I'm usually not a fan of min-maxing, but I stumbled across this build while messing around making a Hexblade. All you need is a longsword and some medium armour, so here we go! I'm gonna detail how this comes online, level by level, it's a fun, flavorful and mechanically cool build!

Race: Half-Elf of any flavour (put your two stats in DEX and CON). This becomes important later. Make CHA your highest stat, and put respectable scores in DEX and CON. With Point Buy, put a 15 in CHA and DEX, and a 13 in CON.
Level 1: Fighter. Pick up the Defense fighting style.
Level 2: Warlock, Hexblade patron, take Eldritch Blast (obviously), True Strike (a good samurai recognizes a battle before it is upon them), Hellish Rebuke and Shield. This gives a lot of options in melee combat already, useful ranged ability, and the ability to grant yourself advantage. This is also important.
Level 3: Keep going in Fighter. Action Surge is great.
Level 4: Fighter, and take the Samurai subclass. True Strike was useful, but Fighting Spirit is gonna take over from here.
Level 5: Fighter, and make sure you get the Elven Accuracy feat, and boost either DEX or CHA. Triple advantage whenever we want with Fighting Spirit and True Strike? Sweet!
Level 6: Fighter, get hold of extra attack, and save us an invocation later.
Level 7: Warlock, and take the Fiendish Vigor and Agonizing Blast invocations. Take Hex too, because why not.
Level 8: Warlock, take Pact of the Blade, and replace one of the two invocations with Improved Pact Weapon. Now we're getting somewhere. Take Hold Person as your spell.
Level 9: Warlock, and pick up Medium Armor Master. Take Mirror Image as your spell, and whatever cantrip. Friends or Minor Illusion are good fun.
Level 10: Warlock. This is where it gets silly. Take Eldritch Smite. Take Counterspell to shut down those pesky mages. Eldritch Smite is the key here. At this level, you can do 1d10+4d8+9 damage, with the ability to grant triple advantage at will, and the ability to do 4 attacks in a round with Action Surge. For a potential of 93 damage per attack, if all dice are maximized. Damn.
Level 11: Warlock. Nothing particularly interesting at this level. Take Blur or Misty Step as your spell, either is fine.
Level 12: Warlock. Take Relentless Hex as your invocation, and 4th level spell slots for an extra d8 on your Smite, which is pretty dope. Dimension Door is a nice spell to have.
Level 13: Warlock. Get that CHA score to 20. Grab whichever you didn't before out of Misty Step and Blur. It should already be damn hard to hit this character, and both of these make it even harder to pin them down.
Level 14: Warlock. Grab the Cloak of Flies invocation for a lil more damage output. Get Hold Monster as your 5th level spell, and revel in your 6d8 Smite damage.
Level 15: Warlock. The best ability. Armor of Hexes. 50% chance for any Cursed target to miss you? Sweet! Get yourself a nice cantrip to celebrate. It should be nigh impossible to hit this character with this, given our ability to grant disadvantage with Blur and nullify hits with Mirror Image, and that's without throwing Shield up.
Level 16: Warlock. Take whatever 6th level you want for your Mystic Arcanum, but Investiture of Stone gives you a chance to knock multiple enemies prone, and prone means advantage, which we like. Get Far Step on your spell list.
Level 17: Warlock. This is where we peak. Pick up Lifedrinker as your invocation. We now do 1d10+6d8+17 damage to anything not resistant or immune to Necrotic damage with our Smite. That's a potential of 133 damage on a crit with all dice maximized. Pick up the Tough feat while your here, or boost CON, either is fine. From here, you can either carry on in Samurai (getting two ASIs or Feats), or keep going in Warlock for a 7th and 8th level spell and another invocation. Power Word Stun is a nice one for 8th level, automatic paralysis under 150 hitpoints for yet another way of granting advantage, and to be able to transfer your Hexblade's Curse feature.

To summarize; this character is fearsome in melee combat. Incredibly tough to hit with a high AC, Shield, Mirror Image and Blur on top of Armor of Hexes, can punish those who do connect with Hellish Rebuke, can take hits like a champ thanks to high CON and Tough, and hits like a dang freight train with a plethora of ways to grant themselves triple advantage with Elven Accuracy, an increased crit chance through Hexblade's Curse, and obscene amounts of dice to double on a crit with Eldritch Smite. I like the idea of a Hexblade who is already a very skilled warrior, and uses the power bestowed upon them to its fullest to make them nigh unstoppable (eventually).

So, some maths; with Elven Accuracy, you have a 27.1% chance to crit on a 19 or 20 with triple advantage. Taking the average, you'd do 49.5 damage per hit, with a Smite, or 22.5 without it. With Action Surge making a crit almost certain in the 4 attacks, assuming 3 Eldritch Smites and one of them being a crit, you would do an average of 203.5 damage in a single round. Saving Smite purely for the crit brings it down to a more modest 149.5. Two normal attacks, one smited, does an average of 72, and two smited crits (entirely possible) would deal an average of 164 damage. The max amount of damage this build could do in a single turn, assuming four crits, Eldritch Smite on three of them, and Hex on the target in addition to Hexblade's Curse, is 484 points of damage, with 116 being necrotic, 288 being force, and 80 being (magical) slashing.

Thanks for reading, and remember, if you're only rolling to hit once, something has gone horribly wrong.

Not sure what you mean by triple advantage, since advantage does not stack.  You either have or you don't.

The Elven Accuracy feat specifically allows you to roll an extra die when attacking with a DEX, INT, WIS or CHA based stat with advantage, meaning you can roll 3d20 instead of 2. As far as I know it's the only method of getting more than just advantage.

It works just like Luck but is more specific and essentially infinite.

3 Smites and a Hex would burn all spell slots at once, but that's a ton of damage...

AT LEVEL 10 CAN YOU BREAK DOWN THE DAMAGE? IM TRYING TO DO THE MATH AND SOMETHING IS ADDING UP.

@coughenour1312

1d10 from weapon +4d8 from eldritch smite + 4(charisma) +4(proficieny from hexblade's curse) +1 (Improved Pact Weapon)

Sure, if you want to blow half of your four spell slots on one nova round with action surge. That's an option.

When I play a Warlock, I save my spells for special situations or crowd control, and I deal my damage with weapons and/or cantrips. In the games I've played, this has been more beneficial to the party. But vs a single BBEG, sure.

Thanks, updated.

Just a correction, Eldritch Smite is once a round. 

Have you considered using Shadow Blade instead of a longsword? With a fifth level spell slot it deals 4d8 damage and behaves like a normal weapon.

i dont really see what fighter adds here, except for a little nova potential. I think Hexblade peaks around lv 5, when they are only slightly behind other spellcasters in spell capacity. For a 20lv build I find it hard to warrant not going over into sorcerer, even as a melee caster.

i would also certainly pick the see in darkness invocation and drop darkness on myself to get full advantage of elev accuracy all the time.

The feat eleven accuracy actually lets you roll a third dice when you have advantage, but otherwise you are correct

I realize this is a resurrected thread, but you just don't need Samurai to get your hands on Advantage - both Darkness and Shadow of Moil are extremely reliable spell sources of it, a Familiar is as well (I admit, this is harder to get on a bladepact than tome or chain), Shroud of Shadow will do it at L15...  and of course for multiclassing, there are other excellent sources for it, like being a Vengeance paladin.  Granted, Fighter is easy to multiclass into, but I'm not sold on Samurai being the best Advantage source, here.  And I'm very, very opposed to relying on True Strike, in general.

Throwing Darkness on yourself will mess with the rest of the team. 

If you are trying to build  a Fighter/Hexblade nova build, I can see why you would use Samurai.   Its ability to provide advantage, when you don't have cover of darkness is pretty nice.  And, not using darkness spells, gives you room for another concentrations spell, like hex or one of the smite spells.

I have been working on a build that is similar to this for an upcoming campaign, with the intent of being able to provide one huge round of damage if needed.

3-5 x Ranger/Gloomstalker: Archery Style.  You will have Dread Ambusher and Umbral Sight.  The DA give use an extra attack in the first round of combat and is available for the next combat without rest.  3 levels of GS will give you first level spell slots.  It will also give you access to Longstrider, Hunters Mark, etc.  GS also allows Wisdom bonus to add to Initiative (and you want to go first or early)

3-4 x Fighter/Samurai (or EK or Champion):  Defense or Two Weapon Fighting (whatever fits your plan).   Samurai provide the much needed Advantage if you don't have ready cover.   EK would give you some interesting spell choices and weapon bond (no disarming).

12-14 x Warlock/Hexblade:  This is primarily an archer, but can shift to shield and rapier in a pinch, or after the big archery booms are done.  You will want Improved Pact Weapon, Devils Sight, and anything else that boosts damage output..and some of the fun invocations.  I am still debating 5 levels of Rangers vs 14 levels of warlock...2nd level darkness spells vs moving hex around in combat.  

It may end up being 12/4/4 to maximize feats/abilities.

This build can take either Dex or Cha to 20 and leave the other around 16.   Wisdom has to be 13 and you want some Con, but if playing at range it may be less important.   You don't need Str, but never pass on a belt of giant strength.  :)    

Use Eladrin for Fey Step.

Feats:  Elven Accuracy,  Sharpshooter and Piercer.  1xAbilities to get to 20 on primary  ability.

First Turn of Combat:  If close enough Hex Curse the biggest baddie. Bonus Action First:  Hex, Hunters Mark, etc.   Action:  3xAttack + Action Surge for 3 more attacks.   Use Sharpshooter for -5 to attack and +10 to damage per hit.   All of these will be at advantage due to environmental conditions or Samurai special.  This give you 6 attacks with 3x d20 roll for each.   You should hit 6 times.   If any of them are Crits, then pile on with an Eldritch Smite.   Add up all of the damage bonuses from spells, conditions, feats, etc. then add on the sharpshooter bonus (as much as 60 more damage).  Since you can only use one Eldritch Smite per turn, you will still be crit fishing for a couple more turns.   

You could use Champion instead of Samurai to maintain the 19-20 crit range across all targets.  

One of the posters above is correct: you can only Eldritch Smite once on your turn, no matter how many attacks you get to make per Attack action.  I don't think that tanks this build, though, particularly because you automatically knock the target prone when you land the hit (assuming it's Huge or smaller).  You get to leverage your extra attacks (see below) at this point to keep pounding it into the dirt with with advantage (although you probably had that anyway), and other melee attackers (especially Rogues) will love you for it.

As for updates, I'd suggest eventually substituting in Spirit Shroud (from TCoE) for Hex.  The downside to Spirit Shroud is that it's not up nearly as long as Hex can be (one minute max versus potentially the whole day for Hex).  However, maintaining Hex for that long means that you can't cast any other concentration spells, which does eventually stink.  The upsides to Spirit Shroud are: (1) it does better damage (eventually 2d8 versus Hex's 1d6); (2) you can vary between radiant, necrotic, and cold when you cast the spell, allowing you to avoid potential resistances or immunities; (3) it prevents hit point regeneration until the start of your next turn; and (4) it reduces the movement of all enemies within 10 feet of you by 10 feet until the start of your next turn.  That's a good bit of battlefield control for a front-line fighter, to help keep the enemies off of the back-line spellcasters and ranged attackers.

I'd also suggest looking into substituting in Thirsting Blade for Cloak of Flies.  CoF does have a lot to recommend it; guaranteed damage per round to everything near you is nothing to sneeze at (unless the targets have resistance or immunity to poison damage).  You can only pop it once during a short/long rest period, though.  TB, by contrast,  is always on and stacks with the extra attack you're already getting from the Fighter dip, letting you swing 3 times per Attack action (6 times if you Action surge).  You're never going to get up to the ridiculous 8/9 potential swings a pure Samurai can take, but 6 is respectable.

I haven't gamed this thought out that well yet, but looking into one of the summoning spells from TCoE may also be worthwhile.  They're also concentration (yuck), but they last an hour each, and there are some nice options for the Warlock in there.  Summon Undead and Summon Shadowspawn are both very flavorful for this build.  Notably, the Putrid undead summons tosses around the tasty, tasty poisoned condition like candy and can potentially paralyze enemies as well (and a paralyzed enemy equals a dead enemy), and the Ghostly summons can cause the target to become frightened, keyed off a failed Wisdom save.  Both options give the target disadvantage on Attack rolls, which helps out the party's survivability.  They don't take any action on your part to command, and you can set up some nice flanking situations with them for advantage on Attack rolls.  Plus, it's never bad to have more bodies on your side to soak damage, set off traps, etc.

Quote from BrianT888 >>

I'd also suggest looking into substituting in Thirsting Blade for Cloak of Flies.  CoF does have a lot to recommend it; guaranteed damage per round to everything near you is nothing to sneeze at (unless the targets have resistance or immunity to poison damage).  You can only pop it once during a short/long rest period, though.  TB, by contrast,  is always on and stacks with the extra attack you're already getting from the Fighter dip, letting you swing 3 times per Attack action (6 times if you Action surge).  You're never going to get up to the ridiculous 8/9 potential swings a pure Samurai can take, but 6 is respectable.

 Extra Attack or a similar ability (like Thirsting Blade) from different classes do not stack.  It is covered in the multiclassing rules which you can have a quick look at here:

https://www.dndbeyond.com/sources/basic-rules/customization-options#ExtraAttack

Ah, good catch.  Thanks!

This is intriguing.  Gonna save this and tinker.  It looks fun.