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Also note this build wont really take of until you are in act 3 since most of the crit red on roll items are there. Only item that gives crit red on rolls is a shortsword from the mountain pass area Knife of the Undermountain King.
As for act 3 if what gear you want comes down to game choices seeing as if you are willing to become a unholy assasin of Bhaal you can either use Nyrulna or Selûne's Spear of Night/Shar's Spear of Evening (depending on what you happens to the Nightsong). If not you will end up using Balduran's Giantslayer. Other set items are Sarevok's Horned Helmet and The Dead Shot.
You should also pick up Luck of the Far Realms from Illithid powers also the ring you get in act 2 Killer's Sweetheart is nice as well.
I am gone level with you I think that going ranged(using Titanstring Bow until act 3) on champion is stronger option since then you will have have Knife of the Undermountain King + Bloodthirst which is another -2 roll needed for a critical. However you wont get benefit from bigger crits orcs get from melee weapons.
As for melee you would be better of being a paladin since they benefit the most from crits as melee.
Fighter Champion (3) get you ReduceCriticalAttackThreshold(1) (Roll of 19 or 20 crit).
This works weapons attacks, type does not matter.
Half Orc gets you CriticalHitExtraDice(1, MeleeWeaponAttack) (adds an extra crit die).
This works Melee Weapons attacks only, type does not matter.
Beyond these two elements the most important thing you want to do is get Advantage on your melee attack rolls. This gives you double the chance of a critical hit. You can have a +300 to hit rate and it will not increase your critical hit chance, only rolling more dice or rerolling dice events will matter.
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I took 'one' level of Warlock(The Old Ones) for the ClarifiedMortality which causes fear on critical. This gives you advantage on attacks against those targets and CCs them. There are plenty of other classes and methods to get advantage.
There are plenty of other methods and even an item or two that give you additional reduce critical, which does stack and additional critical dice which also stacks. But that one level of Warlock (The old ones) this gives you the most by level 4 (Half Orc / Warlock lvl 1 / Fighter lvl 3) and persists until the end. No need for charisma in my build since it has no effect on the spells at level one and I do not intend to do so for mine character.
If your like me an run two front line players side by side as a front line I would suggest the feat Sentinel since it gives you Advantage on AOO and if your partner is attack it lets you get an Reaction Attack. If you fight alone do not take this feat.
also keep in mind that for weapons, even if not actively wielding them, passives given from just having them equipped generaly apply even if wielding your other weapon(i.e the crit range increase from knife of the undermountain king found in act 1 applies to ranged weapon attacks and spells with attack rolls)
then after planning your route to these items increasing number of hits per round is your goal
more rolls = more chances for crits
Instead of increasing your crit chance, You may want to increase your crit damage
-picking Half-Orc and using greataxe
-Paladin lvl 2 (Divine smite damage also doubles with crit and have all benefits from being half-orc and savage attacker feat)
-Savage attacker feat (all your damage die rolled twice for highest result)
-Sneak attack from rogue
-Use your supports to guarantee a critical hit like ( sleep, eyebite asleep, hold person, hold monster, exposing bite from wild-shape wolf)
-also other effects to gurantee crit: like paralysing ray, Luck of the Far Realms , Killer's Sweetheart, Assassinate:Ambush,
MY OPINION:
one ofbest build for this 5 level battlemaster-figher and 7 level assasin rogue (any race doesnt matter)
Assassinate:Ambush, extra attack, Assassin's Alacrity, battle maneuvers, cunning actions, action surge. sharpshooter feat and alert feat
You will use archery in this build and arrow of many targets, start combat from afar and crit everyone in surprise in one shot, you can shoot 5 times crit before enemy take their turn
other really good build is Half Orc 2 level paladin - 10 level sword bard
you will have divine smite, lots of spell slots for dvine smite, flourish with d10 Improved Bardic Inspiration and extra attack, great weapon mastery feat and savage attacker feat
(and you will have lots of spell for other usage)
You can use your companions especcialy druids or sorcerers to set you up for guaranteed crit, And you can blast them with divine smite (incredible damage)
Race: Half Orc obviously
Background: Charlatan as this character is my door / chest opener
Starting Class: Fighter with the dual wield fighting technique
Level 2: Rogue
Level 3: Cleric Tempest for melee retaliation option (It's what I chose) or go War for the 3 extra attacks / long rest
Level 4: Warlock The Great Old One for aoe fear on crit
Cleric + Warlock gives you some extra utility with spells like Command or Hex.
Level 5-7: Rogue for Thief and that extra bonus attack so you can now hit 3 times per round and using hand cross bows as well. Also get a feat.
Level 8+: Fighter to eventually get that last main attack, Champion and 2 feats.
Hex is really good for getting those bits of damage that add up + chaining into other spells or abilities for crowd control (Hex Wisdom into Command Drop Weapon to trivialise some bosses) or making an enemy prone giving your crit build advantage. I'm using Gale as a Swords Bard / Wizard, Shadowheart and Lae'zel as what they start with.
2 handed builds can also be great for the higher damage output. Great Weapon Master can be good if your character has the accuracy to fully utilise that feat. Even then it's really nice. Lae'zel uses that feat with battlemaster to knock enemies prone making it far more likely to hit with the +10 damage (otherwise get used to switching the passive on and off when needed).
edit: For Feats I'll be going with Alert (Honour Mode), Resilience Constitution for concentration spells and then Dual Wielder for more options and the +1 AC.
Also wasting a feat on sentinel is sort of well a waste the AI in the game is horrible even on Honour Mode it dose things that make no sense in terms of picking it´s target.
I am confused about that first build are you talking about him going 2 in paladin the reason you multi-class paladin with full casters is to get more spell slots on it. Just having 2 levels in paladin and going into something like rogue and fighter will give you next to no spell slots.
at first paragraph I only list things that increase damage with crit
I list my builds at second and third paragraph
1. BUILD: 5 level battlemaster-fighter and 7 assasin rogue : it is about dealing crit damage damage with bow to surprised targets (nothing to do with paladin)
2. BUILD: 2 level paladin and 10 level sword Bard: using Bard spell slots to deal divine smite. If you want you can also take 2 lvl paladin + 2 level fighter + 8 level sword bard too for Action surge of course.
There's a helmet that lets you crit 1 roll lower. As a fighter there's a fighting style that lets you crit 1 roll lower. Then there's a spear/glave thing that's invisible, IDR the exact name, but it lets you crit 1 roll lower. Then there's the elixir of viciousness that gives you another -1 to crit rolls.
My fighter is using two handed weapons with the Great Weapons perk or whatever. My crits are about 33 - 45 depending. With the great weapon perk I can make up to 5+ attacks in a single round, with most being criticals.
I have a ring that puts all saving throws for you at disadvantage but all attacks at advantage. That fighter, even with the great weapon passive, still almost always has 85% chance to hit, even on high defense enemies.
IDR the rest of the build I'm using but it's been fun, I crit a lot. A lot a lot. I think there's a few more ways to lower it but I'm only just coming out of Act 2 with this playthrough right now.
Why barb? Because you can always attack with advantage. Which basically means +50% to your flat crit chance (if you have 20% crit, with advantage it will be ~30%).
Use dual wield. Each weapon +5% to crit.
Use bow + 5% crit.
Use elixir for another +5% crit.
So this setup above already gives you ~45% crit chance. Best check wiki where and when to get these items.
Go dex 18, then equip The Graceful Cloth to boost dex to 20, and get advantage for dex skills checks. No need to have a rogue in your party.