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Fighters generally seem to be best-off with a flickmace or a reach polearm to capitalize on Attack of Opportunity, but some might instead prefer to emphasize their striker side and more directly eliminate enemies.
I was running some numbers on 1st- through 4th-level fighters earlier, comparing pick and light pick Double Slice, generic one-hander and generic agile Double Slice, greatpick Strike Strike, generic two-hander Strike Strike, greatpick Power Attack, and generic two-hander Power Attack, all against various ACs. My assumption was that the third action would never be used to attack due to MAP, and would instead be used to do something else, like reposition. The results were inconclusive and showed that which had the best DPR was strongly dependent on the specific target AC. From 1st through 4th, a fighter may as well just take Sudden Charge at 1st and simply Strike + Brutish Shove with a two-hander.
5th-level, though, is a different story. It seems to me that from 5th level onwards, a pure striker fighter's best choice for raw damage is pick and light pick Double Slice. The principle is simple. Double Slice is the best way for a fighter to land as many critical hits as possible. Pick critical specialization is devastating, since it cranks up the damage even further, possibly ending the enemy right then and there.
Given a striking rune and doubling rings, a 5th-level fighter's pick deals 2d6+4 damage (average 11) on a regular hit, and 4d10+8+1d10+6 (average 41.5) on a critical hit. The same character's light pick deals 2d4+4 damage (average 9) on a regular hit, and 4d8+8+1d8+6 (average 36.5) on a critical hit. Those are some nutso numbers. Given a rogue multiclass, Sneak Attacker, and attacking a flat-footed enemy, it seems to me that a pick and light pick Double Slicer is the single best pure striker fighter from 5th level onwards. Is there anything in the fighter that can compete for this damage purpose?
The Minecraft fighter seems unusually effective.
Average 5th-level AC is 22, with 75 hit points. A 5th-level fighter likely has an attack bonus of 4 ability modifier + 5 level + 6 master + 1 item = +16. That gives a regular hit chance of 50%, and a critical hit chance of 25%. Given the damage numbers above, if even one of those attacks is a critical hit, that lays waste to roughly half of the monster's hit points, with a regular hit on top of that generating further damage. There is also the off-chance (6.25%) that the enemy is one-turn-KOed outright.
The numbers above improve with flat-footing, bonuses to attack rolls, and so on.
It is a gambler's build for sure, though; lacking in consistency means that it is on the more luck-dependent side, and it can easily run into overkill issues when focusing fire with other party members.
A variant could be a greatpick fighter multiclassing into a spellcasting class for true strike, but that is limited by per-day uses.
A Multiclass Rogue sneak attack is 1d4 (at level 4) and 1d6 (at level 6) and requires the target to be flat footed. This is only dealt once each round.
A Multiclass Barbarian rage attack there are few options at level 6.
Dragon Instint which will deal 4 damage per attack. So hit twice with double slice that is 8 damage (6 when one weapon is agile). The enemy does not need to be flat footed. The entire attack can be your dragons type.
Giant Instint which will deal 6 damage per attack. So hit twice with double slice that is 12 damage (9 when one weapon is agile). The enemy does not need to be flat footed.
You will loose 1 AC but gain Temporary HPs to offset it. Agile weapons will do less rage damage but even then the barbarian will do equal or more damage then the rogues max. For giant instint you gain clumsy condition which is a dex penalty. If you wear Full Plate Armor as a fighter then it wont matter unless you need to make a dex check.
What is important other than the increased damage though is the ability to change the damage type of the entire weapon damage. Just looking through the book there are a ton of enemies with resistances and being able to change it to say acid (dragon) or positive/negative (spirit) if you tend to fight a lot of undead/evil is great. The positive/negative one lowers the damage though to 6 if both attacks hit (5 when one of those is an agile weapon).
That is through a pure damage viewpoint. Rogues Archetype has a few nice feats that are worth it imo.