The character takes the hide action but no roll is required until a potentially threatening enemy(PTE) could reasonably detect it at which time a stealth check is made. The players stealth check is then compared to all PTE passive perception(PP). If all PTE PP are overcome then the character remains hidden as long as they remain out of any enemies line of sight, do not make a sound louder than a whisper, an enemy doesn't find them, they don't make an attack roll, or they don't cast a spell with a Verbal component. Hidden means any creature with a lower PP than the stealth check cannot see or hear the character and does not know their location. Any creature can discern whether it is detected by a creature it can see. The hiding characters stealth check is the DC for any creature that attempts to find the sneaking character with a Wisdom Perception check. If the stealth check is not greater than a PTE PP then that PTE is aware of the sneaking character and initiative is called. Any PTE that had a lower PP than the stealth check is surprised but also aware as it's assumed the PTE that detected the sneaking character revealed their location if that is reasonable given the circumstances. These rules are repeated for each group of PTE. One stealth check does not persist through multiple encounters. If a DM wants to include directional vision during an out of combat encounter this may allow players to sneak up and attack npcs from behind. The sneaking character would still have to roll a higher stealth check than the PTE PP as they could still detect through other senses. Immediately after the attack initiative should be rolled counting all PTE as aware of the sneaking character but surprised.
Frankly, for out of combat there's no reason not to keep doing that. It's in combat where it's really a mess.
Specifically, the mess is any time you actually use the rules for the hide action. As long as you treat it as a generic skill check that functions just like any other generic skill check, it doesn't have any real problems other than inconsistent interpretations by different DMs.
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"Can I sneak up on that guard?"
"Yeah, he's been at his post for awhile and isn't very alert. Roll a DEX check to see if you stumble or make noise."
"16"
"OK, what do you do now?"
Frankly, for out of combat there's no reason not to keep doing that. It's in combat where it's really a mess.
Specifically, the mess is any time you actually use the rules for the hide action. As long as you treat it as a generic skill check that functions just like any other generic skill check, it doesn't have any real problems other than inconsistent interpretations by different DMs.
The 15 rankles me.
"Sooner or later, your Players are going to smash your railroad into a sandbox."
-Vedexent
"real life is a super high CR."
-OboeLauren
"............anybody got any potatoes? We could drop a potato in each hole an' see which ones get viciously mauled by horrible monsters?"
-Ilyara Thundertale