Maximum Persuasion (5e Optimized Character Build)
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Do you want to be so persuasive that people will think your tongue is literally made of silver? Well you've come to the right place.
Whether you're using the point-buy system or are rolling for stats, you're going to want your Charisma to be your highest stat (obviously), but your going to want Wisdom to be equal to your Charisma and you'll also need your Dexterity to be at least 13 (more on these later).
This one might seem a bit odd since it gets a +2 to Dexterity, but if you're playing an Eberron campaign (or if your DM allows you to use this regardless), you can go with the Mark Of Hospitality subrace. This grants a +1 to Charisma, but, thanks to the Ever Hospitable trait, you can roll a d4 every time you make a Persuasion check, among other things. Being a Halfling might also be helpful at lower levels due to the fact they have their own version of Lucky, which allows you to reroll any Nat 1s you get.
This is definitely the race you'll want, but, if for whatever reason your DM might not allow you to use it, here are some alternatives:
Thanks to Mordekainen's Tome of Foes, there are many options for this delightfully devilish race, although most of it is in what spells they learn. All Tieflings subraces, aside from the standard variant, retain the +2 Cha normal Tieflings get, but for this you'll want to go with the Fierna subrace, as it gets a +1 to Wisdom, plus the spells they get innately (Friends, Charm Person, Suggestion) fit thematically with this build. It might be a good idea to go with this race especially if your DM is allowing starting feats, in which case you should pick Infernal Constitution to boost your resistances.
With a +2 Cha and +1 to two other stats of your choice, you can choose Wisdom and one other stat (probably Dexterity or Constitution), plus you gain two proficiencies of your choice, meaning you can start right off with Persuasion, plus, while you don't get any innate magic, you get more than Tieflings do (Fey Ancestry and an Extra Language, or whatever you choose based on your heritage).
You could even try this with an Aasimar, which gains +2 to Charisma. If you go this route, you might want to go for Protector as your subrace since it gets a +1 to Wisdom, plus the resistance to Necrotic and Radiant damage as well as Healing Hands aren't too bad.
Any background that gives additional languages would be the most ideal for such a build, given how you'll want to try to know as many languages as you can to make the most out of your persuasiveness.
Now that you've picked your race, you're going to want to start off as a Bard and do this for 16 levels, choosing the College of Lore at level 3. As for the 3 skills of your choice you gain from starting as a Bard, choose any ones you want, but make sure you have proficiency in both Persuasion (obviously) and Insight. Same goes with the Bonus Proficiencies you get from College of Lore at 3rd level.
For Expertise, which you get at the 3rd and 10th level, choose any you wish, but this time you can either choose Persuasion and Insight, or save getting those skill expertises when you choose your feats, which we'll get into later. When picking your spells for Bard, go for Geas and, once you get your 8th level spell, Glibness.
You can use the Fey Wanderer Ranger subclass, which allows you to add your Wisdom modifier to all Charisma checks, minimum of +1. This is why you need the 13 Dexterity and want to max out Wisdom.
Ability Score Improvements
Having 16 in Bard and 4 in Ranger should net you 5 Ability Score Improvements/Feats, not counting the starting feat. While you should obviously focus on maximizing your Charisma, don't forget about Wisdom. For feats, I recommend, even if you've already given yourself expertise in Insight, going for Empathic. Doing so will allow you to do the following:
You can use your action to try to get uncanny insight about one humanoid you can see within 30 feet of you. Make an Insight check contested by the target's Deception. If your check succeeds, you have advantage on attack rolls and ability checks against the target until the end of your next turn.
This will allow you to get advantage on your Persuasion checks. The reason why I wouldn't go for Diplomat, despite it helping with Persuasion, is because you need to talk with a creature for 1 minute, then pass a check to see if it becomes charmed. Taking it might be useful if you're looking for that one extra point in Charisma, though. However, since not every creature can be charmed, it seemed somewhat pointless, especially with the wait time of 1 minute. You'll also want to, at some point, go for the Lucky feat, since forcing rerolls in case someone beats your Persuasion, especially with a pesky Nat 20, is always nice. You might also want Linguist to get some extra languages.
If you chose the Mark of Hospitality Halfling, you might want to get the Greater Dragonmark feat, as this will turn your d4 intuition die into d6s and give you a +1 to Charisma.
Speaking of Persuasion, let's go over how all of this helps make our silver tongue shine!
A Bard at level 15 means their Bardic Inspiration is at their maximum potency, a d12, and one from the College of Lore at level 14 can use their own Bardic Inspiration to increase the roll of any ability check they make through their Peerless Skill feature. Fey Wanderer adds your Wisdom modifier to your Charisma checks as well. Lastly, remember Glibness? This Bard/Warlock exclusive spell makes all of your Charisma checks a 15, assuming you don't roll higher than 15, and makes it so no one can tell if you're lying even through magic. Now, assuming you have a 5 in Charisma and a 5 in Wisdom, let's add all this up:
(For simplicity, we're going to assume you're a Mark of Hospitality Halfling with Greater Dragonmark.)
Glibness: 15 (base) Persuasion: +22 (5 Cha + 5 Wisdom + Expertise) Peerless Skill: 1-12 Halfling's Ever Hospitable w/ Greater Dragonmark: 1-6
Assuming you rolled lower than a 15 and rolled a 1 with your Peerless Skill and your intuition die, you'd still roll an impressive 39. Heck, even if you had a +1 Charisma, you'd still roll, at base, a 35. Very impressive indeed, but we can do better than that. What would happen if you rolled the highest number for every die?.
20 (d20 roll) + 22 (Persuasion with Expertise and max Charisma and Wisdom) + 12 (Bardic Inspiration) + 6 (Hospitality Dragonmark) = 60
That's quite the accomplishment, but.....can we go even higher? Assuming you're able to give yourself God-like Charisma and Wisdom and get them all the way up to 30, giving you a +10 instead of a +5, your Persuasion becomes a 32 instead of a 22, meaning you can end up with a roll as low as 1 (d20 roll) +1 (dragonmark) +1 (bardic inspiration) +10 (Charisma) +12 (Expertise) +10 (Wisdom) = 35 minimum, 49 with Glibness, and a max of 70.
Now THAT is a silver tongue. Just remember that you only have 10 minutes to use it at it's full potential (with Emissary of Peace) or at least an hour (with Glibness), after which you'll need a long rest. For those 10 minutes, though, you'll be a virtual god of persuasion.
You could also have a Druid or a Cleric Party member cast Guidance on you to give you an additional d4 for one ability check, and, if you happen to be played a young adult, you could have a Cleric or a Paladin cast Ceremony on you using Coming of Age, which would give you an additional d4 for every ability check you make for 24 hours. However, since a creature can only benefit from such a rite only once, you'd have to make sure you really wanted that additional d4 before using it. However, given how Bards have Magical Secrets, you could just choose Guidance and Ceremony and cast them on yourself, although giving a Coming Of Age ceremony to yourself might be rather weird...
Having a Wild Magic Sorcerer in the party would also prove helpful if he at least has 6 levels in Sorcerer and is willing to use 2 Sorcery points on Bend Luck to give you another 1d4 to the roll.
So, with those three d4s in mind, the highest total for Persuasion you can get now becomes a massive 82. Additionally, if you're attuned to three Stones of Good Luck, your saving throws and ability checks all get a +3, meaning you can get Persuasion as high as 85. If your DM allows magical items from Eberron: Rising from the Last War and you get your hands on the uncommon version of a glammerweave, you can add another d4 to the roll, meaning a max of 89. An Artificer can use their reaction to lend a hand with their Flash of Genius feature, which gives us, if they have a 30 Intelligence, a total of 99.
Assuming your DM is giving out boons, hope they give you the Boon of Luck and another player the Boon of Fate. With the Boon of Luck, you can add a d10 to any ability check , attack roll or saving throw you make while Boon of Fate allows you to add a d10 to any ability check , attack roll or saving throw another creature makes that is within 60 feet of you. With these additional d10s, we can actually manage to get a 119 max persuasion. Everyone now bows down before you.