spell time stop grants extra rounds during which the creature that cast the spell time stop can take extra turns, and during those extra turns the creature can activate effects that last until the end of the creature's turn, and those effects will end when the creature's turn ends. The round continues, however, until the character can next take a turn, at which point it's the next round.
The spell time stop doesn't change how time works but instead gives the caster more of it.