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For theoretical optimization I want to create a character with artisan's tools:

Using any official or UA content, magic items, classes, feats, any amount of time or preparation, any party composition and size, et cetera.

What is the highest average result you can get in one roll using a set of artisan's tools?

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    \$\begingroup\$ Somewhat related: "What is the highest total result one can get for a skill check?" \$\endgroup\$
    – Medix2
    Feb 27 '20 at 17:35
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    \$\begingroup\$ I want to figure out the best way to maximize my character's crafting rolls \$\endgroup\$
    – KAmber
    Feb 27 '20 at 17:48
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    \$\begingroup\$ So, you're not an exact duplicate of the related post Medix2 mentioned (highest possible roll), but the average can be inferred from the choices made there. Until someone gives your question an answer, it is indeed worth a look. \$\endgroup\$
    – Axoren
    Feb 27 '20 at 18:28
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    \$\begingroup\$ Should the roll be a one-off high average, or something that can be achieved consistently? Do you have a level cap in mind? Should the character be able to achieve this solo, or is requiring the support of the party allowed? \$\endgroup\$ Feb 27 '20 at 22:51
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    \$\begingroup\$ Does the player making the ability checks using tool proficiency need to be able to reach the highest average consistently, or is one roll with the high average sufficient? \$\endgroup\$ Feb 28 '20 at 15:37
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The maximum average result for a ability check using a tool is at least 85.5

The Rules

In order to maximize an ability check using a tool, we must use the following variant rules:

The Party

Our party consists of at least three characters:

  • A bard 15 ----------------------------------------------------------------------- (for guidance via Magical Secrets and Bardic Inspiration)
  • At least one School of Divination wizard 10 -------------------------------- (for Portent)
  • An artificer 7/The Fiend warlock 6/Wild Magic sorcerer 6/any 1 ------- (for enhance ability, Tool Expertise, Dark One's Own Luck, Bend Luck, the Lucky feat, and Boon of Luck)

The Gear

The Calculation

  • Ability score is 30 (or a +10 modifier)
  • Flash of Genius adds 10 (Intelligence)
  • a Hero Point adds 1d6 (average 3.5)
  • Bardic Inspiration adds 1d12 (average 6.5)
  • Bend Luck adds 1d4 (average 2.5)
  • guidance adds 1d4 (average 2.5)
  • Tool Expertise results in doubled 1d12 (average of 13)
  • Dark One's Own Luck adds 1d10 (average 5.5)
  • Boon of Luck adds 1d10 (average 5.5)
  • luckstone adds 1
  • Ioun Stone of mastery adds 2 (thanks to Tool Expertise)
  • The Lost Crown of Besilmer adds 1d6 (average 3.5)
  • Portent results in a 20 on the d20 roll.

This gives us a total of 85.5

Epic Boons of Fate

Finally, there is an epic boon called Boon of Fate which lets you add 1d10 to an ability check of any creature you can see. With enough creatures that have this epic boon you can make the total check immense. So basically, add an average of 5.5 for each character with the Boon of Fate within 60 feet. Since you could use the Minimus Containment imprisonment spell to place them in extremely small spaces, there is effectively no limit to the amount of creatures you can fit in that 1.7 million cubic feet.

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Highest average roll

Generally speaking, talking about the highest possible roll and the highest average roll are the same thing, you have a bonus (calculated by your stats and proficiency or expertise) and you have a variance associated with the dice you roll (always a d20 in this case). The variance will always mean you get some number between 1-20 (average 10.5) then you add a bonus.

Let's say the tools you use require dexterity, step one is to max out your dexterity on your character. Next you would like to get proficiency or ideally expertise to get the maximum bonus possible.

A note about Artisan's Tools

Most tools do not have a stat bonus officially associated with them, talk to your DM about whether tools use DEX, INT.. etc.

An example build

6th level Artificer

A 6th level artificer gets the following feature:

Tool Expertise

Starting at 6th level, your proficiency bonus is doubled for any ability check you make that uses your proficiency with a tool.

Let's say that your chosen tools require DEX, get your DEX as high as possible. For this example we can use 18. At level 6 your proficiency bonus is +3 so we would have DEX +(3 x 2) - totalling +10 in this example. With these stats you would have a high roll of 30 and an average of 20.5

Get Advantage

When you have advantage, your average goes from 10.5 to 13.825 (reference) before adding a bonus. You can use the Lucky feat to simulate this effectively.

Use Enhance Ability

Enhance Ability Will allow you to gain advantage for any type of ability check reliably, this also stacks with Lucky. It's worth noting if you Lucky a roll with advantage this gives you an average of 15.49 (reference using the string "3d20D2")

Effective roleplay

Talk to your DM about if they would allow advantage for Artisan's Tools under special circumstances, such as inventive roleplaying or having special equipment (such as working in a laboratory).

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  • \$\begingroup\$ You can use multiple luck points on a single roll; this improves the average roll to 17.146 \$\endgroup\$ Feb 28 '20 at 17:22

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