What is the highest average damage that a level 10 character can deal in response to being hit or damaged?


Premise

Typically, you deal damage by hitting the other guy with a stick (or a fireball) [citation needed]; however, spells like fire shield damage enemies who hit you:

In addition, whenever a creature within 5 feet of you hits you with a melee attack, the shield erupts with flame. The attacker takes 2d8 fire damage from a warm shield, or 2d8 cold damage from a cold shield.

Similarly, hellish rebuke allows you to damage enemies in response to them damaging you. Either way, the enemy wouldn’t have taken damage if they chose to just ignore you. This leads to my question: what is the highest average damage that a level 10 character can deal in response to being hit or damaged?

Restrictions

Character

  • Level 10.
  • May use the PHB and one of the following: EE, MToF, SCAG, VGtM, or XGtE. This restriction extends to spells, as well. (If the spell is one your build allows you to copy from a scroll or spellbook, however, you may pick it from any of those sources.)
  • No variant rules besides multiclassing, feats, and variant human.
  • Up to three magic items from DMG Tables F or G with a maximum rarity of Rare.

Combat

  • Four encounters; Combat 1, Combat 2, Short Rest, Combat 3, Combat 4 (each of these events is separated by 30 minutes). The Short Rest is mandatory.
  • Each combat encounter has you face off against two earth elementals. These elementals do not have any damage vulnerabilities, damage immunities, or condition immunities. They keep their damage resistances.
  • Each combat lasts three rounds. All participants get a turn in each round.
  • Enemies move next to the PC and attack normally.
  • Enemies do not make opportunity attacks.
  • For the sake of simplicity, treat enemies and the PC as if they had infinite health.
  • You may not use the Ready action. (Mainly to prevent "I ready blight for when I get damaged" from being the best answer.)
  • Any spell or ability that lasts 10 minutes or longer may be activated before entering combat. Any spell or ability that lasts longer than 8 hours may be activated the day before.
  • You may not spend more than 100 gp on spells that consume costly material components. (So casting identify and find familiar is fine, because identify doesn’t consume its costly component, but casting glyph of warding is not.)
  • You never lose concentration as a result of taking damage.
  • Allies cannot help you, unless you summon/create them yourself (via conjure animals, animate dead, etc.)

Damage calculation

  • Damage should be the average damage per round over the course of the adventuring day.
  • Only count damage dealt to enemies (the earth elementals) in direct response to, and in the same turn as, being hit or damaged. Hellish rebuke is fine. The extra damage dealt by absorb elements is not. You may still deal damage in other ways (in case it’s necessary for setup), you just can’t count it in the total.

What’s the highest amount of ranged attacks a pure fighter can make in one turn consistently?

I’ve been working on a 20th level character concept for a while and trying to optimize it for use in a future game, the requirements would be as follows:

  • Only 3.X WotC handbooks (No 3rd party books, no magazines, no online-only content except for web enhancements of handbooks, no adventure-specific content).
  • Only handbooks from the D&D 3E standard setting/Greyhawk (no eberron, faerun, dragonlance, etc).
  • The only base class used must be fighter, any prestige class is ok as long as it doesn’t grant any magical abilities (includes psionics, incarnum, etc), also no martial powers.
  • Optimized for ranged damage output, without relying on allies, consumables, or very low frequency abilities (1/day stuff and the like).

Given that, the concept I’ve got so far is a pure SAD dexterity fighter dual wielding auto-realoading hand-crossbows, boosting damage with feats Dead Eye and Crossbow Sniper, plus specialization and mastery feats. The damage per attack is not too bad (1d4+31), and I’m now looking for ways to increment the number of attacks I could make.

So far I get 4 attacks from BAB, 3 from TWF, 1 from Rapid Shot, and 1 from Haste, for a total of 9 attacks.

I’m specifically looking for methods to increase the number of attacks per full attack action. But I’d also welcome any general advice to improve the build given the previous requirements.

What is the highest hit point that one character can have?

By reading others questions like Highest damage in one melee attack and Highest AC possible.

How many hit points can a character have, and also highest achievable hit points possible in an instant?

Conditions :

We’re looking at a level 20 character and no multiclass.
Feats are allowed.
Magic items are those on the tables in the D&D 5th Edition DMG.
Spells, skills, feats and abilities available to a player character are eligible for use/consideration.
No other help from an ally.

How to find the square with the highest total sum

I have an integer matrix of size 4n x 4n. I need to select a part of the matrix of size n^2 from which adds up to the most.

For example if n = 3. I have a matrix of size 12 x 12. In the below picture, you can clearly see that n^2 square (outlined in red) adds up to the most. For simplicities sake, I made all the numbers 5, expect for 9 of the boxes which are 9999 so its clear that that is the n^2 squares that add up to the most.

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My approach to solving this problem was to essentially create a n^2 square and brute force the entire 4n x 4n matrix. However, that runs in O(n^4) time complexity. How can I do it in O(n^2)?

What is the highest possible damage you can do with a level 20 character

Let’s say no multiclassing aloud and no magic items. For this we also can say that you are just going to take the average of all damage. Next, this is an AC 20 monster and has 20 in all stats (which is absurd I know, but just go with it.)It also has proficiency in strength and dexterity saving throws. The proficiency for this monster is a +5. Also, we can say you have 1 prep round before battle, then you have to try to do as much damage as you can in one round. Also, there would be no other people in your party, it would just be you. For the Wild Magic Table for Sorcerers, we can say that you can pick what you get on the table which means it is fine if you have slightly ideal damage there. Although for any damage rolls, we can say it is average damage. For this, you would use an average roll which would be 10ish on a d20. Also we can say that with saving throws, the monster rolls a 10 and then adds all of its modifiers and proficiency bonuses if any in that saving throw. Lastly, it is not allowed to do polymorph then power word kill.

Highest Possible DC for Circle of Death

What is the highest possible DC for Circle of Death?

Restrictions:

  • Level 12 Wizard (you may choose an archetype, as long as it has a familiar)
  • Cyphergull Familiar
  • At least 3 unused general feat slots and a bonus feat slot (if the archetype removes bonus feat slots, 4 general slots must be left open.)
  • Pathfinder 1e content only, pathfinder content written in 3.5 (Elves of Golarion, Curse of the Crimson Throne, etc.) are not allowed.
  • Crafting magic items is allowed, but you are restricted to a total of 1.5 WBL for a level 12 character.
  • Custom magic items are not allowed, you are restricted to printed magic items only.
  • Aside from permanent/instantaneous duration spells, you are allowed to factor in 1 round of buffs. You are not allowed to debuff the targets of the spell.
  • Available spells (from items, spellcasting services, etc.) are restricted to spells that only casters level 12 or lower could cast.
    • Ex. Psychics get ethereal jaunt as a 6th level spell, and are able to cast it at level 12, so it is available. Wish is not able to be cast by any level 12, and therefore not available.
    • Ally/Army Across Time, Simulacrum, Planar Binding, and Planar Ally are not available.
  • Items that impose a penalty, such as Void Shard count as improving the DC of the spell by that much. Ex, Void Shard counts as raising the DC of Circle Death by 2.

What is the highest possible unarmored AC?

What is the highest possible AC a character can get by themselves with no armor or a shield?

Constraints:

  • Must be obtainable with a single character, by themselves, with no help from any other characters (allies, enemies, summons, etc.)
  • Must be completely unarmored and not wearing a shield.
  • Magic items are fine such as Ring/Cloak of Protection or Robes of the Archmagi.
  • You may use any combination of classes and races from official sources, not including Unearthed Arcana. (You may use the versions of Eberron races as seen in Wayfinder’s Guide to Eberon as opposed to Rising from the Last War if you wish.)
  • Character can be assumed to be level 20 with an epic boon if applicable to the build.
  • Stats may be determined via point buy.
  • Character does not need to be particularly viable in a game, this is pure theory crafting.
  • You may have as much time as you need as long as it’s within a typical lifetime for a character. (So no abusing infinite readings of Manual of Quickness of Action or similar items, one or two (different) manuals may be considered acceptable.)

The best answer should contain both a permanent max unarmored AC as well as the highest you can get via spells if it’s higher (and still meets the above criteria).

The highest I can come up with is 24 for a level 20 barbarian with 20 DEX and 24 CON but I’m sure you guys can do better.

AnyDice: Sum of dice pool + highest value from the same roll

I want to calculate the sum of a mixed dice pool, but add the nth highest value of that pool twice.

For example the code

output 2d4+1@2d4 

Gives the sum of 2d4 and the highest value of a separately rolled 2d4. Instead I’d like to add the highest value of the same 2d4.

This does produce different results; in the example above the probability of rolling a total of 3 is 0.39%, while in the situation I’m after the probability should be 6.25%.

Ideally the solution should be able to handle rolling mixed die pools such as 2d10+1d8+1d6+the second highest value rolled, but I would still find solutions that cannot do so useful.