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The Arcane Archer fighter (Xanathar's Guide to Everything, p. 28-30) gets a number of Arcane Shot options, allowing them to unleash special magical effects when they fire a longbow/shortbow. One of their Arcane Shot options is Banishing Arrow:

You use abjuration magic to try to temporarily banish your target to a harmless location in the Feywild. The creature hit by the arrow must also succeed on a Charisma saving throw or be banished. While banished in this way, the target’s speed is 0, and it is incapacitated. At the end of its next turn, the target reappears in the space it vacated or in the nearest unoccupied space if that space is occupied.

If a creature gets banished in a group of enemies and no one sees the creature get banished, do the other creatures notice he is gone and are still surprised if you decide to attack them next round?

(Obviously before the creature comes back at the end of its next turn... although THAT might get tricky depending on initiative rolls and when the DM states "it's now this guy's next turn", but for the sake of simplicity, we'll say that because you don't act on a surprise round he doesn't get the first turn when he's hit.)

As far as I can tell this is really a matter of timing. If you hit a creature and it's able to do ANYTHING (even saying 'ow') before being banished, then it's obvious that this is your surprise round and you don't get to grab another one... On the other hand, if the creature is banished THEN gets to say 'ow', well, no one can hear him; and if no one saw him go "poof", then you're likely to be able to just get another round out next turn with people still not knowing you're there.

Your Attack Reveals You

I am not sure whether a creature getting banished makes any noise. It's possible that the creature disappears without any sound, or that it vanishes in a flash of light screaming. Either way, that isn't what will give you away: it's the attack you needed to make to banish the creature.

Banishing Arrow states that:

The creature hit by the arrow must also succeed on a Charisma saving throw or be banished. (XGtE, p. 29)

Since you need to hit a creature to banish it, you needed to make an attack. However, the rules on unseen attackers and targets state that:

If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses. (PHB, p. 195)

Note that it doesn't say you give away your location only to the target of the attack. When you attack while Hidden, you lose your Hidden status. Naturally, you wouldn't become visible to someone miles away, but basically anyone who could have been alerted by an "ow" from your initial target has already been alerted by your attack. (You can't even get around this with the Skulker Feat, because your attack needs to have hit).

They could still be surprised, but it depends on a number of things.

One particularly important part about Surprise is that the DM has to be the one actively deciding each time it's applied. Unlike stealth, buffs, healing, or other calculations regarding how it works, Surprise isn't necessarily as simple as "I rolled high, so now they're Surprised".

Generally, for Surprise to work, the people in question need to believe there is no active threat. This means that they shouldn't be doing guard duty, couldn't have heard or seen someone get banished, or have any reason to believe that combat has initiated.

Surprise is not a type of round, it's a condition that nullifies their first action in combat. If they don't know there's combat, then they're not taking combat actions, and they aren't surprised yet. Since the surprise hasn't been ruined, they could easily be surprised in later rounds, when the players do get around to spooking the enemy out of their pants.

To make this simpler, I'd roll initiative for the entire encampment + players, but if a combatant doesn't know there's any reason for alarm, they simply do not take combat-related actions until they do or until they're Surprised. Mechanically, though, it should be treated as a
string of short fights, which are individually considered for Surprise Rounds.

This is separate from being "hidden" which is just one way to avoid being detected to get a Surprise Round. Another method could be to simply start attacking someone who thinks of you as an ally. Even without a stealth check, Surprise can still be obtained.

I thought the way a "surprise" round worked in 5th edition was that everyone rolls initiative as normal. Everyone who is surprised misses their standard, bonus and move actions and only gets their reaction after their turn comes up. The exception being certain barbarians who can act provided they rage immediately when their turn starts.

In any case I'd say you could take out that initial target or any number of targets without starting combat provided you can justify the remaining enemies not noticing anyone vanish. If they are all sitting around a campfire chatting and one of them suddenly vanishes there is pretty much no way they aren't going to be alerted. If one of them got up to answer the call of nature and you managed to take them out such that the others couldn't see or hear the attack then combat would not have started. The DM could still call for initiative rolls but not have the other enemies do something since they wouldn't know anything is going on.