What is the maximum possible Stealth bonus?

Question

I realised we do not have a version of this rather (in)famous optimization problem: What is the maximum possible bonus to a Dexterity (Stealth) check?

Bonus is here taken to mean anything that is added to the result of the d20. Any added dice can be assumed to roll their maximums.

Constrains:

• Official, non-UA material only

• 20 level character with any number of boons

• Magic items are fine, except items which increase ability scores above 20.

• Assistance from up to 4 allies

• Do not use play style variant rules (such as proficiency dice). Character creation variant rules (such as multiclassing and feats) are ok.

• The bonus only has to be applied to a single check

• No using wish for anything other than replicating a spell of 8th level or lower.

Answer 1

At most +156.

This does not include the 20 from the d20. The maximum rolled result would be 176.

Requirements:

Your character must have...

• At least 10 levels in Ranger, to get Hide in Plain Sight.
• At least 1 level in Rogue, or 3 levels in Bard, to get Expertise.
• At least 6 levels in Warlock (The Fiend), to get Dark One's Own Luck.
• 20 levels total.
• Dexterity score of 20. You can start lower, but you need 20 by 20th level.
• Wisdom and Charisma scores of 13+ to meet multiclassing prerequisites.
• Boon of Luck, Boon of Undetectability, and five Ability Score Improvements as epic boon alternatives.

Your magic items must include...

• Stone of Good Luck (requires attunement)
• Ioun Stone of Mastery (requires attunement)

Your 4 allies should include...

• A bard of at least 14th level, who uses a d12 for their Bardic Inspiration die.
• A Wild Magic sorcerer of at least 6th level, for their Bend Luck feature.
• A Circle of Dreams druid of at least 6th level, for their Hearth of Moonlight and Shadow feature.
• An Artificer (from Eberron: Rising from the Last War) of at least 7th level, with 20 Intelligence, for their Flash of Genius feature and the guidance cantrip.
• Someone wearing the Lost Crown of Besilmer (from Princes of the Apocalypse)
• Each of your four allies has 20 levels total, and a Boon of Fate.

The Math:

Start with your character's Dexterity modifier. Without magic items, you can get 20 Dexterity. You then ask your DM for five Ability Score Improvements (listed as epic boon alternatives), raising your Dexterity to 30. Your Dexterity modifier is +10.

As a 20th level character with the Ioun Stone of Mastery, your Proficiency bonus increases by 1, from +6 to +7. And with Expertise in Dexterity (Stealth), you add your Proficiency bonus twice to the stealth check. This becomes a +14 bonus.

Also, your Boon of Undetectability adds +10 to Dexterity (Stealth), and your Stone of Good Luck gives an extra +1 to ability checks. So far, you have a total +35 Stealth bonus, without any temporary or situational benefits.

But wait, there's more! As a Ranger, you cast pass without trace, which gives a +10 bonus for the next hour. Then you take a minute to camouflage yourself via Hide in Plain Sight, which will give you another +10 bonus.

This next hour will be a short rest. Your druid ally uses Hearth of Moonlight and Shadow to give everyone a +5 bonus to Dexterity (Stealth).

Your bard ally gives you a d12 Inspiration die. And if they're wearing the Lost Crown of Besilmer, they can use their next bonus action give you another +1d6.

The Artificer ally casts guidance, which will add +1d4 to the check. Also, the Artificer has five Ability Score Improvements as epic boons, which boosted their Intelligence from 20 to 30. When you make the check, they use their Flash of Genius feature to add their Intelligence modifier of +10.

If your Wild Magic sorcerer ally can see you, then their Bend Luck feature can add +1d4 to your check. The sorcerer should then run away and hide elsewhere, lest they randomly explode and accidentally reveal your location.

Both the Dark One's Own Luck feature and your Boon of Luck each add +1d10. Your four allies' Boons of Fate each add another +1d10.

The total bonus is +(10 + 14 + 10 + 1 + 10 + 10 + 5 + 1d12 + 1d6 + 10 + 2d4 + 6d10) = +156 maximum.

Answer 2

The maximum result for a Stealth bonus with those restrictions is 157
^{(a minimum of +69 with 1s on all the dice, and an average of +113)}

The Party

Our four allies are listed below:

• A bard 20 ----------------------------------------------- (for guidance via Magical Secrets, Bardic Inspiration, and Boon of Fate)
• A Circle of the Dreams druid 20 --------------------- (for pass without trace, Hearth of Moonlight and Shadow, and Boon of Fate)
• A Wild Magic sorcerer 20 ----------------------------- (for Bend Luck and Boon of Fate)
• A Peace Domain cleric 20 ------------------------------ (for Boon of Fate)

...and our hider, from Theros:

• A human Oracle The Fiend Warlock 6/ranger 10/Rune Knight fighter 4 --- (for Oracle's Insight, the Prodigy feat, Dark One's Own Luck, Hide in Plain Sight, Rune Carver: Frost Rune, Boon of Luck, and Boon of Undetectability)

The Gear

• A luckstone
• An Ioun Stone of Mastery
• The Lost Crown of Besilmer
• an object inscribed with a Frost Rune
• fresh mud, dirt, plants, soot, and other naturally occurring materials (for Hide in Plain Sight)

The Calculation

• Dexterity score is 20 (or a +5 modifier)
• Bardic Inspiration adds 1d12 (maximum 12)
• Bend Luck adds 1d4 (maximum 4)
• invoked Frost Rune adds 2
• pass without trace adds 10
• guidance adds 1d4 (maximum 4)
• Emboldening Bond adds 1d4 (maximum 4)
• Hearth of Moonlight and Shadow adds 5
• Prodigy results in a doubled 6 for 12
• Dark One's Own Luck adds 1d10 (maximum 10)
• Oracle’s Insight adds 1d10 (maximum 10)
• Hide in Plain Sight adds 10
• 4 Boons of Fate add 4d10 (maximum 40)
• Boon of Luck adds 1d10 (maximum 10)
• Boon of Undetectability adds 10
• luckstone adds 1
• Ioun Stone of mastery adds 2 (thanks to Prodigy)
• Lost Crown of Besilmer adds 1d6 (maximum 6)

Grand total: +157

Answer 3

Arbitrarily large

A 20th level character with the Boon of Fate can add +1d10 to the ability check of one target within 60 feet as a non-action. Since Epic Boons are not " spells, class features, feats, racial traits, monster abilities, [or] magic items" (DMG errata) and no other text includes epic boons within the definition of 'game features', they are not subject to the DMG errata that broadened the prohibition on magical effects with the same name stacking to all 'game features'. Therefore, a character-- though limited to only one copy of the Boon of Fate-- can benefit from infinitely many applications of said boon on a single roll.

A 20th level Wizard can cast simulacrum. With the Boon of High Magic they can do this via Wish twice per day without needing material components. With the Boon of Spell Recall you can do it three times per day. With a Tome of the Stilled Tongue they can do it four times per day. With more Tomes of the Stilled Tongue they can do it more times, though they will need to attune a new tome after each casting.

A 20th level Wizard lacking a tome of the stilled tongue and epic boons can store a casting of simulacrum in a glyph of warding. This does not make the simulacrum 'appear as close as possible... and attack' when the glyph is activated, because simulacrum creates a friendly, rather than hostile, creature. After creating such a glyph, the wizard can regain spell slots without losing access to the simulacrum spell.

Either way, a 20th level Wizard can create a simulacrum of themself able to itself create a simulacrum via Wish. The wizard can then create another simulacrum, dispelling the first one but leaving the one it created unharmed, as the second simulacrum makes another copy of the wizard. This allows the simulacrum creation process to be exponential rather than linear in growth-- each surviving simulacra creates perhaps three other dying simulacra who make 1 surviving simulacra each, the whole process of which takes no more than 6 rounds. After 24 hours, as an example, such a wizard would have 3^67200 simulacra, or around 35 decmilliasescensexoctogintillion simulacra.

Unlike most checks, a Stealth check's total lasts "until you are discovered or stop hiding", and is reused against the Wisdom(perception) total of a chacter that is searching for you. Our wizard, then, can make a stealth check to hide from a rat but not the simularcra. The simulacra within range can add 1d10 each to the stealth check via their Boons of Fate, and then teleport out of the way via a contingency spell tied to a plane shift. More can then teleport in via an action, add to the check total, and then teleport out via contingency, all within each of their turns. With a sufficiently large bag of rats, then, to ensure a large number of initiative counts, even all 35 decmilliasescensexoctogintillion simulacra should be able to efficiently discharge their stealth buffs into you within a few rounds. That would give you approximately a + 175 decmilliasescensexoctogintillion bonus to your stealth check. Note that since Perception checks don't carry over a total to new checks like this, you can't pump them up to astronomical heights in the same way-- if you are careful to protect against direct observation and have even just 10 full 60' spheres of simulacra buff your Stealth there's no way anyone is ever going to find you unless you give yourself up-- they can't get more of a bonus to Perception than you have to Stealth.

Answer 4

The past answers seem to lack some of the newer sources, so here's mine. Max 197.

The party:

The hider is an autognome (with the gift of Oracle's Insight from MOoT) and a level 1 Divine soul sorcerer, level 3 Soulknife rogue, level 6 Fiend warlock, and level 10 ranger of any kind, having taken the Battlemaster initiate feat for access to Ambush.

Ally 1 is a level 6 Circle of Dreams druid, level 6 Wild Magic barbarian, level 1 Peace cleric, and level 7 Wild Magic sorcerer

Ally 2 is simply a level 15 bard.

Ally 3 is a level 6 Circle of Stars druid, level 7 Artificer.

Note: I have assumed that epic boons (specifically Fate) does not stack with itself, and cannot be used by multiple allies on the same check. If it does in your game, add 20 to the total.

The features:

• Dexterity (+10 with epic boon alternatives)
• Built for Success (autognome: 1d4)
• Oracle's Blessing (1d10)
• Favoured of the Gods (Divine soul sorcerer: 2d4)
• Expertise (Rogue: +14 with Ioun stone of mastery)
• Psi-boosted Knack (Soulknife rogue: 1d6)
• Dark One's Own Luck (Fiend warlock: 1d10)
• Pact of the Talisman (Warlock: 1d4)
• Ambush (Battlemaster: 1d6)
• Pass without Trace (Ranger: +10)
• Hide in Plain Sight (Ranger: +10)
• Epic boon of Luck (1d10)
• Epic boon of Undetectability (+10)
• Hearth of Moonlight and Shadow (+5)
• Bolstering Magic (Wild magic barbarian: 1d3)
• Emboldening Bond (peace cleric: 1d4)
• Guidance (cleric: 1d4)
• Bend Luck (wild magic sorcerer: 1d4)
• Epic boon of Fate (1d10)
• Bardic Inspiration (1d12)
• Cosmic Omen: Weal (Circle of stars druid: 1d6)
• Flash of Genius (Artificer: +10 with epic boon alternatives)
• Lost Crown of Besilmer (magic item: 1d6)
• Luckstone (magic item: +1)