Hide [Action]
With the Hide action, you try to conceal yourself. To do so, you must succeed on a DC 15 Dexterity (Stealth) check while you’re Heavily Obscured or behind Three-Quarters Cover or Total Cover, and you must be out of any enemy’s line of sight; if you can see a creature, you can discern whether it can see you.
On a successful check, you have the Invisible condition. Make note of your check’s total, which is the DC for a creature to find you with a Wisdom (Perception) check.
I have a very straight-forward way of interpreting this. The check requires a minimum 15 to hide (become "invisible") and is also the DC for perception against how well the PC is hidden.
Leaving obscurement or cover places the character into line of sight and breaks the condition. They're only "invisible" while maintaining the conditions needed to hide.
For example, the rogue sees the light of torches or hears voices approaching. They crawl under a desk and curl up to hide, keeping silent until the lights and voices leave. The character has +7 to the roll and rolls a 4, but being a rogue treats it as a 10 for a total of 17. Rogues are awesome at this. No one is searching for them and passive perception isn't good enough in most cases.
I don't see this as complicated. Leaving obscurement or cover placing the character in line of sight breaks the "invisible" condition. The wording is awkward, though.
Heavily Obscured
You have the Blinded condition while trying to see something in a Heavily Obscured space.
And if someone is trying to find the character using heavy obscurement then blindness works in that direction whether the stealth check to hide is successful or not.
Blinded [Condition]
While you have the Blinded condition, you experience the following effects.
Can’t See. You can’t see and automatically fail any ability check that requires sight.
Attacks Affected. Attack rolls against you have Advantage, and your attack rolls have Disadvantage.
So a paladin in the warlocks's Darkness spell who rolls high might hide. If they fail someone might hurl a javelin at him with disadvantage.
Cover
Cover provides a degree of protection to a target behind it. There are three degrees of cover, each of which provides a different benefit to a target: Half Cover (+2 bonus to AC and Dexterity saving throws), Three-Quarters Cover (+5 bonus to AC and Dexterity saving throws), and Total Cover (can’t be targeted directly). If behind more than one degree of cover, a target benefits only from the most protective degree.
Similarly, a character using cover to hide gains the benefits of that cover whether or not the stealth check succeeds. Trying to hide and failing still carries that advantage.
Help [Action]
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Assist an Ability Check. Choose one of your skill or tool proficiencies and one ally who is near enough for you to assist verbally or physically when they make an ability check. That ally has Advantage on the next ability check they make with the chosen skill or tool. This benefit expires if the ally doesn’t use it before the start of your next turn. The DM has final say on whether your assistance is possible.
This is still an option.
The rogue might drape a dark blanket over the paladin to hide some shiny metal armor and dull sounds a bit while keeping close and showing where to step. Describe how to help and see if the DM grants advantage.
Invisible [Condition]
While you have the Invisible condition, you experience the following effects.
Surprise. If you’re Invisible when you roll Initiative, you have Advantage on the roll.
Concealed. You aren’t affected by any effect that requires its target to be seen unless the effect’s creator can somehow see you. Any equipment you are wearing or carrying is also concealed.
Attacks Affected. Attack rolls against you have Disadvantage, and your attack rolls have Advantage. If a creature can somehow see you, you don’t gain this benefit against that creature.
The "invisibilty" from hiding or the spell grants these features. The rogue in my example above would have advantage on initiative if they attacked, and may or may not maintain the benefits of cover depending on how they attacked.
Different features that grant the invisible condition end that condition under different circumstances.
Group Checks
Group checks are a tool you can use when the party is trying to accomplish something together and the most skilled characters can cover for characters who are less adept at the task. To make a group ability check, everyone in the group makes the ability check. If at least half the group succeeds, the whole group succeeds. Otherwise, the group fails.
Group checks aren’t appropriate when one character’s failure would spell disaster for the whole party, such as if the characters are creeping across a castle courtyard while trying not to alert the guards. In that case, one noisy character will draw the guards’ attention, and there’s not much that stealthier characters can do about it, so relying on individual checks makes more sense. Similarly, don’t use a group check when a single successful check is sufficient, as is the case when finding a hidden compartment with a Wisdom (Perception) check.
I think some of you might be conflating stealth checks with the hide action having read that example from the DMG. The party moving across the castle courtyard aren't using the hide action. They're moving quietly while the guard's attention is elsewhere.
That doesn't necessarily mean the rest of the group cannot try to muffle noise somehow while taking the hide action. The halfling rogue could snuggle up to the paladin and help keep him still. Describe it for the DM and see how the DM chooses to handle it.
Just because that particular example said they wouldn't use a group check doesn't mean never use a group check.
That's my perspective anyway. Hope it helps.